spine_to_extras_bridge_holds
plain-language theorem explainer
Given T0 (logic from cost), T5 (unique J-cost), and T6 (φ forced), the extras package follows: no self-negating configs, a unique existent at the J-minimum, forced reference and zero-cost consistency, and canonical RS constants c=1, ℏ=φ^{-5}, G=φ^5/π with fixed exponents. Cite this when wiring the spine into Gödel-dissolution or constants-from-φ. Proof is a term-mode structure pack of four specialized bridges.
Claim. Assume logic is forced from recognition-work cost (consistent configs cost zero, inconsistent ones cost positive), the cost $J$ is the unique continuous solution of the Recognition Composition Law with reciprocity, normalization $J(1)=0$, and calibration, and $\varphi$ is the unique positive root of $x^2=x+1$. Then the extras bridge holds: no biconditional self-negating configuration exists; there is a unique existent; zero-cost is consistent and a reference is forced; and the RS constants take the canonical forms $c=1$, $\hbar=\varphi^{-5}$, $G\cdot\pi=\varphi^5$, with duality $G\cdot\hbar=1/\pi$ and the matching Planck length/mass exponents.
background
The Unified Forcing Chain module claims that T-1 through T8 are inevitabilities from the cost foundation (Recognition Composition Law plus normalization and calibration), not optional compatibility layers. T0 says logic is the zero/positive split of recognition work on the Boolean floor: consistency is cheap, contradiction is expensive. T5 pins $J(x)=\frac12(x+1/x)-1$ on $(0,\infty)$ via reciprocity, composition, normalization, calibration, and continuity. T6 forces $\varphi=(1+\sqrt5)/2$ as the unique positive self-similar scaling ratio in a discrete ledger.
The extras target is a bridge certificate from the T0–T6 spine into two downstream packages: impossibility of biconditional self-negation (classical consistency, not a Gödel-I refutation), and constants-from-φ with fixed canonical exponents rather than bare existentials. Upstream, T6 already yields a canonical φ-constants bridge naming $c_{\mathrm{RS}}=1$, $\hbar_{\mathrm{RS}}=\varphi^{-5}$, $G_{\mathrm{RS}}\cdot\pi=\varphi^5$, and $G\cdot\hbar=1/\pi$. T5 supplies unique-existent and reference/zero-cost witnesses via the analytic identification of defect with $J$.
proof idea
Term-mode structure construction, not a tactic script. From the T6 hypothesis, obtain the canonical φ-constants bridge (unit $c$, fixed $\hbar$ and $G$ exponents, inverse duality, Planck length/mass forms). From T5, obtain the canonical-reference bridge and the canonical-existent bridge (unique existent, zero-cost consistency, forced reference). From T0, obtain the classical-logic-and-unique-minimizer bridge (no self-negating config). The result is the structure whose fields are exactly those extracted witnesses, plus the algebraic-in-φ statements for $\hbar$ and $G$ from the constant-derivations layer. No new analysis is done here; it is pure reassembly of already-proved bridges.
why it matters
This is the wiring theorem that lets the T0–T6 spine discharge the extras half of the complete forcing chain: Gödel-style self-ref queries are blocked at the T0 consistency floor, ontology gets a unique existent from the T5 $J$-minimum at 1, and the RS unit system is fixed by T6 rather than postulated. The module doc frames the stronger claim as a complete inevitability chain (every level forced, constants derived from φ). Framework landmarks hit directly: T5 J-uniqueness, T6 φ as self-similar fixed point, and the native constants $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$. Downstream the complete-chain section packages T0–T8 plus quarter-turn, Hamiltonian, and measurement layers; this bridge is how spine nodes feed those extras without reopening exponent choice. No open scaffold remains on this declaration itself (status proved).
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