IndisputableMonolith.Gravity.Analysis.ReggeM2SymFullProbe4D
Analysis module probing the full symmetric midpoint mass-squared identity for 4D Regge calculus against transverse-traceless (TT) kernel certificates. Gravity workers cite it when checking that discrete curvature/mass-squared relations hold under the complete symmetry group in four dimensions. The module is organized around imported decide-only kernel certificates generated from scale-32 tables; it does not introduce new analytic proofs.
claimIn 4D Regge calculus, the full symmetric midpoint $m^2$ identity is probed against the transverse-traceless (TT) kernel: discrete curvature and mass-squared relations are checked for consistency under the complete symmetry action, using certified kernel tables at fixed scale.
background
Recognition Science gravity work treats discrete spacetime via Regge calculus: edge lengths and deficit angles replace continuum metric and curvature. The midpoint $m^2$ identity relates a discrete mass-squared (or curvature-squared) observable evaluated at edge midpoints to a TT projection of the curvature data.
The sole import is the generated kernel-certificate module for the exact midpoint $m^2$ TT identity in 4D. That upstream package is produced by scripts/qg/regge_4d_m2_kernel_certs_20260721.py and exposes Int List.foldl plus scale-32 tables, with proofs discharged only by decide (no native_decide). This probe module sits in the Gravity.Analysis layer and uses those certificates as the ground truth against which a full-symmetry sweep is run.
proof idea
Definition and certificate-consumption module rather than a single theorem proof. It imports the midpoint $m^2$ TT kernel certificates and organizes a full-symmetry probe: each symmetry orbit or representative configuration is checked against the certified kernel tables. Discharge is by the upstream decide-only lemmas; there is no new analytic derivation inside this file.
why it matters in Recognition Science
Closes a verification gap in the 4D Regge sector of the Recognition gravity stack: after the exact midpoint $m^2$ TT identity is kernel-certified, one still needs a full-symmetry probe to confirm the identity is not an artifact of a reduced stabilizer. Downstream consumers (none listed yet in the graph) would use a successful probe as a gate before promoting the identity into continuum-limit or continuum-matching arguments. In the broader RS forcing picture this is infrastructure for discrete gravity consistency, not a T0–T8 landmark itself.
scope and limits
- Does not prove a new continuum Einstein or Regge identity; only probes discrete kernel certificates.
- Does not claim the identity for dimensions other than 4.
- Does not replace or re-derive the generated scale-32 kernel tables.
- Does not establish continuum limits, renormalization, or physical mass spectra.
- Does not list downstream theorems; used_by is currently empty.