Gap6LookalikeReceiptStatus
plain-language theorem explainer
Status record for the Gap-6 lookalike-falsify receipt: five booleans track whether the R0 residual is closed, whether the frozen V1 Wick-action schema and deficit-sum branch remain open, whether the V2 ledger terminal is still open, and whether the Lorentzian-action flag has flipped. Gravity auditors cite it as the frozen dashboard for Wave C4 R0 after F3. It is a plain structure definition with no proof obligations.
Claim. A status bundle consisting of five boolean flags: (i) the R0 lookalike-falsify residual is closed; (ii) the frozen V1 Wick-action schema is open; (iii) the deficit-sum branch is open; (iv) the Wick-action ledger terminal is open; (v) the Gap-6 Lorentzian-action ledger flag is set. Instantiations record the post-F3 close via the V2 continuation terminal (family conjunct plus physical coupling $\alpha=1$).
background
Wave C4 Gap-6 is the residual that a Lorentzian Wick continuation must supply a genuine 4D action-level ledger terminal, not a kinematical or lower-dimensional lookalike. The module packages separation certificates: each banked lookalike is proved to hold, together with a post-close witness that it does not discharge the V2 terminal (domain mismatch, V1 action-field kill, or distinct closer).
The real terminal is wick_action_continuation_4d_v2: for every coupling $\alpha>7/12$ the V2 certificate holds, and it holds at the physical value $\alpha=1$. That succeeds the frozen V1 terminal, which is provably unsatisfiable. Ledger language here means double-entry recognition events (balanced debit/credit), as in the foundation and recognition ledgers; holographic closed flags on plaquettes and glued dominos are the local parity witnesses for zero-sum loops.
The typed residual conjoins eight certificates (3D continuation not 4D action, 4D kinematical not action-level, hinge data and $C_{m4}$ sign not action-level, branch regularity not deficit-sum, two-pent not interior action, EH recovery not Gap-6, plus the V2 ledger terminal guard). This structure is the status face of that residual after the 2026-07-23 F3 flip.
proof idea
No proof body: the declaration is a structure with five Bool fields and doc-comments fixing their meaning. Downstream, a single definitional instance fills the fields (lookalikeReceiptClosed := true, schema/branch/terminal open-flags := false, gap6LorentzianAction := true), recording that the typed residual is closed and Gap-6 has flipped via the V2 terminal. Field semantics are pinned by the residual Prop and by the V2 continuation definition, not by tactics here.
why it matters
In the Seven Gaps gravity campaign this is the frozen R0 dashboard after honesty patch F3: lookalike mathematics is retained, but obsolete "Gap-6 stays false" conjuncts are replaced by post-close separation. Downstream gap6LookalikeReceiptStatus is the sole consumer and hard-codes the closed configuration.
It sits under the Wick-action certification family that aims at a 4D Lorentzian continuation suitable for Einstein-Hilbert recovery on the recognition ledger. Framework contact is the gravity side of the forcing chain (spatial $D=3$ and eight-tick structure already fixed upstream): Gap-6 is about whether the action-level continuation, not merely a hinge or sign certificate, is on the ledger. Binding detail is the V2 close status that ties the Lorentzian-action flag to the V2 terminal. No open scaffold remains in this structure; the residual Prop is already proved closed in-module.
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