ReggeTTSymbolPreflightStatus
plain-language theorem explainer
Status-flag record for Stage-1 Regge TT symbol preflight on the true nonlinear 3D Regge action. Six booleans track flat-point vanishing of deficits and action, frozen conformal identification, TT Bloch symbol symmetries, non-vacuity of the TT constraint set, and the still-open continuum isotropy value. Gravity/QG auditors cite it as the protocol ledger; the mathematics lives in the grounding theorems, not in the flags. Pure structure definition, no proof body.
Claim. A protocol status record with six boolean fields: (i) all edge deficits vanish on the flat edge-length field; (ii) the true Regge action $S(\ell)=\sum_e\sqrt{\ell_e}\,(2\pi-\sum\theta)$ vanishes at flat; (iii) the frozen conformal-ansatz action equals the true action on conformal fields; (iv) the TT Bloch symbol object is well-formed (even second difference, sign-flip under polarization reversal, zero action profile at amplitude zero); (v) the TT constraint set is nonempty (axis plus/cross polarizations are TT, axis wave vector nonzero); (vi) continuum symbol value proved (must remain false while the open target that the continuum TT symbol equals $-1/4$ is unproved).
background
This module is Stage 1 of the QG full-theory ReggeTTContinuumSymbol campaign. It defines the true nonlinear 3D Regge action on the canonical periodic Freudenthal torus as a function of an arbitrary edge squared-length field $\ell$: $S(\ell)=\sum_e\sqrt{\ell_e}\cdot(2\pi-\sum_{\mathrm{tets}}\theta)$, with dihedral angles from Cayley–Menger cofactors (dihedralAngle3Sq) via the existing deficit machinery.
At conformal fields the true action is identified with the frozen model reggeAction (the content of reggeAction_conformal_eq). The TT Bloch symbol object is built from plane-wave edge fields, second differences, and polarization constraints. The named open target ReggeTTContinuumIsotropyTarget asserts that for every nonzero integer wave vector and every TT polarization the continuum symbol exists and equals $-1/4$ (the linearized Einstein–Hilbert TT coefficient). C10 numerics support isotropy and that value on 14 directions but are tagged NUMERICAL EVIDENCE only.
The structure is documentation-only: every true flag must be grounded by a kernel theorem via status_flags_grounded; the continuum-value flag is required to stay false until a kernel proof exists.
proof idea
No proof: this is a structure definition (six Bool fields with docstrings pointing at the theorems that ground each flag). Instantiation lives in the sibling reggeTTSymbolPreflightStatus, which sets the first five flags to true and continuum_symbol_value_proved to false. Grounding of those true values is deferred to status_flags_grounded, which ties each flag to named kernel lemmas (deficitOfField_flatEdgeField, trueReggeAction_flatEdgeField, reggeAction_conformal_eq, the TT second-difference/symmetry lemmas, and the axis TT polarization non-vacuity lemmas).
why it matters
This record is the Stage-1 ledger for the Regge TT continuum-symbol program: it separates what is kernel-proved (flat point, frozen conformal identification, symbol-object symmetries, nonempty TT set) from what remains OPEN (ReggeTTContinuumIsotropyTarget). Downstream, reggeTTSymbolPreflightStatus is the canonical instance with five greens and one forced red on continuum value.
In the broader Recognition gravity stack this sits under discrete Regge calculus on the Freudenthal lattice toward continuum GR recovery. Matching $K(0)=-(1/4)I_{TT}$ would align the true nonlinear action’s TT sector with linearized Einstein–Hilbert; the structure deliberately forbids flipping that flag on numerics alone. Parent consumers read the record rather than re-auditing each lemma name. No T0–T8 forcing step is discharged here; the link is the QG campaign’s continuum-symbol goal, not the phi/octave chain.
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