ExactActionSymbolStatus
plain-language theorem explainer
Status record of seven boolean flags tracking the exact flat cross-term continuum rebind for the 4D Regge Hessian on the Freudenthal torus. Gravity analysts cite it to read which pieces of the H_fold pivot are closed versus open (star offsets, edge-origin m² bank, S_RS inhabitance, gap-action recovery). It is a pure data structure: no proof content.
Claim. A status package of seven booleans for the exact-action continuum rebind: continuum rebounded to the exact symbol; fold retained as legacy; $t_{11}$/$t_{12}$ star-member cube offsets defined; other-orbit offsets still incomplete; edge-origin $m^2$ certificates banked; recognition ledger action $S_{RS}$ inhabited; gap-action recovery holds.
background
At flat background, Regge deficits vanish and Schläfli reduces the second variation to the cross term $S''=\sum_h (dA_h)(d\delta_h)$. This module names that Hessian on plane-wave class strains with position-resolved deficit phasing. Oracle verdict $H_{\mathrm{fold}}$ (2026-07-21): the true Hessian annihilates vertex-gauge modes and sends normalized TT on axisTTPlus / symbolDir to $-1/4$. The distinct-hinge transported fold mis-transports (t12/t13 gauge residue) and is not the continuum object.
Binding uses $t_{11}$ star-member cube offsets and, for $t_{12}$/$t_{13}$/$t_{22}$ and complements, per-edge transported origins. Tier tags separate MODEL objects (exactFlatCrossTermFold, finiteExactReggeSymbol) from THEOREM structural lemmas and OPEN items: continuum Tendsto for all modes, ledger $S_{RS}$ inhabitance, and gap-action recovery.
The structure packages those closure flags so a single inhabitant can report the rebind state without scattering booleans across the module.
proof idea
No proof. Structure declaration with seven Bool fields and default constructor. Downstream, a single definition inhabits it by assigning concrete true/false values for each flag.
why it matters
Gives a single typed status face for the exact-action continuum rebind that the module's OPEN list tracks. The sole downstream inhabitant exactActionSymbolStatus sets continuum rebound, legacy fold retention, $t_{11}$/$t_{12}$ star offsets, and edge-origin $m^2$ banking to true, and marks other-orbit offsets incomplete as false; ledger $S_{RS}$ inhabitance and gap-action recovery remain the open/false items called out in the module doc.
In the broader gravity stack this sits under the flat cross-term Hessian assembly and the banked edge-origin certificates on symbolDir (axis TT plus/cross, decoy gauge). It does not itself flip fold-internal gauge-zero closure. Framework role is bookkeeping for the continuum-symbol path toward a Schläfli-elevated exact Regge action, not a forcing-chain (T0–T8) step.
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