hingeDataNotActionLevelCertificate
plain-language theorem explainer
Separation certificate that complete Wick hinge-data continuation (branch-regular cosine paths on single-simplex opposite pairs) is not an action-level Lorentzian target. Auditors of the gap-6 lookalike-falsify residual cite it to keep hinge mathematics without promoting it to the ledger closer. The proof is a two-field term pairing hinge-data completeness with V1 action-path unsatisfiability at the endpoint.
Claim. The S2 certificate holds: for every pair of distinct vertices of the 5-point simplex, the four-one and three-two causal-pent edge continuations are branch-regular on $(0,1)$, their cosine paths are continuous on $[0,1]$ and equal $-1/4$ at $t=1$; and simultaneously the V1 continuous Wick action path on $[0,1]$ is unsatisfiable. Hinge data alone therefore does not discharge the action-level Wick continuation target.
background
This module is the Wave C4 R0 gap-6 lookalike-falsify receipt. After gap 6 closed via the V2 action-level Wick continuation (Ioc domain plus cutLimit family assembly), each banked lookalike is retained as a positive theorem together with a post-close separation witness: the lookalike holds, yet would not have sufficed for the action-level closer.
Hinge data here means single-simplex opposite-pair continuation: branch regularity of the complex edge paths and continuous cosine paths for the four-one and three-two causal pent types, with the cosine endpoint fixed at $-1/4$. That is kinematical geometry on one simplex, not a deficit-weighted three-pent action functional.
The companion conjunct is V1 unsatisfiability: continuous-on-$[0,1]$ of the unit Wick action path fails, so hinge completeness can coexist with failure of the older action-field formulation.
proof idea
Term-mode pair constructor. The first component is the already-proved completeness theorem for Wick hinge-data continuation (branch regularity and cosine paths on all opposite pairs for both causal pent types). The second is the V1 fact that the continuous action path at parameter one is not satisfiable on $[0,1]$. No further rewriting: the certificate Prop is exactly that conjunction.
why it matters
Feeds the package theorem that closes the typed residual TypedResidual_gap6_lookalike_decoys_fail, which conjoins the four lookalike separation certificates (3D Lorentzian continuation, 4D kinematical continuation, hinge data, and cm4 sign). In the Seven Gaps gravity campaign this is the S2 post-close critic: it blocks renaming hinge-data completeness into the ledger terminal that only V2 action continuation discharges.
Framework role is bookkeeping honesty after gap 6 closed, not a new dynamical law. It sits downstream of the causal-simplex and Wick hinge assemblies and upstream of the residual DAG receipt, keeping kinematical hinge facts cleanly separated from Lorentzian action-level Wick continuation.
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