exactActionSymbolStatus_flags
plain-language theorem explainer
Records the boolean status board for the exact flat Regge cross-term continuum symbol: continuum rebound and t11/t12 star offsets are closed, other-orbit offsets are not incomplete, edge-origin m² certs are banked, while ledger S_RS inhabit and gap-action recovery stay false. Gravity auditors of the H_fold pivot cite it as the machine-checked flag snapshot. Proof is a single decidability discharge on the concrete status record.
Claim. The exact-action-symbol status record satisfies: continuum rebound to the exact symbol is true; the fold is retained as legacy true; $t_{11}$/$t_{12}$ star-member cube offsets are defined true; other-orbit offsets incomplete is false; edge-origin $m^2$ certificates are banked true; the RS ledger entropy $S_{\mathrm{RS}}$ is inhabited false; and gap-action recovery is false.
background
This module treats the exact flat cross-term continuum symbol for 4D Regge calculus on the Freudenthal torus. At flat background, deficits vanish, so Schläfli reduces the Hessian cross term to $S''=\sum_h (dA_h)(d\delta_h)$ on plane-wave class strains with position-resolved deficit phasing. Oracle verdict $H_{\mathrm{fold}}$: the true Hessian annihilates vertex-gauge modes and sends normalized TT on axisTTPlus/symbolDir to $-1/4$; the distinct-hinge transported fold is not the continuum object.
The status structure is a local ledger of which geometric pieces are closed. Continuum rebound to exact, legacy fold retention, and $t_{11}$/$t_{12}$ star offsets are marked true; other-orbit offsets are not flagged incomplete; edge-origin $m^2$ decide-certs live in the banked family (axis TT plus/cross, decoy gauge, etc.). Upstream four-tet signed-deficit status already closed the $N=5$ torus extension. RS-native units fix $c=1$, $\hbar=\varphi^{-5}$.
Local doc: flags remain open in the sense that geometric ContinuumSymbolIs Tendsto is the Preflight gate; banked edge-origin certs do not inhabit $S_{\mathrm{RS}}$.
proof idea
One-line decidability proof. The status definition is a concrete structure of booleans; decide evaluates each field equality against the stated true/false pattern and closes the seven-way conjunction. No geometric lemmas are invoked at this site.
why it matters
Sits in the THEOREM tier of the exact-flat-cross-term module: structural status flags that make the H_fold pivot auditable without re-reading the whole pipeline. Module doc binds ContinuumSymbolIs to finiteExactReggeSymbol Tendsto in Preflight (not a constant face), and keeps ledger $S_{\mathrm{RS}}$ / gap-action recovery open/false—exactly the last two flags here.
No downstream consumers yet (used_by empty); the value is as a freeze-frame for gravity analysis: continuum rebound and banked edge-origin $m^2$ certs are on, while inhabit of $S_{\mathrm{RS}}$ and gap-action recovery remain deliberately false. Does not touch the forcing chain T0–T8 or RCL; it is discrete Regge Hessian bookkeeping on the 4D torus, parallel to the 3D second-difference factor-2 convention. Touches the open ContinuumSymbolIs / FoldAlongM2Tendsto and e0-isotropy questions only by recording that they are not closed here.
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