T0_T8_holds
plain-language theorem explainer
Names the proposition that the full T0–T8 forcing spine holds: logic through meta-principle, discreteness, ledger, recognition, unique J-cost, forced φ, eight-tick octave, and D=3. Cited by anyone assembling the quantum-gravity master statement or the non-circularity audit. Pure definitional alias of the concrete carried conjunction of UnifiedForcingChain theorem surfaces.
Claim. Let $P$ be the proposition that the Recognition Science forcing chain holds end-to-end: logic is forced, the meta-principle is forced, discreteness is forced, the ledger is forced, recognition is forced, the cost $J$ is unique, $\varphi$ is forced as the self-similar fixed point, the eight-tick octave (period $2^3$) is forced, and spatial dimension $D=3$ is forced. Then $P$ is exactly that nine-fold conjunction.
background
Gravity Track 7.A authors the master quantum-gravity statement as a twelve-clause conjunction. Eight clauses are closed from existing theorems; five remain hypothesis inputs. The first closed atom is the substrate-forcing piece D1: the T0–T8 chain from Foundation.UnifiedForcingChain.
That chain is the Recognition Science backbone. T5 forces the unique cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$). T6 forces $\varphi$ as the self-similar fixed point. T7 forces the eight-tick octave. T8 forces three spatial dimensions. The carried form packages T0 through T8 as an explicit $\wedge$-conjunction of named theorem surfaces, avoiding universe metavariables from the larger CompleteForcingChain package while still transitively exposing those surfaces to the master atom.
This declaration is only the named Prop wrapper around that carried conjunction. The inhabiting proof lives next door as the proven theorem that assembles the nine t0_holds…t8_holds witnesses.
proof idea
One-line definitional alias: the proposition is definitionally equal to the carried nine-fold conjunction of UnifiedForcingChain surfaces (T0_Logic_Forced through T8_Dimension_Forced). No tactics, no lemmas applied at this site. Inhabitation is deferred to the sibling theorem that packages the nine concrete t*_holds results from the foundation module.
why it matters
This is the first conjunct of the master statement template: (T0_T8_holds ∧ CostUniqueness ∧ Lorentzian_1_3) ∧ …. Downstream, RSQuantumGravityMaster and the conditional master theorem of both require it as the substrate-forcing D1 atom. The non-circularity audit uses it twice: carried_clauses_hold discharges it via the proven sibling, and master_theorem_non_circularity_certificate records both the definitional equality to the carried prop and that the clause holds.
Framework landmarks: it is exactly the T0–T8 forcing chain (primer), so J-uniqueness, φ, the eight-tick octave, and D=3 enter the gravity master theorem as closed, not hypothesized. It does not touch the five still-open tracks (classical continuum/Bianchi, unconditional amplitude linearity, Page curve, PTA stochastic GW, strong-field discriminators).
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