IndisputableMonolith.Gravity.SevenGaps.WickActionCutLimitAudit
Audit companion to the Wave C4 N4 cut-boundary limit for the complex arccos (carccos) used in the Wick-rotated gravitational action. It records what the six-lemma route actually closed: the cut-edge limit at the unit circle and the Lorentz anchor at one. Gravity workers tracking SevenGaps ledger status cite it to separate proved analytic limits from still-open family Props and unflipped gap6 Bools.
claimModule-level audit of the cut-boundary limit $\operatorname{carccos}(z)\to$ value as $z$ approaches the branch cut at the unit circle, together with the Lorentz anchor identity at $1$, as established by the L1--L6 route in the sibling Wick action cut-limit development. No new terminal gap6 claim is asserted.
background
In the Recognition Science gravity stack, SevenGaps tracks unfinished analytic bridges between the recognition cost and continuum GR. Wave C4 N4 concerns the Wick-rotated action and the complex inverse cosine $\operatorname{carccos}$ near its branch cut. The cut-boundary limit controls how the Euclideanized action meets the Lorentzian sheet; the Lorentz anchor at one fixes the normalization of that matching.
The sibling module WickActionCutLimit (binding design D-gap6-n4-cut-limit-design-20260723) lands two concrete statements via a six-lemma route: tendsto of carccos at the cut, and the Lorentz anchor at one. It deliberately does not inhabit the gap6 terminal proposition or flip ledger Bools; the family Prop remains open in that session.
This audit module imports that development only. Its role is documentary and ledger-facing: state what was proved, what was left open, and what a referee should not read into the cut-limit lemmas.
proof idea
No independent proof content. The module is an audit shell over the imported six-lemma route (L1--L6) that establishes carccos tendsto at the cut and the Lorentz anchor at one. Structure is import-plus-status notes rather than new tactic or term proofs. Treat any local statements as restatements or status markers for the upstream cut-limit theorems.
why it matters in Recognition Science
SevenGaps work needs a clean split between analytic lemmas that closed and ledger terminals that did not. Upstream lands the cut-boundary limit and Lorentz anchor without claiming the gap6 terminal or flipping Bools. This audit makes that non-claim explicit so downstream gravity and gap-closure arguments cannot silently treat N4 as fully discharged.
In the broader RS gravity program the Wick cut limit is a technical step toward matching recognition-cost action to continuum curvature terms. Until the open family Prop and gap6 terminal are inhabited, the cut-limit lemmas remain intermediate infrastructure, not a finished gap closure. No used-by edges are recorded yet; the module is a status checkpoint rather than a proof feeder.
scope and limits
- Does not prove the gap6 terminal proposition or flip any SevenGaps ledger Bools.
- Does not close the open family Prop left unresolved in the Wick cut-limit session.
- Does not supply new analytic lemmas beyond the imported L1--L6 cut-limit route.
- Does not claim a full Wick-action equivalence to continuum GR.
- Does not extend the carccos limit off the designed cut-boundary regime.