template
plain-language theorem explainer
Session-102 ledger for the gravity master statement: fourteen clauses, eight fully closed and six structural (five retired hypothesis inputs plus factor-product amplitude linearity), with zero free hypotheses left. Gravity auditors cite it as the fully structural checkpoint before dynamical upgrades. The content is a clause-count identity assembled from prior track retirements, not a new dynamical derivation.
Claim. The fully structural RS quantum-gravity master statement has fourteen clauses: eight closed theorems, five clauses discharged by structural witnesses (Page-curve Track 3.C; PTA stochastic GW Track 6.B; strong-field Track 6.C; and Session-102 structural retirements of Tracks 1.B/1.C and 2.C/2.D), plus one structural clause under the factor-product form of forced amplitude linearity. No free hypothesis inputs remain in that master statement.
background
Module setting is Gravity Track 7.A: the master theorem in fully structural form (zero RS-internal axioms, zero sorry, closure dated 2026-05-22). Recognition Science packages quantum-gravity claims as a fixed clause ledger. Early Session 97 authored the master statement with five open hypothesis inputs. Sessions 100–101 retired PTA (6.B), strong-field (6.C), and Page-curve (3.C) structurally. Session 102 retires the remaining Track 1.B/1.C and 2.C/2.D inputs structurally, leaving none free.
Upstream pieces include the forced spatial dimension $D=3$ (T8/T9), the polarized birth interface edge set $B(t)$, the PTA structural hypothesis that retires the inflation-distinct GW input, circle-winding injectivity on $H_1(S^1;\mathbb{Z})$, and hinge-aware Regge zero-mode geometry. Amplitude linearity under a factor-product witness is already part of the unconditional amplitude package and contributes the sixth structural clause.
Structural here means each retired input is a named hypothesis type with a canonical inhabitant, theorem-grade in Lean, not yet a full dynamical derivation from the triangulation or continuum limit.
proof idea
No multi-step tactic script: the declaration is a static clause ledger. It sums the eight originally closed master clauses, folds in the five structural witnesses produced across Sessions 100–102 (Page curve, PTA GW, strong-field tests, and the Session-102 Track 1.B/1.C plus 2.C/2.D retirements), and adds the factor-product structural witness already attached to forced amplitude linearity, totaling fourteen with an empty free-hypothesis list. Dependencies are the structural hypothesis packages and the prior partial/deeper master templates; the arithmetic identity is discharged by decision on the counts rather than by new geometric analysis.
why it matters
This is the Session-102 endpoint of the structural trajectory for the RS quantum-gravity master theorem: the first form with zero hypothesis inputs. Downstream master-theorem infrastructure records the upgraded closure status, re-exports the structural template into partial and deeper-partial master modules, and feeds strong-field distinctness packaging. Framework-wise it sits on the gravity side of the forcing chain aftermath (spatial $D=3$, eight-tick discrete time already fixed upstream) and packages phenomenological tracks (PTA stochastic GW vs inflation, strong-field tests vs pure GR, Page curve) as structural witnesses rather than open props.
It does not finish the program. The module doc is explicit that the fully unconditional (dynamical) master theorem still needs Track 1.B as a geometric residual $|S_{\mathrm{Regge}}-S_{\mathrm{EH}}|\le C\cdot\mathrm{spacing}$ on the physical triangulation and Track 1.C as Schläfli for that same triangulation. Those remain multi-session analytic work. Until then, this declaration is the honest structural ceiling auditors should cite.
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