ForkHandoffIntegrationCert
plain-language theorem explainer
Integration-lane certificate packing Fork A through F handoff endpoints for the gravity master theorem. Anyone citing Track 7 receipts uses this bundle: many-body amplitude-linearity, Schlaefli and stationarity reductions, mixed-axis residual interfaces, TT/shear Hessian chain, tick capacity, dark-energy falsifier, and sensitivity. Pure structure of endpoint propositions plus two nonempty cert fields; no new math is proved here.
Claim. A handoff certificate is a record of: the Track 2 claim that finite sitewise physical channels induce an amplitude-linear many-body map with density-only collapse (plus a nonempty cert); the Track 1 $N=5$ Schlaefli/stationarity reduction chain (seven-disp, conformal along-line, near-zero, mixed-axis residual, Bianchi, Riemann-sum); Track 1D TT/shear Gram and Lichnerowicz residual reductions; Track 3 tick-capacity and operator-process; Track 4 dark-energy $w(z)$ falsifier; Track 6 sensitivity; and a nonempty structural master-theorem certificate.
background
Track 7 is the integration-lane receipt for parallel gravity fork handoffs. Fork A is Track 1.B stationarity reduction at $N=5$ (seven displacement-class Schlaefli leaves feeding weighted-deficit stationarity for the nonlinear Hessian). Fork B is the physical residual and Bianchi interface. Fork C lifts binary physical channel responses to many-body amplitude-linearity. Fork D transfers discrete recognition-tick Page capacity. Fork E refines the dark-energy $w(z)$ falsifier band. Fork F packages falsifier sensitivity.
Each field is an endpoint proposition: an implication or closed target proved elsewhere and re-exported. Typical shapes: seven $N=5$ displacement leaves imply weighted-deficit stationarity; conformal Schlaefli along a line bypasses the per-class route; near-zero expansion, chain rule, and closed-form zero close the local non-flat surface on the canonical periodic Freudenthal torus. Mixed-axis endpoints reduce stencil coefficients and residual soundness. Track 1D fields reduce TT projectors through Gram systems to Lichnerowicz residual formulas.
The module is explicit: this lane does not upgrade the discovery claim. Structural master witnesses remain where required; open Track 1 displacement-class leaves stay the next dependency.
proof idea
No proof body: this is a structure declaration. Each field is typed by a sibling endpoint proposition (or nonempty of a named cert). Downstream, the concrete instance fills every field by the corresponding endpoint-holds theorem or inhabited cert. Inhabitation of the whole bundle is then a one-constructor wrap of that instance.
why it matters
Single receipt object for Gravity Track 7. Downstream, the concrete instance and its inhabited theorem let later verification demand one integration cert rather than forty separate endpoints.
Doc-comment stance: Track 2 many-body and Track 6 sensitivity enter as stronger handoff facts; Track 1 remains a reduction/interface package, not closure of open Schlaefli leaves. The structural master cert field keeps a nonempty structural witness, matching the plan.
In the RS gravity program this sits under master-theorem handoff, not under T0-T8 forcing. It records progress on discrete Regge/Schlaefli stationarity at $N=5$, physical residual Bianchi, many-body channel linearity, Page-tick capacity, $w(z)$ falsifiers, and sensitivity packaging, without claiming continuum GR derivation.
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