forkHandoffIntegrationCert_inhabited
plain-language theorem explainer
The fork handoff integration certificate is inhabited: there exists a concrete package bundling Track 1 Schläfli/displacement stationarity reductions, the Track 2 many-body amplitude-linear endpoint, and the companion residual, Page-capacity, dark-energy, and falsifier-sensitivity handoffs. Gravity auditors cite it as the receipt that the parallel forks assemble without upgrading the master discovery claim. The proof is a one-line term packing the explicit certificate instance.
Claim. There exists an integration certificate for forks A--F: a package containing the Track 2 many-body endpoint with a nonempty many-body physical-channel amplitude-linear certificate, the Track 1 Schläfli reduction endpoint, the Track 1 displacement-zero base-vertex and stationary reduction endpoints, the Track 1 displacement-stationarity reduction endpoint, and the remaining residual, Page-capacity, dark-energy $w(z)$, and falsifier-sensitivity handoff fields required by the structure.
background
Module setting is Gravity Track 7, the integration-lane receipt for parallel fork handoffs. Fork A is Track 1.B 1B-SCH stationarity reduction at $N=5$; Fork B is Track 1.B-PHY / 1.C physical residual and Bianchi interface; Fork C is Track 2.C many-body / PiTensorProduct amplitude-linear lift; Fork D is Track 3.C discrete recognition-tick Page-capacity transfer; Fork E is Track 4.C dark-energy $w(z)$ falsifier-band refinement; Fork F is Track 6 falsifier-sensitivity packaging. The module does not upgrade the discovery claim; it records what the new endpoints prove and leaves remaining Track 1 displacement-class leaves as the next dependency.
ForkHandoffIntegrationCert is the structure that packages those endpoints. Its doc states that the structural master theorem still uses structural witnesses where the master plan requires them; the Track 2 many-body endpoint and Track 6 sensitivity package enter as stronger handoff facts, while Track 1 remains a reduction/interface package, not a closure of the open Schläfli leaves. The companion definition forkHandoffIntegrationCert is the concrete instance filling every field from the corresponding endpoint theorems (for example track2_many_body_endpoint_holds, track1_schlaefli_reduction_endpoint_holds, and the displacement-stationarity endpoints).
proof idea
One-line term proof. The certificate instance forkHandoffIntegrationCert already inhabits the structure, so the proof is simply the anonymous constructor ⟨forkHandoffIntegrationCert⟩, which is the standard Lean witness for Nonempty ForkHandoffIntegrationCert. No additional lemmas are applied at this site; all substantive work lives in the field constructors of that instance.
why it matters
This is the inhabitedness receipt for the Track 7 fork-handoff integration certificate. Downstream consumers that need a Nonempty witness rather than the bare structure can cite it without reconstructing the six-fork package. In the Recognition gravity lane it marks that Forks A--F have been assembled into one certificate: Track 1 Schläfli and displacement-stationarity reductions, Track 2 many-body amplitude linearity, physical residual / Bianchi interface, discrete Page-capacity transfer, dark-energy $w(z)$ band refinement, and Track 6 falsifier sensitivity.
It deliberately does not close the open Schläfli leaves or upgrade the structural master theorem. The module doc is explicit: remaining Track 1 displacement-class leaves stay the next dependency. Session 565 projection notes that the certificate exposes the direct uniform displacement-stationarity endpoint for Track 1.B-SCH. No used_by edges are recorded yet; the declaration is a terminal integration receipt rather than an intermediate lemma in a longer chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.