gap1_bridge_blocker_certified
plain-language theorem explainer
Certifies that the recognition-ratio bridge does not follow from a bare recognition ledger alone: coboundary strains telescope, budget imposition is circular, and opposite signed sources can yield the same two-cell ledger. Anyone tracking Pillar 2 (quantum amplitude / substrate-to-geometry bridge) of the full-theory QG campaign cites this blocker. One-line term proof: it is exactly the terminal bare-ledger blocker lemma.
Claim. The recognition-ratio substrate blocker certificate holds: $recognition\_ratio\_derived$ does not follow from a bare recognition ledger. Coboundary strains telescope, the imposed-budget route is circular, and a single bare two-cell ledger can arise from opposite signed sources. Supplying a named deficit-source constitutive coupling derives the ratio bridge (with cubic remainder) on a nontrivial small-mesh family; without that coupling the bridge stays underived.
background
This module is the live full-theory ledger for the quantum-gravity campaign. Three pillars must close: classical recovery to Einstein gravity, a well-defined quantum amplitude (substrate-to-geometry bridge plus convergent path-sum measure), and at least one discriminating prediction. A boolean flag flips only when its target is kernel-checked and axiom-audited; the master claim that the full theory is not yet closed stays provable until every flag is true.
Pillar 2 requires a derived bridge from the recognition ledger to geometry. The recognition ratio is the log-ratio content of ledger events (the spectrum multiset of $\log$ ratios). A bare recognition ledger records postings and strains but does not, by itself, fix how deficit sources couple into that ratio. The upstream terminal result states that on a bare ledger the ratio bridge fails in three independent ways: telescoping coboundaries, circular budget imposition, and non-uniqueness of signed sources for a two-cell ledger.
The positive half of the story is conditional: if a named deficit-source constitutive coupling is supplied, the ratio bridge (cubic remainder included) follows on a nontrivial small-mesh family. Deriving that coupling from richer substrate structure is still open.
proof idea
Pure term proof: the theorem is definitionally the upstream certificate recognition_ratio_derived_bare_ledger_terminal. No extra tactics, no new axioms, no local rewriting. The certificate type packages the negative claim (bare ledger does not yield the ratio bridge) together with the conditional positive claim (coupling premise implies the bridge on a small-mesh family). Applying the terminal lemma discharges the whole package in one step.
why it matters
This is the P2.1 bridge blocker on the path to gap1_bridge_derived. Pillar 2 of the full-theory campaign demands a derived substrate-to-geometry bridge before any path-sum measure can be called well-defined. By locking the bare-ledger failure modes into a machine-checked certificate, the ledger keeps gap1_bridge_derived false until the deficit-source constitutive coupling is itself derived from richer structure.
No downstream theorems currently consume this declaration (used-by count zero); its role is status-record integrity inside FullTheoryLedger. It anchors the starting line inherited from the seven-gaps campaign so the full-theory flags cannot drift from the campaign record. Framework-wise it sits under the quantum-amplitude pillar, not under the T0–T8 forcing chain or the classical J-uniqueness / eight-tick / $D=3$ landmarks; those are upstream physics inputs, not what this blocker proves.
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