{
  "schema_version": "2.0.0",
  "release_version": "v2.1",
  "claim_count": 53,
  "claims": [
    {
      "id": "VAC-01",
      "title": "Absolute vacuum offset is scheme dependent",
      "display_order": 1,
      "sector": "foundations",
      "statement": {
        "public": "Absolute zero-point energy is not by itself a scheme-independent observable.",
        "technical": "In renormalised semiclassical gravity, a constant shift of the matter Lagrangian renormalises the cosmological counterterm. The split between an absolute homogeneous matter-vacuum offset and the renormalised cosmological term is therefore convention dependent."
      },
      "status": "standard_input",
      "type": "standard_input",
      "depends_on": [],
      "evidence": [
        {
          "reference_id": "REF-009",
          "role": "foundation"
        },
        {
          "reference_id": "REF-013",
          "role": "foundation"
        },
        {
          "reference_id": "REF-016",
          "role": "foundation"
        },
        {
          "reference_id": "REF-017",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “The compact-S⁴ vacuum-energy ambiguity”.",
          "structure_id": "sec:wellposedness",
          "section_title": "The compact-S⁴ vacuum-energy ambiguity"
        }
      ],
      "qualifier": "This concerns the absolute homogeneous offset. It does not say that vacuum fluctuations do not exist or that physical energy differences never gravitate.",
      "limits_and_open_issues": "Casimir differences, phase transitions, interfaces and inhomogeneous stresses remain physical.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1; wording aligned to the cosmological-constant paper v2.0."
      },
      "status_label": "Standard input",
      "status_class": "standard",
      "downstream_claims": [
        "EXT-01",
        "GR-02",
        "VAC-02",
        "VAC-03"
      ],
      "graph_depth": 0,
      "reference_ids": [
        "REF-009",
        "REF-013",
        "REF-016",
        "REF-017"
      ]
    },
    {
      "id": "VAC-02",
      "title": "Compact S⁴ sharpens the vacuum ambiguity",
      "display_order": 2,
      "sector": "foundations",
      "statement": {
        "public": "On compact round S⁴, the ambiguity is especially sharp: the homogeneous vacuum term and cosmological counterterm are the same local volume operator.",
        "technical": "On closed round S⁴ without boundary, the homogeneous matter-vacuum term and the cosmological counterterm both reduce to the same functional ∫√g d⁴x ∝ H⁻⁴, with no intrinsic geometrical label separating them."
      },
      "status": "derived",
      "type": "identity",
      "depends_on": [
        "VAC-01"
      ],
      "evidence": [
        {
          "reference_id": "REF-009",
          "role": "foundation"
        },
        {
          "reference_id": "REF-013",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “The compact-S⁴ vacuum-energy ambiguity”.",
          "structure_id": "sec:wellposedness",
          "section_title": "The compact-S⁴ vacuum-energy ambiguity"
        }
      ],
      "qualifier": "A compact-background sharpening of standard renormalisation freedom.",
      "limits_and_open_issues": "The statement is about a single compact homogeneous saddle, not differences between physically distinct configurations.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1; wording aligned to the cosmological-constant paper v2.0."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "CMP-01",
        "EXT-01"
      ],
      "graph_depth": 1,
      "reference_ids": [
        "REF-009",
        "REF-013"
      ]
    },
    {
      "id": "VAC-03",
      "title": "Physical differences survive the quotient",
      "display_order": 3,
      "sector": "foundations",
      "statement": {
        "public": "Removing the homogeneous offset does not erase Casimir effects, phase transitions, interfaces or inhomogeneous stresses.",
        "technical": "Quotienting a strictly homogeneous constant shift leaves scheme-independent differences between configurations and nonhomogeneous stress-tensor structure untouched."
      },
      "status": "standard_input",
      "type": "standard_input",
      "depends_on": [
        "VAC-01"
      ],
      "evidence": [
        {
          "reference_id": "REF-020",
          "role": "foundation"
        },
        {
          "reference_id": "REF-089",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “Why Casimir observables are different”.",
          "structure_id": "loc-005",
          "section_title": "Why Casimir observables are different"
        }
      ],
      "qualifier": "Scope guard for the vacuum-energy quotient.",
      "limits_and_open_issues": "No claim is made that all vacuum phenomena are unphysical.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1."
      },
      "status_label": "Standard input",
      "status_class": "standard",
      "downstream_claims": [],
      "graph_depth": 1,
      "reference_ids": [
        "REF-020",
        "REF-089"
      ]
    },
    {
      "id": "EXT-01",
      "title": "Euler extraction theorem on conformally flat S⁴",
      "display_order": 4,
      "sector": "matter",
      "statement": {
        "public": "Within the stated compact response class, one nonzero universal matter datum survives: the type-A Euler anomaly coefficient.",
        "technical": "Among local linear constant-Weyl responses of the renormalised effective action on round conformally flat S⁴ satisfying counterterm invariance (C1) and conformal-flatness universality (C2), the unique nonvanishing H-independent scheme-independent matter datum is the type-A Euler anomaly coefficient a."
      },
      "status": "derived",
      "type": "theorem",
      "depends_on": [
        "VAC-01",
        "VAC-02"
      ],
      "equation_ids": [
        "eq:counterterms"
      ],
      "evidence": [
        {
          "reference_id": "REF-018",
          "role": "foundation"
        },
        {
          "reference_id": "REF-019",
          "role": "foundation"
        },
        {
          "reference_id": "REF-025",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Theorem “Euler extraction on conformally flat S⁴”.",
          "structure_id": "sec:extraction",
          "theorem_title": "Euler extraction on conformally flat S⁴"
        }
      ],
      "qualifier": "Class-relative uniqueness: local, linear constant-Weyl response on round conformally flat S⁴ under C1 and C2; not uniqueness across all nonlocal observables or backgrounds.",
      "limits_and_open_issues": "The theorem identifies the protected matter coordinate. It does not by itself produce the cosmological curvature.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1; current theorem wording follows the cosmological-constant paper v2.0."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "CMP-01",
        "CORR-01",
        "EXT-02",
        "GR-01",
        "IR-01",
        "MAT-01",
        "SM-01"
      ],
      "graph_depth": 2,
      "reference_ids": [
        "REF-018",
        "REF-019",
        "REF-025"
      ]
    },
    {
      "id": "EXT-02",
      "title": "Euler projector isolates the protected coordinate",
      "display_order": 5,
      "sector": "matter",
      "statement": {
        "public": "A constant-Weyl projector removes local counterterm contamination and isolates the Euler response.",
        "technical": "At a conformal fixed point, A[Γ]=−(1/4) Π_H0(dΓ/d ln H) and Π_H0(dΓ/d ln H)=−4a. Away from a fixed point, the corresponding local-RG Euler-cocycle projection is applied after beta-function and operator-mixing responses are separated."
      },
      "status": "derived",
      "type": "identity",
      "depends_on": [
        "EXT-01"
      ],
      "equation_ids": [
        "eq:calA",
        "eq:weylvar"
      ],
      "evidence": [
        {
          "reference_id": "REF-025",
          "role": "foundation"
        },
        {
          "reference_id": "REF-026",
          "role": "foundation"
        },
        {
          "reference_id": "REF-027",
          "role": "foundation"
        },
        {
          "reference_id": "REF-033",
          "role": "foundation"
        },
        {
          "reference_id": "REF-049",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Euler-extraction theorem, Eq. defining A[Γ] and proof.",
          "structure_id": "sec:extraction"
        }
      ],
      "qualifier": "The running-theory statement requires separation of beta-function and operator-mixing terms.",
      "limits_and_open_issues": "The projector extracts the protected coordinate; it does not assert that the rest of the effective action vanishes.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1; sign and running-theory scope aligned to v2.0."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 3,
      "reference_ids": [
        "REF-025",
        "REF-026",
        "REF-027",
        "REF-033",
        "REF-049"
      ]
    },
    {
      "id": "EXT-03",
      "title": "Standalone Type-A theorem across two de Sitter realisations",
      "display_order": 6,
      "sector": "matter",
      "statement": {
        "public": "A standalone theorem publication finds that the protected local logarithmic anomaly response common to the closed-sphere and round static-patch descriptions of de Sitter is uniquely type A, with microscopic coordinate a.",
        "technical": "Within the parity-even fixed-point local four-derivative logarithmic anomaly sector of exact round de Sitter, the universal paired closed-sphere/static-patch quotient has one-dimensional image generated by the Euler/Wess-Zumino class, and the transmitted QFT coordinate is a(Q)."
      },
      "status": "derived",
      "type": "theorem",
      "depends_on": [],
      "evidence": [
        {
          "reference_id": "REF-018",
          "role": "foundation"
        },
        {
          "reference_id": "REF-019",
          "role": "foundation"
        },
        {
          "reference_id": "REF-025",
          "role": "foundation"
        },
        {
          "reference_id": "REF-090",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-091",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-092",
          "role": "structural_convergence"
        }
      ],
      "locations": [
        {
          "work_id": "type-a-paper",
          "locator_text": "Standalone Type-A theorem publication, current public record; exact theorem and scope on its own paper page."
        }
      ],
      "qualifier": "Independent cross-realisation theorem. It is not an incoming dependency of the cosmological numerical chain.",
      "limits_and_open_issues": "Does not establish the QCD state-preparation premise, the boundary-member prescription, u_max=1 UV-domain normalization, contour choice, quantum dressing, global source pairing or numerical cosmological result.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained as an independent v2.0 programme record."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 0,
      "reference_ids": [
        "REF-018",
        "REF-019",
        "REF-025",
        "REF-090",
        "REF-091",
        "REF-092"
      ]
    },
    {
      "id": "SM-01",
      "title": "Minimal Standard Model Euler coefficient",
      "display_order": 7,
      "sector": "matter",
      "statement": {
        "public": "For the minimal Standard Model free-field census, the protected type-A coefficient is a_SM = 1991/720.",
        "technical": "For four real Higgs scalars, 45 Weyl fermions and 12 vector bosons, a_SM=4/360+45(11/720)+12(31/180)=1991/720=2.76527778."
      },
      "status": "computed",
      "type": "computed_value",
      "depends_on": [
        "EXT-01"
      ],
      "equation_ids": [
        "eq:aSMvalue"
      ],
      "evidence": [
        {
          "reference_id": "REF-004",
          "role": "observational_input"
        },
        {
          "reference_id": "REF-010",
          "role": "foundation"
        },
        {
          "reference_id": "REF-011",
          "role": "foundation"
        },
        {
          "reference_id": "REF-035",
          "role": "foundation"
        },
        {
          "reference_id": "REF-036",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “Standard Model evaluation of the extracted datum”.",
          "structure_id": "sec:anomaly",
          "section_title": "Standard Model evaluation of the extracted datum"
        }
      ],
      "qualifier": "Leading free-field Standard Model value; the full interacting curved-space coefficient is CORR-01.",
      "limits_and_open_issues": "Not a statement that no additional ultraviolet degrees of freedom exist, and not a calculation of the full interacting a_eff.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1; old provisional 0.5% uncertainty removed."
      },
      "status_label": "Computed",
      "status_class": "derived",
      "downstream_claims": [
        "CORR-01",
        "NUM-01",
        "TEST-02"
      ],
      "graph_depth": 3,
      "reference_ids": [
        "REF-004",
        "REF-010",
        "REF-011",
        "REF-035",
        "REF-036"
      ]
    },
    {
      "id": "IR-01",
      "title": "Direct Planck-scale mechanisms tested do not supply the linear IR factor",
      "display_order": 8,
      "sector": "matter",
      "statement": {
        "public": "A distinct infrared readout is required; the direct Planck-scale mechanisms tested do not generate the needed linear QCD hierarchy.",
        "technical": "Within the stated compact treatment, the local analytic heat-kernel mass expansion begins in even powers of dimensionless mass and perturbative Planck-scale Yang-Mills instanton weights are far too suppressed; neither supplies a term linear in m_p/M_P. The protected Euler coefficient itself is order one."
      },
      "status": "derived",
      "type": "no_go",
      "depends_on": [
        "EXT-01"
      ],
      "evidence": [
        {
          "reference_id": "REF-015",
          "role": "foundation"
        },
        {
          "reference_id": "REF-044",
          "role": "foundation"
        },
        {
          "reference_id": "REF-045",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, end of Sec. “Standard Model evaluation of the extracted datum”.",
          "structure_id": "sec:anomaly",
          "section_title": "Standard Model evaluation of the extracted datum"
        }
      ],
      "qualifier": "Limited exclusion of the tested direct/local routes, not a no-go theorem for every nonlocal or UV-complete effect.",
      "limits_and_open_issues": "The construction obtains the infrared factor through the prepared QCD+QED sector instead.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained and simplified from v1; no midpoint-scale machinery remains."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 3,
      "reference_ids": [
        "REF-015",
        "REF-044",
        "REF-045"
      ]
    },
    {
      "id": "TOP-01",
      "title": "Normalized Euler-Chern unit on S⁴",
      "display_order": 9,
      "sector": "geometry",
      "statement": {
        "public": "The oriented round spin sphere carries one intrinsic normalized Euler-Chern unit: N_E = χ(S⁴)/2 = c₂(Σ⁻) = 1.",
        "technical": "For the chosen orientation on S⁴, N_E=(1/64π²)∫√g E₄=χ(S⁴)/2=1, while ⟨c₂(Σ⁻),[S⁴]⟩=+1 and ⟨c₂(Σ⁺),[S⁴]⟩=−1."
      },
      "status": "derived",
      "type": "identity",
      "depends_on": [],
      "equation_ids": [
        "eq:Eulerunit",
        "eq:intrinsicunit",
        "eq:spinChern",
        "eq:spinclasses"
      ],
      "evidence": [
        {
          "reference_id": "REF-021",
          "role": "foundation"
        },
        {
          "reference_id": "REF-023",
          "role": "foundation"
        },
        {
          "reference_id": "REF-078",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “One intrinsic Euler-Chern unit on the round sphere”.",
          "structure_id": "loc-015",
          "section_title": "One intrinsic Euler-Chern unit on the round sphere"
        }
      ],
      "qualifier": "Purely geometric; it does not identify spin SU(2) with QCD flavour SU(2).",
      "limits_and_open_issues": "Fixes the primitive geometric integer, not its physical QCD state preparation.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "CMP-01",
        "TOP-02"
      ],
      "graph_depth": 0,
      "reference_ids": [
        "REF-021",
        "REF-023",
        "REF-078"
      ]
    },
    {
      "id": "TOP-02",
      "title": "Degree-one equatorial clutching map",
      "display_order": 10,
      "sector": "geometry",
      "statement": {
        "public": "The chiral spin bundle’s equatorial transition map is a primitive degree-one map S³→SU(2).",
        "technical": "With Σ⁻ trivialised on the two hemispheres of S⁴, its transition function g₋:S³→SU(2) satisfies deg g₋=(1/24π²)∫Tr(g₋⁻¹dg₋)³=1 and N_E=⟨c₂(Σ⁻),[S⁴]⟩=deg g₋=1."
      },
      "status": "derived",
      "type": "identity",
      "depends_on": [
        "TOP-01"
      ],
      "equation_ids": [
        "eq:clutchdegree",
        "eq:clutchmap",
        "eq:intrinsicunit"
      ],
      "evidence": [
        {
          "reference_id": "REF-022",
          "role": "foundation"
        },
        {
          "reference_id": "REF-023",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “The equatorial clutching map has degree one”.",
          "structure_id": "loc-016",
          "section_title": "The equatorial clutching map has degree one"
        }
      ],
      "qualifier": "Relative Chern class is represented by the boundary clutching/Chern-Simons transgression; the half-sphere curvature integral need not itself be integer.",
      "limits_and_open_issues": "A geometric spin-bundle statement, not yet a QCD claim.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "TOP-03"
      ],
      "graph_depth": 1,
      "reference_ids": [
        "REF-022",
        "REF-023"
      ]
    },
    {
      "id": "TOP-03",
      "title": "Explicit degree-one spin-holonomy representative",
      "display_order": 11,
      "sector": "geometry",
      "statement": {
        "public": "The same primitive spin class has an explicit group-valued representative U_spin with deg U_spin=1 and [U_spin]=[g₋].",
        "technical": "The Levi-Civita-induced charge-one SU(2) connection on Σ⁻ has Atiyah-Manton holonomy U_spin:S³→SU(2)_spin satisfying deg U_spin=⟨c₂(Σ⁻),[S⁴]⟩=1 and [U_spin]=[g₋]."
      },
      "status": "derived",
      "type": "identity",
      "depends_on": [
        "TOP-02"
      ],
      "equation_ids": [
        "eq:spinholonomydegree"
      ],
      "evidence": [
        {
          "reference_id": "REF-082",
          "role": "direct_construction_input"
        },
        {
          "reference_id": "REF-085",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, paragraph “An explicit degree-one spin-holonomy representative”.",
          "structure_id": "loc-017",
          "paragraph_title": "An explicit degree-one spin-holonomy representative"
        }
      ],
      "qualifier": "Connection-level representative of the geometric spin class. No SU(2)_spin=SU(2)_flavour identification is asserted.",
      "limits_and_open_issues": "The physical class transfer to QCD remains QCD-03.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "QCD-03"
      ],
      "graph_depth": 2,
      "reference_ids": [
        "REF-082",
        "REF-085"
      ]
    },
    {
      "id": "QCD-01",
      "title": "QCD supplies a physical infrared mass scale",
      "display_order": 12,
      "sector": "qcd",
      "statement": {
        "public": "QCD dimensional transmutation generates a hadronic infrared scale, and the measured proton-to-Planck ratio is m_p/M_P = 7.685×10⁻²⁰.",
        "technical": "QCD dimensional transmutation generates the confined hadronic spectrum. Using the physical proton mass and unreduced Newton mass M_P=G⁻¹/² gives m_p/M_P=7.68514844×10⁻²⁰."
      },
      "status": "standard_input",
      "type": "standard_input",
      "depends_on": [],
      "equation_ids": [
        "eq:hierarchy"
      ],
      "evidence": [
        {
          "reference_id": "REF-004",
          "role": "observational_input"
        },
        {
          "reference_id": "REF-046",
          "role": "foundation"
        },
        {
          "reference_id": "REF-047",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, QCD section and numerical audit.",
          "structure_id": "sec:gauge"
        }
      ],
      "qualifier": "This record supplies the standard QCD scale and measured ratio only; it performs no state selection or spin-to-QCD matching.",
      "limits_and_open_issues": "The role of the B=1 sector is established only after QCD-03.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained as a standard foundation; the v1 selected-endpoint claim QCD-02 is superseded."
      },
      "status_label": "Standard input",
      "status_class": "standard",
      "downstream_claims": [
        "QCD-04"
      ],
      "graph_depth": 0,
      "reference_ids": [
        "REF-004",
        "REF-046",
        "REF-047"
      ]
    },
    {
      "id": "QCD-03",
      "title": "QCD state-preparation class identification",
      "display_order": 13,
      "sector": "qcd",
      "statement": {
        "public": "The compact channel assumes that the infrared QCD chiral boundary state is prepared in the homotopy class of the intrinsic degree-one spin field.",
        "technical": "At confinement the physical premise is [U_IR]=φ_*[U_spin]=φ_*[g₋] in π₃(SU(2)_flavour), with φ orientation preserving at the level of the abstract SU(2) groups."
      },
      "status": "structural_premise",
      "type": "structural_premise",
      "depends_on": [
        "TOP-03"
      ],
      "equation_ids": [
        "eq:qcd_state_preparation",
        "eq:skyrmionB"
      ],
      "evidence": [
        {
          "reference_id": "REF-079",
          "role": "foundation"
        },
        {
          "reference_id": "REF-080",
          "role": "foundation"
        },
        {
          "reference_id": "REF-086",
          "role": "foundation"
        },
        {
          "reference_id": "REF-087",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “One class-level QCD boundary premise”.",
          "structure_id": "loc-018",
          "section_title": "One class-level QCD boundary premise"
        }
      ],
      "qualifier": "The paper’s single new matter-side physical premise. It is class-level only, not a connection-level spin-flavour identification.",
      "limits_and_open_issues": "A microscopic derivation from Standard Model plus gravity remains open.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0; supersedes the v1 endpoint/fold matching architecture on the matter side."
      },
      "status_label": "Structural premise",
      "status_class": "premise",
      "downstream_claims": [
        "CMP-01",
        "CMP-03",
        "QCD-04",
        "TEST-02"
      ],
      "graph_depth": 3,
      "reference_ids": [
        "REF-079",
        "REF-080",
        "REF-086",
        "REF-087"
      ]
    },
    {
      "id": "QCD-04",
      "title": "Prepared B=1 QCD+QED sector has proton spectral floor",
      "display_order": 14,
      "sector": "qcd",
      "statement": {
        "public": "Given the QCD state-preparation premise, the degree-one sector is B=1 and its gauge-consistent QCD+QED spectral floor is the proton.",
        "technical": "QCD-03 transfers the primitive winding to the infrared chiral field, giving B=+1 (and B=−1 for conjugate orientation). In the compatible electromagnetic superselection sector, the regulated long-time energy difference tends to m_p; the conjugate sector gives the antiproton."
      },
      "status": "derived_given_premise",
      "type": "conditional_result",
      "depends_on": [
        "QCD-03",
        "QCD-01"
      ],
      "equation_ids": [
        "eq:Bfromclutch",
        "eq:chargedfloor",
        "eq:gaussedge"
      ],
      "evidence": [
        {
          "reference_id": "REF-004",
          "role": "observational_input"
        },
        {
          "reference_id": "REF-072",
          "role": "methodological_foundation"
        },
        {
          "reference_id": "REF-073",
          "role": "methodological_foundation"
        },
        {
          "reference_id": "REF-074",
          "role": "methodological_foundation"
        },
        {
          "reference_id": "REF-075",
          "role": "methodological_foundation"
        },
        {
          "reference_id": "REF-081",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, “From the B=1 sector to the proton channel” and “Gauge-consistent proton floor”.",
          "structure_id": "loc-020"
        }
      ],
      "qualifier": "The proton is not chosen from a scored candidate list; it follows as the spectral floor once B=1 is prepared.",
      "limits_and_open_issues": "Depends on QCD-03. Electromagnetic edge flux dresses the charged subsystem but does not change baryon winding.",
      "relations": [
        {
          "type": "supersedes",
          "target_id": "QCD-02"
        }
      ],
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0; replaces the selected proton-endpoint record QCD-02."
      },
      "status_label": "Derived given premise",
      "status_class": "conditional",
      "downstream_claims": [
        "QCD-05"
      ],
      "graph_depth": 4,
      "reference_ids": [
        "REF-004",
        "REF-072",
        "REF-073",
        "REF-074",
        "REF-075",
        "REF-081"
      ]
    },
    {
      "id": "TRC-01",
      "title": "Hamiltonian trace-source normalization",
      "display_order": 15,
      "sector": "qcd",
      "statement": {
        "public": "The proton response is read with a trace source whose normalization is fixed by H(σ)=H(0)+σΘ+O(σ²), so H′(0)=Θ.",
        "technical": "Define Θ=∫_Σ√h T^μ_μ d³x and H(σ)=H(0)+σΘ+O(σ²), hence H′(0)=Θ. This Hamiltonian source convention is distinct from the geometric Weyl parameter used in the Euler extraction."
      },
      "status": "defined_source_normalization",
      "type": "defined_observable",
      "depends_on": [],
      "equation_ids": [
        "eq:tracesource"
      ],
      "evidence": [
        {
          "reference_id": "REF-069",
          "role": "methodological_foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Eq. defining the trace source.",
          "structure_id": "loc-022"
        }
      ],
      "qualifier": "Definition of the source coordinate used by the proton response theorem; not a new dynamical assumption.",
      "limits_and_open_issues": "The source normalization fixes how the derivative is read; it does not prepare the B=1 sector.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Defined source normalization",
      "status_class": "defined",
      "downstream_claims": [
        "QCD-05"
      ],
      "graph_depth": 0,
      "reference_ids": [
        "REF-069"
      ]
    },
    {
      "id": "QCD-05",
      "title": "Proton Weyl-slope theorem",
      "display_order": 16,
      "sector": "qcd",
      "statement": {
        "public": "For the prepared proton channel, the normalized long-time trace-source slope is m_p/M_P.",
        "technical": "With TRC-01 and the regulated proton correlator, −lim_{s→∞}(1/s)∂_σ ln[C_p(s;σ)/C_p(s;0)]|_{σ=0}=m_p√G=m_p/M_P. The result follows from spectral projection, field-theoretic Feynman-Hellmann and the exact forward energy-momentum-tensor normalization."
      },
      "status": "derived_given_premise",
      "type": "theorem",
      "depends_on": [
        "QCD-04",
        "TRC-01"
      ],
      "equation_ids": [
        "eq:dimensionlessslope",
        "eq:weylslope"
      ],
      "evidence": [
        {
          "reference_id": "REF-069",
          "role": "methodological_foundation"
        },
        {
          "reference_id": "REF-070",
          "role": "methodological_foundation"
        },
        {
          "reference_id": "REF-076",
          "role": "foundation"
        },
        {
          "reference_id": "REF-077",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Theorem “Proton Weyl-slope theorem”.",
          "structure_id": "loc-022",
          "theorem_title": "Proton Weyl-slope theorem"
        }
      ],
      "qualifier": "Derived once the prepared B=1 proton channel exists; endpoint overlaps and subextensive edge dressings drop out of the normalized long-time slope.",
      "limits_and_open_issues": "Does not derive QCD-03.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Derived given premise",
      "status_class": "conditional",
      "downstream_claims": [
        "MAT-01"
      ],
      "graph_depth": 5,
      "reference_ids": [
        "REF-069",
        "REF-070",
        "REF-076",
        "REF-077"
      ]
    },
    {
      "id": "UNIT-01",
      "title": "Planck-unit normalization covariance",
      "display_order": 17,
      "sector": "qcd",
      "statement": {
        "public": "Reduced and unreduced Planck conventions are algebraically equivalent when every normalization is transformed consistently; changing notation does not add a physical choice.",
        "technical": "With M_P=G⁻¹/² and M̄_P=(8πG)⁻¹/², m_p/M_P=(1/√(8π))(m_p/M̄_P) and GΛ=(1/8π)(Λ/M̄_P²). Consistent conversion transforms both response and curvature observable."
      },
      "status": "normalization_covariance",
      "type": "normalization_covariance",
      "depends_on": [],
      "equation_ids": [
        "eq:Planckcovariance"
      ],
      "evidence": [
        {
          "reference_id": "REF-004",
          "role": "observational_input"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Eq. “Planck covariance”.",
          "structure_id": "loc-022"
        }
      ],
      "qualifier": "Algebraic covariance of conventions, not a dynamical selection.",
      "limits_and_open_issues": "Changing only one denominator while holding a coefficient-one source law fixed would define a different normalization.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Normalization covariance",
      "status_class": "derived",
      "downstream_claims": [
        "MAT-01"
      ],
      "graph_depth": 0,
      "reference_ids": [
        "REF-004"
      ]
    },
    {
      "id": "MAT-01",
      "title": "Normalized matter/IR composite",
      "display_order": 18,
      "sector": "qcd",
      "statement": {
        "public": "The strict channel defines the matter/IR composite as q_matter = a_eff·(m_p/M_P), with coefficient one between two separately normalized response coordinates.",
        "technical": "Define A_E≡a_eff and Q_p≡m_p/M_P, then q_matter^(1)≡A_E Q_p=a_eff(m_p/M_P). This is the channel’s definition of the normalized matter/IR composite; any coefficient coupling the composite to curvature belongs to the separate global source map."
      },
      "status": "defined_strict_channel_composite",
      "type": "defined_observable",
      "depends_on": [
        "EXT-01",
        "QCD-05",
        "UNIT-01"
      ],
      "equation_ids": [
        "eq:qmatter"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “Normalized matter/IR composite”.",
          "structure_id": "loc-023",
          "section_title": "Normalized matter/IR composite"
        }
      ],
      "qualifier": "Defined observable, not a separately derived dynamical interaction.",
      "limits_and_open_issues": "The leading numerical evaluation substitutes a_eff→a_SM; the full a_eff remains CORR-01.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Defined strict-channel composite",
      "status_class": "defined",
      "downstream_claims": [
        "ASM-01"
      ],
      "graph_depth": 6,
      "reference_ids": []
    },
    {
      "id": "SAD-01",
      "title": "Round-S⁴ Einstein action and Euler-normalized form",
      "display_order": 19,
      "sector": "gravity",
      "statement": {
        "public": "For round Euclidean de Sitter, the Einstein-Hilbert action has magnitude |S_EH|=24π²/u, and the same result can be written (24π²/u)N_E.",
        "technical": "For R_{μν}=Λ_UVg_{μν} on round S⁴, S_EH=−24π²/(κ²Λ_UV). With u=κ²Λ_UV and N_E=1, |S_EH|=(24π²/u)N_E. The magnitude also equals the de Sitter entropy."
      },
      "status": "derived",
      "type": "identity",
      "depends_on": [],
      "equation_ids": [
        "eq:SEH",
        "eq:SEHNE",
        "eq:geometric_identity"
      ],
      "evidence": [
        {
          "reference_id": "REF-021",
          "role": "foundation"
        },
        {
          "reference_id": "REF-024",
          "role": "foundation"
        },
        {
          "reference_id": "REF-038",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “Round-sphere action”.",
          "structure_id": "loc-024",
          "section_title": "Round-sphere action"
        }
      ],
      "qualifier": "Classical on-shell Einstein result. It does not by itself select u=1 or a path-integral contour.",
      "limits_and_open_issues": "Quantum dressing and higher-curvature shifts are CORR-02.",
      "relations": [
        {
          "type": "structural_parallel",
          "target_id": "REF-055",
          "target_type": "reference",
          "note": "Independent Λ>0 gravitational-EFT analysis finds round S⁴ leading-order dominant",
          "evidence_role": "direct_architectural_support"
        },
        {
          "type": "structural_parallel",
          "target_id": "REF-059",
          "target_type": "reference",
          "note": "Exact canonical gravity independently realises primitive SU(2) winding with inverse dimensionless cosmological coupling",
          "evidence_role": "direct_architectural_support"
        }
      ],
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained/reframed from v1; direct v2.0 support relations added. v2.1 (2026-09-07): saddle notation aligned to the paper's Λ_UV; no content change."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "CMP-01",
        "CORR-02",
        "DET-01",
        "INT-04",
        "SAD-02",
        "SAD-03",
        "SAD-04",
        "SAD-06"
      ],
      "graph_depth": 0,
      "reference_ids": [
        "REF-021",
        "REF-024",
        "REF-038"
      ]
    },
    {
      "id": "SAD-02",
      "title": "Decaying compact thimble",
      "display_order": 20,
      "sector": "gravity",
      "statement": {
        "public": "The strict channel selects the decaying orientation of the compact round-S⁴ thimble.",
        "technical": "The cosmological compact observable is defined so that the round-S⁴ thimble contributes with the damped orientation e^{−|S_EH|}. The opposite sign would replace suppression by an enormous enhancement and is not the channel analysed."
      },
      "status": "selected_contour",
      "type": "selected_sector",
      "depends_on": [
        "SAD-01"
      ],
      "equation_ids": [
        "eq:instanton_value"
      ],
      "evidence": [
        {
          "reference_id": "REF-039",
          "role": "foundation"
        },
        {
          "reference_id": "REF-040",
          "role": "foundation"
        },
        {
          "reference_id": "REF-053",
          "role": "foundation"
        },
        {
          "reference_id": "REF-065",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, paragraph “Suppressed-thimble clause”.",
          "structure_id": "loc-027",
          "paragraph_title": "Suppressed-thimble clause"
        }
      ],
      "qualifier": "Contour inclusion/orientation is selected, not derived by the compact action formula.",
      "limits_and_open_issues": "Broader contour selection depends on Stokes data, boundary conditions and observable.",
      "relations": [
        {
          "type": "structural_parallel",
          "target_id": "REF-060",
          "target_type": "reference",
          "note": "Explicit de Sitter Lefschetz thimble with damped anisotropic fluctuations",
          "evidence_role": "direct_architectural_support"
        }
      ],
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1; v2.0 adds direct thimble support."
      },
      "status_label": "Selected contour",
      "status_class": "selected",
      "downstream_claims": [
        "CMP-03",
        "INT-04",
        "SAD-06"
      ],
      "graph_depth": 1,
      "reference_ids": [
        "REF-039",
        "REF-040",
        "REF-053",
        "REF-065"
      ]
    },
    {
      "id": "SAD-04",
      "title": "Exact reduced-Planck-density UV endpoint",
      "display_order": 21,
      "sector": "gravity",
      "statement": {
        "public": "The strict compact channel declares the reduced-Planck-density domain 0<u≤1 and fixes its exact upper endpoint at u_max=1.",
        "technical": "With u=κ²Λ_UV=ρ_UV/M̄_P⁴, the declared ultraviolet domain is 0<ρ_UV≤M̄_P⁴, equivalently 0<u≤1, with u_max=1 ⇔ ρ_UV=M̄_P⁴."
      },
      "status": "selected_uv_domain",
      "type": "selected_sector",
      "depends_on": [
        "SAD-01"
      ],
      "equation_ids": [
        "eq:u_endpoint"
      ],
      "evidence": [
        {
          "reference_id": "REF-006",
          "role": "foundation"
        },
        {
          "reference_id": "REF-008",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, reduced-Planck-density UV-domain paragraph."
        }
      ],
      "qualifier": "The exact numerical boundary is a selected UV-domain normalization, not a theorem that every ultraviolet completion breaks down at the same coefficient.",
      "limits_and_open_issues": "Microscopic selection of this exact endpoint remains a central gravity target.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but scientifically sharpened in v2.0. v2.1 (2026-09-07): saddle notation aligned to the paper's Λ_UV/ρ_UV; no content change."
      },
      "status_label": "Selected UV domain",
      "status_class": "selected",
      "downstream_claims": [
        "CMP-03",
        "INT-04",
        "SAD-03",
        "SAD-06",
        "TEST-03"
      ],
      "graph_depth": 1,
      "reference_ids": [
        "REF-006",
        "REF-008"
      ]
    },
    {
      "id": "SAD-03",
      "title": "Monotonic ordering within the declared domain",
      "display_order": 22,
      "sector": "gravity",
      "statement": {
        "public": "Within the declared 0<u≤1 domain, B(u)=24π²/u decreases monotonically as u increases; the largest allowed u therefore has the smallest classical action.",
        "technical": "Because B(u)=24π²/u decreases monotonically as u increases, the mathematical ordering is fixed once the domain is declared. For the separately selected decaying factor e^{−B(u)}, this makes u=u_max the least-suppressed member, but the ordering does not itself select evaluation there."
      },
      "status": "derived_given_strict_domain",
      "type": "conditional_result",
      "depends_on": [
        "SAD-01",
        "SAD-04"
      ],
      "equation_ids": [
        "eq:SEHNE",
        "eq:u_domain",
        "eq:u_endpoint"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, compact de Sitter saddle section."
        }
      ],
      "qualifier": "Derived ordering only. Selection of a single boundary member is priced separately in SAD-07; the exact domain endpoint remains SAD-04.",
      "limits_and_open_issues": "Does not define a modulus measure or select the member at which the compact observable is evaluated.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID; v2.0 finalization separates derived monotonic ordering from the selected boundary-member prescription."
      },
      "status_label": "Derived given strict domain",
      "status_class": "conditional",
      "downstream_claims": [
        "SAD-07"
      ],
      "graph_depth": 2,
      "reference_ids": []
    },
    {
      "id": "SAD-07",
      "title": "Boundary-member prescription (no modulus integration)",
      "display_order": 23,
      "sector": "gravity",
      "statement": {
        "public": "The strict compact observable is evaluated at the least-suppressed boundary member u_b=u_max; no integration over u is part of the defined compact observable.",
        "technical": "After SAD-03 establishes the monotonic ordering of the declared domain, the compact channel selects single-member evaluation at u_b=u_max rather than introducing a modulus integral over u. Combined with the selected UV endpoint SAD-04, this gives u_b=u_max=1."
      },
      "status": "selected_compact_sector_prescription",
      "type": "selected_sector",
      "depends_on": [
        "SAD-03"
      ],
      "equation_ids": [
        "eq:ubone"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, compact de Sitter saddle section, boundary-member paragraph."
        }
      ],
      "qualifier": "This is a prescription for the compact observable, not a consequence of monotonic endpoint ordering and not a claim that u is a dynamical modulus with a preferred measure.",
      "limits_and_open_issues": "A microscopic gravitational derivation may reproduce, replace or falsify this prescription. No modulus integration over u is asserted within the defined compact observable.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0 finalization to price separately the single-member evaluation step that had previously been folded into endpoint dominance."
      },
      "status_label": "Selected compact-sector prescription",
      "status_class": "selected",
      "downstream_claims": [
        "CMP-03",
        "INT-04",
        "SAD-06",
        "TEST-03"
      ],
      "graph_depth": 3,
      "reference_ids": []
    },
    {
      "id": "SAD-06",
      "title": "Classical strict-channel gravitational factor",
      "display_order": 24,
      "sector": "gravity",
      "statement": {
        "public": "Given the selected u_max=1 UV endpoint, selected boundary-member prescription u_b=u_max and decaying contour, the classical compact gravitational factor is e⁻²⁴π².",
        "technical": "At the selected member u_b=u_max=1, B_1=|S_EH|=24π². With the selected damped orientation, the strict leading Einstein-Hilbert saddle contribution is e^{−B_1}=e^{−24π²}=1.34414611×10⁻¹⁰³."
      },
      "status": "derived_given_boundary_member_uv_domain_and_contour_selections",
      "type": "conditional_result",
      "depends_on": [
        "SAD-01",
        "SAD-02",
        "SAD-04",
        "SAD-07"
      ],
      "equation_ids": [
        "eq:B1",
        "eq:instanton_value"
      ],
      "evidence": [
        {
          "reference_id": "REF-038",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, “Classical strict-channel factor”.",
          "structure_id": "loc-028"
        }
      ],
      "qualifier": "Classical Einstein-Hilbert factor only; the member prescription, UV endpoint and contour are selected, while quantum/source-dependent dressing is open.",
      "limits_and_open_issues": "Does not assert a universal absolute one-loop prefactor.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0 to price the factor explicitly."
      },
      "status_label": "Derived given boundary-member, UV-domain and contour selections",
      "status_class": "conditional",
      "downstream_claims": [
        "ASM-01"
      ],
      "graph_depth": 4,
      "reference_ids": [
        "REF-038"
      ]
    },
    {
      "id": "DET-01",
      "title": "No canonical absolute determinant constant on round S⁴",
      "display_order": 25,
      "sector": "gravity",
      "statement": {
        "public": "A raw absolute sphere determinant does not carry a universal scheme-independent constant prefactor that can simply be set to one.",
        "technical": "Finite R² and Euler counterterms shift the absolute round-S⁴ effective action by arbitrary constants without changing the local closed-sphere equations. Therefore a raw finite one-loop constant C_grav is not scheme independent without an additional renormalisation and measure prescription."
      },
      "status": "derived",
      "type": "theorem",
      "depends_on": [
        "SAD-01"
      ],
      "equation_ids": [
        "eq:app_detcts",
        "eq:app_rawdet"
      ],
      "evidence": [
        {
          "reference_id": "REF-014",
          "role": "foundation"
        },
        {
          "reference_id": "REF-035",
          "role": "foundation"
        },
        {
          "reference_id": "REF-061",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Appendix “Determinant status of the strict compact weight”.",
          "structure_id": "loc-049"
        }
      ],
      "qualifier": "No unit-prefactor or determinant-cancellation claim is used; source-dependent quantum-gravity corrections remain open.",
      "limits_and_open_issues": "Source-dependent determinants, Stokes changes and higher-curvature shifts remain CORR-02.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0; replaces the old paired-cap determinant-normalisation story."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "CORR-02"
      ],
      "graph_depth": 1,
      "reference_ids": [
        "REF-014",
        "REF-035",
        "REF-061"
      ]
    },
    {
      "id": "ASM-01",
      "title": "Factorized compact assembly",
      "display_order": 26,
      "sector": "assembly",
      "statement": {
        "public": "The leading compact observable is defined by multiplying the normalized matter/IR composite by the selected classical compact factor.",
        "technical": "Define q_comp≡q_matter^(1)e^{−24π²}=a_eff(m_p/M_P)e^{−24π²}. The coefficient-one factorization is the strict-channel observable definition, not a separately derived interaction vertex."
      },
      "status": "defined_strict_channel_composite",
      "type": "defined_observable",
      "depends_on": [
        "MAT-01",
        "SAD-06"
      ],
      "equation_ids": [
        "eq:qcomp_general"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “Leading compact-channel result”.",
          "structure_id": "sec:assembly",
          "section_title": "Leading compact-channel result"
        }
      ],
      "qualifier": "Definition of the compact response. The later map from q_comp to cosmological curvature is separate.",
      "limits_and_open_issues": "Does not upgrade the QCD premise or gravitational selections to derived status.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Defined strict-channel composite",
      "status_class": "defined",
      "downstream_claims": [
        "NUM-01"
      ],
      "graph_depth": 7,
      "reference_ids": []
    },
    {
      "id": "NUM-01",
      "title": "Leading strict-channel compact benchmark",
      "display_order": 27,
      "sector": "assembly",
      "statement": {
        "public": "Within the stated leading strict channel, the compact response is q_comp = 2.85652154×10⁻¹²², with no continuous parameter fitted to the cosmological value.",
        "technical": "Using a_eff→a_SM=1991/720 in ASM-01 together with the physical m_p/M_P and e^{−24π²}, q_comp=(1991/720)(7.68514844×10⁻²⁰)(1.34414611×10⁻¹⁰³)=2.85652154×10⁻¹²²."
      },
      "status": "derived_given_stated_premise_selections",
      "type": "computed_value",
      "depends_on": [
        "ASM-01",
        "SM-01"
      ],
      "equation_ids": [
        "eq:qcomp_numeric_audit",
        "eq:qcomp_result"
      ],
      "evidence": [
        {
          "reference_id": "REF-004",
          "role": "observational_input"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, numerical audit and compact-status ledger.",
          "structure_id": "loc-032"
        }
      ],
      "qualifier": "Compact benchmark only. Its interpretation as cosmological curvature is MAP-01. The QCD premise and gravitational selections enter through upstream dependencies and are not fitted.",
      "limits_and_open_issues": "Full a_eff and gravitational dressing remain open; the formula cannot be retuned to their outcome.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but completely rebased onto the v2.0 geometric/QCD/gravity chain."
      },
      "status_label": "Derived given stated premise/selections",
      "status_class": "conditional",
      "downstream_claims": [
        "CMP-01",
        "CORR-03",
        "CORR-04",
        "INT-02",
        "INT-03",
        "MAP-01",
        "OBS-02"
      ],
      "graph_depth": 8,
      "reference_ids": [
        "REF-004"
      ]
    },
    {
      "id": "GR-01",
      "title": "Ordinary-GR no-go for a linear compact source",
      "display_order": 28,
      "sector": "global",
      "statement": {
        "public": "Ordinary local type-A anomaly backreaction has the wrong scaling: it produces an H⁴ stress and no small branch linear in the compact response.",
        "technical": "On a maximally symmetric branch the type-A anomaly stress scales as Λ_g². In ordinary semiclassical Einstein gravity, Λ_g−Λ_0=(a/3π)(Λ_g²/M_P²); multiplying the anomaly sector by a small ε places ε in the denominator of the nonzero root rather than producing Λ_g/M_P²∝εa."
      },
      "status": "derived",
      "type": "theorem",
      "depends_on": [
        "EXT-01"
      ],
      "equation_ids": [
        "eq:H4obstruction"
      ],
      "evidence": [
        {
          "reference_id": "REF-018",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Proposition “Ordinary-GR no-go for a linear compact source”.",
          "structure_id": "loc-034"
        }
      ],
      "qualifier": "Applies to the ordinary local metric-variation route.",
      "limits_and_open_issues": "Motivates a separate scalar zero-mode equation; it does not rule out all nonlocal/global completions.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 3,
      "reference_ids": [
        "REF-018"
      ]
    },
    {
      "id": "GR-02",
      "title": "Trace-free quotient leaves one scalar mode",
      "display_order": 29,
      "sector": "global",
      "statement": {
        "public": "Removing the volume-counterterm representative leaves a unique trace-free local Einstein equation and one undetermined spacetime-constant scalar mode.",
        "technical": "The unique algebraic projection invariant under E_{μν}→E_{μν}+cg_{μν} and equal to the identity on traceless tensors is E_{μν}−Eg_{μν}/4, yielding R_{μν}−Rg_{μν}/4=(8π/M_P²)(T_{μν}−Tg_{μν}/4). Conservation leaves R+(8π/M_P²)T=4Λ_int."
      },
      "status": "derived",
      "type": "lemma",
      "depends_on": [
        "VAC-01"
      ],
      "equation_ids": [
        "eq:integrationconstant",
        "eq:tracefree"
      ],
      "evidence": [
        {
          "reference_id": "REF-028",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-029",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Lemma “Trace-free quotient projector”.",
          "structure_id": "loc-035"
        }
      ],
      "qualifier": "Determines the representative-independent local equation shape, not a complete physical law or the value of Λ_int.",
      "limits_and_open_issues": "The missing scalar equation is supplied only by the proposed completion.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1."
      },
      "status_label": "Derived",
      "status_class": "derived",
      "downstream_claims": [
        "CMP-02",
        "GS-01"
      ],
      "graph_depth": 1,
      "reference_ids": [
        "REF-028",
        "REF-029"
      ]
    },
    {
      "id": "GS-01",
      "title": "Four-form global-source completion",
      "display_order": 30,
      "sector": "global",
      "statement": {
        "public": "A Henneaux-Teitelboim/sequestering-type four-form action is proposed to supply the scalar-curvature mode omitted by the trace-free local equation.",
        "technical": "The proposed action S_gs[q] contains a rigid Newton variable η, a volume four-form constraint and a source term proportional to η²M_P⁴ q F₄. The compact calculation supplies q=q_comp; the action is varied at fixed rigid q."
      },
      "status": "proposed_completion",
      "type": "proposed_model",
      "depends_on": [
        "GR-02"
      ],
      "equation_ids": [
        "eq:globalaction"
      ],
      "evidence": [
        {
          "reference_id": "REF-028",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-030",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-031",
          "role": "structural_convergence"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Sec. “From compact response to cosmological curvature: global-source completion”.",
          "structure_id": "sec:globalsource",
          "section_title": "From compact response to cosmological curvature: global-source completion"
        }
      ],
      "qualifier": "Gravity-side completion proposed independently of the extraction theorem.",
      "limits_and_open_issues": "Microscopic selection of this action remains open.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID; action rewritten and status sharpened in v2.0."
      },
      "status_label": "Proposed completion",
      "status_class": "proposed",
      "downstream_claims": [
        "CMP-03",
        "GS-02",
        "GS-04",
        "GS-05"
      ],
      "graph_depth": 2,
      "reference_ids": [
        "REF-028",
        "REF-030",
        "REF-031"
      ]
    },
    {
      "id": "GS-05",
      "title": "Branch-unit covariance fixes η² source dependence",
      "display_order": 31,
      "sector": "global",
      "statement": {
        "public": "Within the proposed completion, covariance under the arbitrary branch Newton-unit parametrization fixes the source dependence to η² up to one overall compact-to-global coefficient.",
        "technical": "Replacing η² by f(η), branch-unit independence of Λ/M_N² relative to q requires f′(η)/(2η)=c, hence f(η)=cη²+f₀. The minimal one-source action sets f₀=0; covariance fixes the η² form but not the overall c."
      },
      "status": "derived_from_branch_unit_covariance",
      "type": "identity",
      "depends_on": [
        "GS-01"
      ],
      "equation_ids": [
        "eq:source_covariance"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Appendix “Off-shell variation of the global-source action”.",
          "structure_id": "loc-050"
        }
      ],
      "qualifier": "Derived within the proposed completion; it does not fix the unit coefficient c=1.",
      "limits_and_open_issues": "The remaining coefficient is GS-04.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Derived from branch-unit covariance",
      "status_class": "derived",
      "downstream_claims": [
        "GS-04"
      ],
      "graph_depth": 3,
      "reference_ids": []
    },
    {
      "id": "GS-04",
      "title": "Unit compact-to-global source pairing",
      "display_order": 32,
      "sector": "global",
      "statement": {
        "public": "The proposed completion uses unit pairing between the normalized compact response and the global four-form source.",
        "technical": "After GS-05 fixes the η² dependence, the overall source coefficient c remains undetermined by branch-unit covariance. The paper adopts the unit choice c=1 in S_gs[q]."
      },
      "status": "proposed_unit_pairing",
      "type": "proposed_model",
      "depends_on": [
        "GS-01",
        "GS-05"
      ],
      "equation_ids": [
        "eq:globalaction",
        "eq:source_covariance"
      ],
      "evidence": [
        {
          "reference_id": "REF-028",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-030",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-031",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-032",
          "role": "structural_convergence"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, global-source action and Appendix on branch-unit covariance.",
          "structure_id": "sec:globalsource"
        }
      ],
      "qualifier": "A proposed physical normalization, not fitted after comparison and not derived by the compact anomaly calculation.",
      "limits_and_open_issues": "A microscopic parent could derive a different coefficient and thereby change the curvature map.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but fundamentally revised in v2.0; old v1 source-charge convention is superseded."
      },
      "status_label": "Proposed unit pairing",
      "status_class": "proposed",
      "downstream_claims": [
        "GS-02"
      ],
      "graph_depth": 4,
      "reference_ids": [
        "REF-028",
        "REF-030",
        "REF-031",
        "REF-032"
      ]
    },
    {
      "id": "GS-02",
      "title": "Field equations of the proposed global-source action",
      "display_order": 33,
      "sector": "global",
      "statement": {
        "public": "Once the stated global-source action and unit pairing are adopted, its variations cancel homogeneous matter shifts and fix the residual vacuum relation Λ/M_N²=q.",
        "technical": "Variation gives F₄=*1, ⟨R⟩=4ηM_P²q and G_{μν}+ηM_P²q g_{μν}=(8π/(ηM_P²))(T_{μν}−⟨T⟩g_{μν}/4). On a maximally symmetric vacuum with M_N²=ηM_P², Λ/M_N²=q. Constant shifts of L_m cancel exactly."
      },
      "status": "derived_once_action_and_unit_pairing_are_adopted",
      "type": "theorem",
      "depends_on": [
        "GS-01",
        "GS-04"
      ],
      "equation_ids": [
        "eq:compactsumrule",
        "eq:completedEinstein",
        "eq:vacuumq"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Theorem “Global-source field equations”.",
          "structure_id": "sec:globalsource",
          "theorem_title": "Global-source field equations"
        }
      ],
      "qualifier": "The equations are a theorem of the stated action; the action and unit pairing remain proposed.",
      "limits_and_open_issues": "Does not establish microscopic selection of GS-01/GS-04.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID; equations and normalization updated to v2.0."
      },
      "status_label": "Derived once action and unit pairing are adopted",
      "status_class": "conditional",
      "downstream_claims": [
        "CMP-02",
        "GS-03",
        "INT-01",
        "MAP-01",
        "TEST-01"
      ],
      "graph_depth": 5,
      "reference_ids": []
    },
    {
      "id": "GS-03",
      "title": "Regulator-independent late-time trace-average condition",
      "display_order": 34,
      "sector": "global",
      "statement": {
        "public": "Direct late-time identification of the compact response with the asymptotic cosmological amplitude additionally requires the regulated non-vacuum trace average to vanish.",
        "technical": "For connected future-directed exhaustions M_τ with subextensive boundary/edge terms and regulator-independent limit, require ⟨T_nonvac⟩_reg=lim_{τ→∞}[∫_{Mτ}√−g T_nonvac]/[∫_{Mτ}√−g]=0. Future-eternal asymptotically de Sitter dilution satisfies this standard sufficient regime."
      },
      "status": "amplitude_condition",
      "type": "amplitude_condition",
      "depends_on": [
        "GS-02"
      ],
      "equation_ids": [
        "eq:traceaveragecondition",
        "eq:traceaveragedef"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, late-time exhaustion/trace-average subsection.",
          "structure_id": "sec:globalsource"
        }
      ],
      "qualifier": "Amplitude condition. It fixes the late-time amplitude, not the equation of state, which follows from the spacetime-constant residual source.",
      "limits_and_open_issues": "Not asserted for every recollapsing or non-asymptotic cosmological history.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but reclassified from selected branch to explicit amplitude condition in v2.0."
      },
      "status_label": "Amplitude condition",
      "status_class": "conditional",
      "downstream_claims": [
        "CMP-03",
        "OBS-02"
      ],
      "graph_depth": 6,
      "reference_ids": []
    },
    {
      "id": "MAP-01",
      "title": "Compact response to cosmological curvature map",
      "display_order": 35,
      "sector": "global",
      "statement": {
        "public": "The proposed gravity-side completion identifies the calculated compact response with the residual cosmological curvature; the late-time amplitude comparison additionally uses GS-03.",
        "technical": "With q=q_comp inserted into the proposed action, GS-02 gives Λ/M_N²=q on a maximally symmetric vacuum. Matching to the measured branch Newton unit yields the residual curvature map; direct asymptotic identification Λ_∞/M_P²=q_comp additionally assumes GS-03."
      },
      "status": "proposed_cosmological_identification",
      "type": "proposed_model",
      "depends_on": [
        "NUM-01",
        "GS-02"
      ],
      "equation_ids": [
        "eq:asymptoticq",
        "eq:vacuumq"
      ],
      "evidence": [
        {
          "reference_id": "REF-028",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-030",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-031",
          "role": "structural_convergence"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, global-source completion and asymptotic relation.",
          "structure_id": "sec:globalsource"
        }
      ],
      "qualifier": "Separate from the compact calculation. The identification inherits the proposed action and unit pairing; the observational late-time amplitude inherits GS-03.",
      "limits_and_open_issues": "A different microscopic global source law or pairing would change the cosmological reading without undoing NUM-01.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID; v2.0 cleanly separates compact response from curvature map."
      },
      "status_label": "Proposed cosmological identification",
      "status_class": "proposed",
      "downstream_claims": [
        "CMP-02",
        "INT-01",
        "OBS-02"
      ],
      "graph_depth": 9,
      "reference_ids": [
        "REF-028",
        "REF-030",
        "REF-031"
      ]
    },
    {
      "id": "OBS-01",
      "title": "Planck 2018 flat-ΛCDM inferred benchmark",
      "display_order": 36,
      "sector": "observations",
      "statement": {
        "public": "Planck 2018 flat-ΛCDM-inferred value: (2.846±0.057)×10⁻¹²² in the paper’s GΛ convention.",
        "technical": "The comparison benchmark is (Λ/M_P²)_obs=(2.846±0.057)×10⁻¹²² inferred from Planck 2018 under flat ΛCDM."
      },
      "status": "observational_input",
      "type": "observational_input",
      "depends_on": [],
      "evidence": [
        {
          "reference_id": "REF-003",
          "role": "observational_input"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, abstract/numerical comparison.",
          "structure_id": "loc-032"
        }
      ],
      "qualifier": "Model-dependent cosmological inference, not a direct measurement of an asymptotic constant and not a theory error bar.",
      "limits_and_open_issues": "If evolving dark energy is established, this flat-ΛCDM inference is not the direct asymptotic quantity predicted by the completion.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1."
      },
      "status_label": "Observational input",
      "status_class": "standard",
      "downstream_claims": [
        "CORR-03",
        "OBS-02"
      ],
      "graph_depth": 0,
      "reference_ids": [
        "REF-003"
      ]
    },
    {
      "id": "OBS-02",
      "title": "Numerical comparison with the Planck benchmark",
      "display_order": 37,
      "sector": "observations",
      "statement": {
        "public": "Under the proposed cosmological identification and late-time amplitude condition, the calculated central value differs from the Planck 2018 flat-ΛCDM inference by about 0.4%.",
        "technical": "The leading value 2.85652154×10⁻¹²² differs from 2.846×10⁻¹²² by about 0.4%, equal to about 0.18 times the quoted observational standard deviation. The 0.18 figure is not a combined significance because theory uncertainty is not assigned."
      },
      "status": "derived_comparison",
      "type": "comparison",
      "depends_on": [
        "NUM-01",
        "MAP-01",
        "GS-03",
        "OBS-01"
      ],
      "equation_ids": [
        "eq:mainresult"
      ],
      "evidence": [
        {
          "reference_id": "REF-003",
          "role": "observational_input"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, global-source comparison and correction-budget section.",
          "structure_id": "sec:errorbudget"
        }
      ],
      "qualifier": "Plain benchmark comparison, not a likelihood ratio or sigma-level theory confirmation.",
      "limits_and_open_issues": "Open a_eff and gravitational corrections determine how the benchmark ultimately moves.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID; dependency chain updated to v2.0."
      },
      "status_label": "Derived comparison",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 10,
      "reference_ids": [
        "REF-003"
      ]
    },
    {
      "id": "CORR-01",
      "title": "Full interacting curved-space Standard Model coefficient",
      "display_order": 38,
      "sector": "corrections",
      "statement": {
        "public": "The full interacting curved-space Standard Model coefficient a_eff in the precise compact channel remains to be calculated.",
        "technical": "The leading free-field value a_SM is known, and local-RG/interacting-QFT results constrain the structure of corrections, but the paper does not assign a numerical uncertainty to a_eff without a complete curved-space Standard Model calculation including running, beta-function/operator mixing and the relevant compact projection."
      },
      "status": "open_calculation",
      "type": "open_calculation",
      "depends_on": [
        "EXT-01",
        "SM-01"
      ],
      "equation_ids": [
        "eq:aSMvalue"
      ],
      "evidence": [
        {
          "reference_id": "REF-012",
          "role": "foundation"
        },
        {
          "reference_id": "REF-026",
          "role": "foundation"
        },
        {
          "reference_id": "REF-037",
          "role": "foundation"
        },
        {
          "reference_id": "REF-049",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Standard Model evaluation and correction budget.",
          "structure_id": "sec:anomaly"
        }
      ],
      "qualifier": "Open matter calculation; no numerical theory uncertainty is assigned without the complete curved-space Standard Model calculation.",
      "limits_and_open_issues": "No theory error bar is inferred from partial perturbative information in the released paper.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but completely revised in v2.0; old 0.5% estimate removed."
      },
      "status_label": "Open calculation",
      "status_class": "open",
      "downstream_claims": [
        "CMP-03",
        "CORR-04",
        "TEST-02"
      ],
      "graph_depth": 4,
      "reference_ids": [
        "REF-012",
        "REF-026",
        "REF-037",
        "REF-049"
      ]
    },
    {
      "id": "CORR-02",
      "title": "Quantum gravitational dressing and higher-curvature action shift",
      "display_order": 39,
      "sector": "corrections",
      "statement": {
        "public": "The principal open gravity calculation is the complete source-dependent gravitational dressing and higher-curvature shift of the primitive compact action beyond the Einstein-Hilbert benchmark.",
        "technical": "The strict leading benchmark is the classical Einstein-Hilbert truncation δB=0. This does not assert a universal canonical determinant value C_grav=1. Source-dependent determinants, higher-curvature contributions changing the Planck-boundary action, Stokes changes or nonperturbative changes of the selected compact sector can shift the complete primitive exponent; these effects are not fixed by DET-01."
      },
      "status": "open_calculation",
      "type": "open_calculation",
      "depends_on": [
        "SAD-01",
        "DET-01"
      ],
      "equation_ids": [
        "eq:app_detcts",
        "eq:app_rawdet"
      ],
      "evidence": [
        {
          "reference_id": "REF-061",
          "role": "foundation"
        },
        {
          "reference_id": "REF-091",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-092",
          "role": "structural_convergence"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, determinant/higher-curvature status and correction budget.",
          "structure_id": "loc-029"
        }
      ],
      "qualifier": "The leading benchmark sets the open net correction δB to zero at Einstein-Hilbert order; the physical quantum/higher-curvature shift remains to be calculated.",
      "limits_and_open_issues": "Their size is not inferred from the 0.4% central-value agreement.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but rebased from the old paired-cap cancellation framework."
      },
      "status_label": "Open calculation",
      "status_class": "open",
      "downstream_claims": [
        "CMP-03",
        "CORR-04",
        "TEST-02",
        "TEST-03"
      ],
      "graph_depth": 2,
      "reference_ids": [
        "REF-061",
        "REF-091",
        "REF-092"
      ]
    },
    {
      "id": "CORR-03",
      "title": "Gravity-only δB tolerance",
      "display_order": 40,
      "sector": "corrections",
      "statement": {
        "public": "At fixed a_eff=a_SM, the Planck benchmark allows only a few×10⁻² shift in the complete primitive action.",
        "technical": "For q(δB)=q₀e^{−δB} at a_eff=a_SM, remaining within the quoted Planck 2018 1σ interval requires −0.0161≲δB≲0.0239; the 2σ interval is −0.0356≲δB≲0.0446."
      },
      "status": "derived_sensitivity_bound",
      "type": "test",
      "depends_on": [
        "NUM-01",
        "OBS-01"
      ],
      "equation_ids": [
        "eq:dB1sigma",
        "eq:dB2sigma"
      ],
      "evidence": [
        {
          "reference_id": "REF-003",
          "role": "observational_input"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Eqs. for δB 1σ and 2σ intervals.",
          "structure_id": "sec:errorbudget"
        }
      ],
      "qualifier": "Gravity-only slice of the joint open correction space, not a prior distribution or fitted error bar.",
      "limits_and_open_issues": "Matter and gravity corrections can both move the benchmark; the general combination is CORR-04.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Derived sensitivity bound",
      "status_class": "derived",
      "downstream_claims": [
        "TEST-03"
      ],
      "graph_depth": 9,
      "reference_ids": [
        "REF-003"
      ]
    },
    {
      "id": "CORR-04",
      "title": "Joint matter-gravity correction relation",
      "display_order": 41,
      "sector": "corrections",
      "statement": {
        "public": "The leading joint correction depends on the combination δB−ln(a_eff/a_SM), not on two independently fitted offsets.",
        "technical": "Relative to the leading benchmark, q/q₀=(a_eff/a_SM)e^{−δB}; equivalently ln(q/q₀)=ln(a_eff/a_SM)−δB. The constant-q contours are sensitivity relations between two independently open calculations, not a fit space."
      },
      "status": "derived_correction_relation",
      "type": "identity",
      "depends_on": [
        "NUM-01",
        "CORR-01",
        "CORR-02"
      ],
      "equation_ids": [
        "eq:joint_correction"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, correction-budget paragraph on joint matter-gravity space.",
          "structure_id": "sec:errorbudget"
        }
      ],
      "qualifier": "Sensitivity relation only. The open calculations determine the point; observation does not select it.",
      "limits_and_open_issues": "No cancellation between open sectors is assumed or encouraged.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Derived correction relation",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 9,
      "reference_ids": []
    },
    {
      "id": "TEST-01",
      "title": "Exact w=-1 observational falsifier of the completion",
      "display_order": 42,
      "sector": "tests",
      "statement": {
        "public": "The proposed completion gives a spacetime-constant residual source with w=-1; persistent cross-dataset, systematics-robust evidence for evolving dark energy would falsify that cosmological identification while leaving the compact extraction intact.",
        "technical": "On any fixed branch of GS-02 the residual source is proportional to g_{μν} and has w=-1. DESI/DES evidence for evolution is currently dataset dependent; decisive robust evolution would falsify the proposed global-source identification, not EXT-01 or NUM-01 as compact statements."
      },
      "status": "test",
      "type": "test",
      "depends_on": [
        "GS-02"
      ],
      "equation_ids": [
        "eq:completedEinstein",
        "eq:residuallambda"
      ],
      "evidence": [
        {
          "reference_id": "REF-042",
          "role": "observational_input"
        },
        {
          "reference_id": "REF-043",
          "role": "observational_input"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, observational-tests paragraph.",
          "structure_id": "loc-043"
        }
      ],
      "qualifier": "Falsifier of the proposed completion/observational identification, not of the upstream compact theorem.",
      "limits_and_open_issues": "A preference under one dataset combination/parameterisation is not by itself the stated falsification threshold.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1; status and separation from GS-03 preserved."
      },
      "status_label": "Test",
      "status_class": "test",
      "downstream_claims": [],
      "graph_depth": 6,
      "reference_ids": [
        "REF-042",
        "REF-043"
      ]
    },
    {
      "id": "TEST-02",
      "title": "Microscopic field-content sensitivity",
      "display_order": 43,
      "sector": "tests",
      "statement": {
        "public": "Changes in microscopic field content can move the benchmark through a_eff and, if they alter the spin-to-QCD implementation, through new finite interface terms; that sensitivity remains qualitative until the relevant calculations are done.",
        "technical": "New microscopic degrees of freedom change the protected matter coordinate through the full a_eff calculation, and may also change a microscopic realization of QCD-03 or introduce finite cap/interface terms that belong in δB. The paper does not publish a percentage exclusion table as a current result."
      },
      "status": "test",
      "type": "test",
      "depends_on": [
        "SM-01",
        "CORR-01",
        "CORR-02",
        "QCD-03"
      ],
      "evidence": [
        {
          "reference_id": "REF-004",
          "role": "observational_input"
        },
        {
          "reference_id": "REF-012",
          "role": "foundation"
        },
        {
          "reference_id": "REF-026",
          "role": "foundation"
        },
        {
          "reference_id": "REF-049",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, final paragraph of correction budget/observational tests.",
          "structure_id": "loc-043"
        }
      ],
      "qualifier": "Conditional field-content test, not a present BSM exclusion.",
      "limits_and_open_issues": "Quantitative exclusion requires the full matter and gravity calculations.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but revised in v2.0; legacy percentage scenarios removed from canonical copy."
      },
      "status_label": "Test",
      "status_class": "test",
      "downstream_claims": [],
      "graph_depth": 5,
      "reference_ids": [
        "REF-004",
        "REF-012",
        "REF-026",
        "REF-049"
      ]
    },
    {
      "id": "TEST-03",
      "title": "Primitive-action/UV-boundary precision test",
      "display_order": 44,
      "sector": "tests",
      "statement": {
        "public": "The strict gravitational boundary is sharply testable because any microscopic change of the primitive action moves the prediction exponentially.",
        "technical": "A parent gravitational theory must reproduce, replace or falsify the boundary-member prescription, exact u_max=1 UV-domain normalization and decaying compact contour, and control the complete primitive exponent within the CORR-03 budget if the leading Planck comparison is to remain near its quoted interval. Larger shifts change or falsify the leading benchmark rather than becoming fit parameters."
      },
      "status": "test",
      "type": "test",
      "depends_on": [
        "SAD-04",
        "SAD-07",
        "CORR-02",
        "CORR-03"
      ],
      "equation_ids": [
        "eq:dB1sigma",
        "eq:dB2sigma"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, “Strict compact gravitational channel” and observational tests.",
          "structure_id": "loc-040"
        }
      ],
      "qualifier": "Test of the selected UV model and quantum completion, not a fitted uncertainty.",
      "limits_and_open_issues": "Alternative boundary conventions or higher-curvature actions are different microscopic outcomes, not statistical variations of one fixed model.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but recast around the v2.0 δB budget."
      },
      "status_label": "Test",
      "status_class": "test",
      "downstream_claims": [],
      "graph_depth": 10,
      "reference_ids": []
    },
    {
      "id": "INT-01",
      "title": "Residual-curvature interpretation",
      "display_order": 45,
      "sector": "interpretation",
      "statement": {
        "public": "In the completed model, the cosmological constant is the residual vacuum curvature fixed by the global-source equation, not a separately observable absolute zero-point-energy sum.",
        "technical": "Given GS-01/GS-04 and the derived GS-02 field equations, the compact response enters the rigid scalar source while homogeneous matter shifts cancel from the trace-free local equation. The resulting residual vacuum term is metric proportional."
      },
      "status": "derived_within_proposed_completion",
      "type": "interpretation",
      "depends_on": [
        "GS-02",
        "MAP-01"
      ],
      "equation_ids": [
        "eq:completedEinstein",
        "eq:residuallambda"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, global-source section and Discussion.",
          "structure_id": "sec:globalsource"
        }
      ],
      "qualifier": "Interpretation of the proposed completion; not required for the extraction theorem.",
      "limits_and_open_issues": "Inherits Proposed status through MAP-01.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1, updated to the v2.0 action."
      },
      "status_label": "Derived within proposed completion",
      "status_class": "conditional",
      "downstream_claims": [],
      "graph_depth": 10,
      "reference_ids": []
    },
    {
      "id": "INT-02",
      "title": "103+19 decade decomposition",
      "display_order": 46,
      "sector": "interpretation",
      "statement": {
        "public": "The 122-decade hierarchy separates into about 103 decades from compact gravity and 19 from the QCD-to-Planck ratio, multiplied by an order-one Standard Model coefficient.",
        "technical": "From NUM-01, −log10(e^{−24π²})≈102.87 and −log10(m_p/M_P)≈19.11; a_SM is O(1). The hierarchy is multiplicative rather than a cancellation among large vacuum-energy terms."
      },
      "status": "derived_arithmetic",
      "type": "interpretation",
      "depends_on": [
        "NUM-01"
      ],
      "equation_ids": [
        "eq:qcomp_numeric_audit"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, numerical audit discussion.",
          "structure_id": "loc-032"
        }
      ],
      "qualifier": "Arithmetic decomposition of the leading strict result.",
      "limits_and_open_issues": "Inherits all upstream conditions of NUM-01.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1."
      },
      "status_label": "Derived arithmetic",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 9,
      "reference_ids": []
    },
    {
      "id": "INT-03",
      "title": "Combined-exponent rewriting",
      "display_order": 47,
      "sector": "interpretation",
      "statement": {
        "public": "The two suppressions can be rewritten as a single exponential of the sum of two distinct exponents.",
        "technical": "e^{−24π²}(m_p/M_P)=exp[−24π²−ln(M_P/m_p)]. This is an algebraic rewriting of the gravitational and QCD hierarchies, not evidence that they arise from one thermal or microscopic process."
      },
      "status": "derived_rewriting",
      "type": "interpretation",
      "depends_on": [
        "NUM-01"
      ],
      "equation_ids": [
        "eq:qcomp_general"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, numerical audit/interpretive discussion.",
          "structure_id": "loc-032"
        }
      ],
      "qualifier": "Rewriting only.",
      "limits_and_open_issues": "Does not establish a common dynamical origin of the exponents.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1 as a non-load-bearing interpretation."
      },
      "status_label": "Derived rewriting",
      "status_class": "derived",
      "downstream_claims": [],
      "graph_depth": 9,
      "reference_ids": []
    },
    {
      "id": "INT-04",
      "title": "Compact action-de Sitter entropy identity",
      "display_order": 48,
      "sector": "interpretation",
      "statement": {
        "public": "For the round compact saddle, the magnitude of the classical Euclidean action equals its de Sitter entropy; with the selected damped orientation the weight is e^(−S_dS).",
        "technical": "For the round de Sitter saddle, |S_EH|=3πM_P²/Λ=S_dS. Under SAD-02 and the selected SAD-04/SAD-07 endpoint-member prescription, S_dS=24π² and the classical weight is e^{−S_dS}=e^{−24π²}."
      },
      "status": "standard_identity_applied_to_selected_sector",
      "type": "identity",
      "depends_on": [
        "SAD-01",
        "SAD-02",
        "SAD-04",
        "SAD-07"
      ],
      "equation_ids": [
        "eq:BandS",
        "eq:instanton_value"
      ],
      "evidence": [
        {
          "reference_id": "REF-038",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, action-entropy identity in compact gravity section.",
          "structure_id": "loc-024"
        }
      ],
      "qualifier": "Classical on-shell identity applied to the selected sector, not an all-orders quantum-gravity identity.",
      "limits_and_open_issues": "The entropy belongs to the ultraviolet compact saddle, not the observed late-time horizon.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1."
      },
      "status_label": "Standard identity applied to selected sector",
      "status_class": "conditional",
      "downstream_claims": [],
      "graph_depth": 4,
      "reference_ids": [
        "REF-038"
      ]
    },
    {
      "id": "CMP-01",
      "title": "Specified compact channel closes the leading numerical chain",
      "display_order": 49,
      "sector": "comparison",
      "statement": {
        "public": "The construction closes the leading compact numerical chain while isolating, rather than hiding, the premise and gravitational selections on which it depends.",
        "technical": "The chain supplies a protected matter coordinate, a derived primitive geometric unit, an explicit QCD state-preparation premise with downstream proton response, a specified compact gravitational factor, and a defined factorized compact observable. The cosmological curvature map remains a separate proposed completion."
      },
      "status": "comparative_synthesis",
      "type": "comparison",
      "depends_on": [
        "VAC-02",
        "EXT-01",
        "TOP-01",
        "QCD-03",
        "SAD-01",
        "NUM-01"
      ],
      "equation_ids": [
        "eq:qcomp_result"
      ],
      "evidence": [
        {
          "reference_id": "REF-005",
          "role": "foundation"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Introduction, Discussion and Conclusion.",
          "structure_id": "sec:intro"
        }
      ],
      "qualifier": "Synthesis, not a claim of unique microscopic selection or completed first-principles derivation.",
      "limits_and_open_issues": "Five remaining programme targets are exposed explicitly.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID; v2.0 wording reflects the new architecture."
      },
      "status_label": "Comparative synthesis",
      "status_class": "conditional",
      "downstream_claims": [],
      "graph_depth": 9,
      "reference_ids": [
        "REF-005"
      ]
    },
    {
      "id": "CMP-02",
      "title": "Relation to trace-free and sequestering approaches",
      "display_order": 50,
      "sector": "comparison",
      "statement": {
        "public": "The compact response acts as a candidate selector for the scalar residual that trace-free and sequestering formulations leave undetermined.",
        "technical": "GR-02 gives the trace-free local equation and an undetermined scalar mode; within the proposed GS-01/GS-04 completion, GS-02 assigns that mode through q_comp. This is structurally close to global-variable/sequestering approaches but uses a different source value."
      },
      "status": "comparative_synthesis",
      "type": "comparison",
      "depends_on": [
        "GR-02",
        "GS-02",
        "MAP-01"
      ],
      "equation_ids": [
        "eq:completedEinstein",
        "eq:tracefree",
        "eq:vacuumq"
      ],
      "evidence": [
        {
          "reference_id": "REF-028",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-030",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-032",
          "role": "structural_convergence"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Discussion “Independent structural convergence”.",
          "structure_id": "loc-045"
        }
      ],
      "qualifier": "Comparison conditional on the proposed completion.",
      "limits_and_open_issues": "Does not establish that existing sequestering models derive q_comp or the unit pairing.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1, updated to v2.0."
      },
      "status_label": "Comparative synthesis",
      "status_class": "conditional",
      "downstream_claims": [],
      "graph_depth": 10,
      "reference_ids": [
        "REF-028",
        "REF-030",
        "REF-032"
      ]
    },
    {
      "id": "CMP-03",
      "title": "Microscopic parent-theory derivation-or-falsification test",
      "display_order": 51,
      "sector": "comparison",
      "statement": {
        "public": "The construction exposes a finite set of quantities for a microscopic parent theory to compute; the parent can derive the channel or rule it out.",
        "technical": "A microscopic completion must address the full interacting a_eff; derive or replace QCD-03; derive, replace or falsify the boundary-member prescription, exact u_max=1 UV-domain normalization and decaying compact contour; compute source-dependent quantum/higher-curvature corrections within the δB budget; and derive the global source law/unit pairing together with the late-time amplitude condition. Different results change or falsify the channel rather than provide fit freedom."
      },
      "status": "test",
      "type": "test",
      "depends_on": [
        "CORR-01",
        "QCD-03",
        "SAD-02",
        "SAD-04",
        "SAD-07",
        "CORR-02",
        "GS-01",
        "GS-03"
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Discussion and Conclusion five-target programme.",
          "structure_id": "sec:discussion"
        }
      ],
      "qualifier": "Programme-level falsification-or-derivation test.",
      "limits_and_open_issues": "Does not assume such a parent theory exists.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained ID but completely revised to the v2.0 five-target programme."
      },
      "status_label": "Test",
      "status_class": "test",
      "downstream_claims": [],
      "graph_depth": 7,
      "reference_ids": []
    },
    {
      "id": "CMP-04",
      "title": "Independent support and structural convergence",
      "display_order": 52,
      "sector": "comparison",
      "statement": {
        "public": "Several pieces of the architecture have independent support or close structural precedents, but none of those literature relations is a dependency of the numerical result.",
        "technical": "Direct architectural support includes leading-order S⁴ dominance in Λ>0 gravitational EFT, primitive-SU(2)/inverse-cosmological-coupling structure in exact canonical gravity and an explicit de Sitter Lefschetz thimble. Broader convergence includes sequestering/global-variable, Euler/four-form, pregeometry/topological-Λ and gravitational-instanton/SM-charge constructions. All are encoded as non-dependency relations."
      },
      "status": "comparison_non_dependency",
      "type": "comparison",
      "depends_on": [],
      "evidence": [
        {
          "reference_id": "REF-030",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-032",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-050",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-055",
          "role": "direct_architectural_support"
        },
        {
          "reference_id": "REF-056",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-058",
          "role": "structural_convergence"
        },
        {
          "reference_id": "REF-059",
          "role": "direct_architectural_support"
        },
        {
          "reference_id": "REF-060",
          "role": "direct_architectural_support"
        }
      ],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "the cosmological-constant paper v2.0, Discussion “Independent structural convergence”; website How It Relates.",
          "structure_id": "loc-045"
        }
      ],
      "qualifier": "Comparative context only; cannot upgrade Derived/Selected/Premise/Proposed/Open manuscript statuses.",
      "limits_and_open_issues": "Structural convergence is not validation of the numerical cosmological result.",
      "history": {
        "introduced_in": "v2.0",
        "public_version_history": "Introduced in v2.0."
      },
      "status_label": "Comparison - non-dependency",
      "status_class": "standard",
      "downstream_claims": [],
      "graph_depth": 0,
      "reference_ids": [
        "REF-030",
        "REF-032",
        "REF-050",
        "REF-055",
        "REF-056",
        "REF-058",
        "REF-059",
        "REF-060"
      ]
    },
    {
      "id": "METH-01",
      "title": "Human-AI research-method disclosure",
      "display_order": 53,
      "sector": "method",
      "statement": {
        "public": "The research was developed through human-AI collaboration; the author remains responsible for every published claim.",
        "technical": "AI systems contributed synthesis, mathematical exploration, consistency testing, literature mapping and rapid iteration. Human judgement set research direction, assumptions, interpretations and publication decisions; AI participation is not scientific evidence for the claims."
      },
      "status": "author_disclosure",
      "type": "author_disclosure",
      "depends_on": [],
      "locations": [
        {
          "work_id": "cc-paper",
          "locator_text": "Website Method/About records and author disclosure."
        }
      ],
      "qualifier": "Method disclosure, not a scientific premise or credibility substitute.",
      "limits_and_open_issues": "Operational prompts and internal transcripts are not part of the scientific claim graph.",
      "history": {
        "introduced_in": "v1",
        "public_version_history": "Retained from v1."
      },
      "status_label": "Author disclosure",
      "status_class": "standard",
      "downstream_claims": [],
      "graph_depth": 0,
      "reference_ids": []
    }
  ]
}