Status

Controlled statuses

What is established, proposed, selected and open

The project does not assign one confidence label to the entire construction. Each component carries its own status.

Standard input

Established results used by the work, including vacuum-energy scheme dependence, conformal-anomaly conventions, QCD dimensional transmutation and observational inputs.

Derived

The compact counterterm classification, Euler extraction theorem, ordinary-GR obstruction, trace-free quotient, source-response algebra and variations of the proposed global action.

Proposed

The global-source action, the physical dictionary mapping the compact response to the overall curvature mode, and the two-part paired-cap matching hypothesis.

Selected

The suppressed compact thimble, the exact Planck-boundary unit, the proton endpoint rule and the asymptotic trace-average branch.

Open calculation

The source-dependent gravitational dressing of the cap response, higher-curvature corrections to the primitive Planck-boundary action and the full interacting Standard Model response on \(S^4\); source-independent determinants and phases cancel in the paired-cap construction.

Tests

A decisive departure from \(w=-1\) across flexible parametric and non-parametric reconstructions, a computed source-dependent dressing or boundary-action correction that shifts the result, a modified saddle action or independently established different active field content would change or falsify the strict construction.

Standalone results

An independent matter-side theorem now fixes the first factor. De Sitter space can be described as a closed sphere or as the horizon-bounded region seen by one observer. A second paper of this programme proves that the protected local anomaly signal common to both descriptions is uniquely type A: the Euler coefficient a. For the minimal Standard Model, its leading free-field value is \(a_{\rm SM}=1991/720\). The result strengthens the foundation of the cosmological-constant formula; the proton matching, the compact saddle and the gravity-side curvature map carry their own statuses above (EXT-03; record page).

Overall assessment

The construction is quantitatively closed within the specified channel. It does not yet constitute a derivation of the cosmological constant from established Standard Model and gravitational physics alone: the anomaly coefficient, the proton-to-Planck hierarchy, the saddle exponent and the final arithmetic are each independently checkable, and the remaining microscopic question is whether the full theory selects this saddle, boundary, endpoint matching and global-source normalisation, and, if so, why. The agreement with observation is a nontrivial conditional result, not yet a completed proof.