IndisputableMonolith.Gravity.SevenGaps.WickActionInteriorHingeConfinementAudit
Audit layer for Wave C4 gap-6 work on Wick-rotated interior hinge confinement: Moebius collapse of the α-family on the causal range, imaginary-part confinement, and the Lorentzian cut-boundary value. Gravity and complex-analysis readers cite it to see which N3 claims are closed and which N4 boundary limits remain named hypotheses. Structure is import-and-status bookkeeping over the confinement module, not a new derivation.
claimStatus audit for Wick-rotated interior-hinge confinement: Moebius identification of the $\alpha$-family on the causal range, path equality in the model sector, confinement to $\mathrm{Im}<0$, the $\mathrm{branchRegularSum}$ field shape, and the cut-boundary value of the Lorentzian limit (with named propositions where one-sided $\mathrm{Tendsto}$ for $\log$/$\sqrt{\cdot}$ is not yet discharged).
background
Recognition Science gravity gap-6 work treats the interior hinge of a Wick-rotated action whose complex structure must stay on a controlled sheet. The upstream module (Wave C4 N3+N4, design D-gap6-r1) packages two blocks. N3 closes Moebius collapse of the α-family on the causal range, MODEL-path equality, confinement into the lower half-plane $\mathrm{Im}<0$, and the $\mathrm{branchRegularSum}$ field shape. N4 targets the cut-boundary value in the Lorentzian limit.
Mathlib's one-sided filter API for $\log$ and complex square root blocked a direct $\mathrm{Tendsto}$ proof for that cut boundary after honest effort. The design therefore authorizes named proposition interfaces as the fallback, so downstream gravity statements can depend on an explicit hypothesis rather than a silent sorry.
This audit module sits one import above that confinement development. It does not redefine the action or the Moebius data; it records what is proved versus what remains a named Prop in the N3/N4 package.
proof idea
No independent proof content. The module imports WickActionInteriorHingeConfinement and exposes an audit view of the N3/N4 claim surface: closed theorems for Moebius collapse, model path equality, $\mathrm{Im}<0$ confinement, and branch-regular sum shape, versus design-authorized named Props for the cut-boundary $\mathrm{Tendsto}$ that Mathlib's one-sided $\log$/$\mathrm{csqrt}$ filters resisted. Argument structure is status aggregation over the upstream confinement file.
why it matters in Recognition Science
SevenGaps gravity work needs a single place that states, without reopening the complex-analysis fight, which Wick-hinge confinement facts are machine-checked and which cut-boundary limits are still hypothesis interfaces. N3 being CLOSED means Moebius identification and lower-half-plane confinement can be cited as proved inputs to later gap-6 assembly. N4's named-Prop fallback keeps the Lorentzian boundary value honest rather than stubbed.
No downstream Lean edges are recorded yet (used_by is empty), so the module's role is documentary and gatekeeping inside the Gravity.SevenGaps spine: it freezes the C4 session-2 design decision and prevents silent widening of the N4 gap. Framework-wise it supports the gravity side of the Recognition ladder once the hinge action is confined; it does not itself touch T5–T8 forcing, RCL, or the $\alpha$ band.
scope and limits
- Does not prove cut-boundary Tendsto for log or complex square root.
- Does not redefine the Wick action, Moebius map, or α-family.
- Does not discharge N4 named Props into theorems.
- Does not connect to T5–T8 forcing, RCL, or the fine-structure band.
- Does not supply downstream gravity assembly theorems (no used_by edges).