t0t8_clause_holds

This module is a field-by-field non-circularity audit of the unconditional quantum-gravity master theorem. A referee objection was that witness slots of shape $\Sigma(P:\mathrm{Prop}), P$ can be filled by trivial $\langle\mathrm{True},\mathrm{trivial}\rangle$, so the master statement is only as strong as the concrete propositions plugged in. For each atom the audit discloses what proposition is carried and proves it holds without assuming the master conclusion.

The T0–T8 clause is the substrate-forcing piece of D1. In the master theorem it is definitionally the carried proposition T0_T8_carried_prop, witnessed by concrete surfaces from the unified forcing chain: T5 uniqueness of the cost $J(x)=(x+x^{-1})/2-1$, T6 forcing of $\phi$ as the self-similar fixed point, T7 the eight-tick octave (period $2^3$), and T8 three spatial dimensions. Several cost definitions in the dependency cone (observer J-cost, multiplicative-recognizer derived cost, rung-coarsen total cost) are the same J-family that the chain uniquely determines.

One-line term proof: the goal is definitionally the carried T0–T8 proposition, and the proof applies the existing complete forcing-chain theorem T0_T8_holds_proven from the master-theorem module. No local tactics or new algebraic work.

After the M1 upgrade this clause is no longer a True placeholder: the master conjunction carries a named, non-self-referential forcing-chain proposition that is proved on its own. That is exactly the non-circularity claim the module was written to answer (peer-review findings F1 / Rec 2). Framework landmarks T5–T8 sit inside the chain: unique $J$, forced $\phi$, eight-tick period, and $D=3$. Downstream the audit assembles carried clauses and closed certificates into the honest reading of the unconditional master theorem; this declaration is the T0–T8 atom of that assembly. No further open scaffold remains on this field.