IndisputableMonolith.Gravity.Analysis.ReggeM2BridgeProbe4D
Analysis module that probes the 4D bridge from Regge midpoint discrete data to the m² transverse-traceless identity. It sits on generated kernel certificates (scale-32 integer tables, pure `decide`) and packages the probe surface for gravity audits. Citation target for anyone checking that the discrete TT mass-squared relation holds at the midpoint before continuum or continuum-limit arguments. Structure is import-and-probe: no independent heavy proof body beyond the certified kernel.
claimIn 4D Regge calculus, the midpoint discrete data satisfy the transverse-traceless $m^2$ identity on the certified kernel (integer fold tables at scale 32). The module exposes that bridge probe: midpoint configuration $\mapsto$ verified $m^2$ TT relation, with certificates discharged by kernel decision only.
background
Recognition Science gravity analysis treats Regge discretizations as the finite skeleton on which continuum identities must already hold exactly at certified sample points. The midpoint $m^2$ TT identity is the discrete statement that the transverse-traceless sector carries the correct mass-squared relation at the barycenter of a 4D Regge cell complex.
The sole import is the generated kernel-certificate module for that identity. Its doc states it is produced by scripts/qg/regge_4d_m2_kernel_certs_20260721.py, built from Int List.foldl and scale-32 tables, and proved with kernel decide only (no native_decide). This module therefore inherits a fully constructive, machine-checked table identity rather than an analytic continuum argument.
Local setting is Gravity analysis: bridge probes that connect discrete Regge certificates to the continuum TT sector used downstream in curvature and graviton-mode bookkeeping.
proof idea
This is a thin probe module, not a self-contained proof development. It imports the generated midpoint $m^2$ TT kernel certificates and surfaces them as the 4D bridge probe. The mathematical work lives upstream: integer fold-tables at scale 32 are decided in-kernel, yielding exact discrete identities. Here the argument structure is packaging and naming of that certified bridge for gravity analysis consumers.
why it matters in Recognition Science
Places a named 4D Regge midpoint $m^2$ TT bridge probe in the Gravity analysis layer so later continuum or mode-decomposition arguments can cite a machine-checked discrete identity rather than an unchecked numerical check. Upstream supplies the kernel certificates; this module is the probe façade. No downstream edges are recorded yet, so it currently terminates the certificate chain as an audit surface. In the broader RS gravity stack it supports exact discrete control before continuum limits, consistent with forcing-chain discipline that identities hold on the discrete skeleton first.
scope and limits
- Does not prove a continuum TT or graviton mass-squared theorem.
- Does not extend certificates beyond the generated scale-32 midpoint kernel.
- Does not address non-midpoint sample points or other Regge gauges.
- Does not record downstream consumers; used_by is empty.
- Does not replace analytic continuum limits with the discrete probe alone.