forkHandoffIntegrationCert
plain-language theorem explainer
Bundles every parallel fork-handoff endpoint (Tracks 1.B–1.D Schläfli/stationarity reductions, Track 2 many-body amplitude linearity, Page-capacity, dark-energy w(z), and Track 6 sensitivity) into one inhabited integration certificate. Gravity auditors cite it as the Track 7 receipt that the structural master theorem may consume without upgrading discovery claims. Construction is a pure field-wise assembly of already-proved endpoint theorems.
Claim. There is a concrete integration certificate whose fields are: the Track 2 many-body endpoint and its physical-channel amplitude-linear certificate; the Track 1 Schläfli reduction, displacement-0 base-vertex and stationary reductions, full displacement-stationarity and seven-stationarity packs, conformal Schläfli (global, local-expansion, near-zero chain-rule/closed-form/local/stationarity) endpoints; mixed-length audit and mixed-axis stencil/coefficient/translation/soundness endpoints; Track 1.D tensor-shear and TT-projector reductions; plus the Track 3–6 Page-curve, dark-energy $w(z)$, and falsifier-sensitivity handoffs.
background
Track 7 is the integration-lane receipt for six parallel gravity forks. Fork A is the Track 1.B Schläfli stationarity reduction at period $N=5$; Fork B is the physical residual and Bianchi interface; Fork C is the Track 2 many-body $\Pi$-tensor-product amplitude-linear lift; Fork D transfers discrete recognition-tick Page capacity; Fork E refines the dark-energy $w(z)$ falsifier band; Fork F packages Track 6 falsifier sensitivity.
The certificate structure records exactly those handoffs. 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 facts, while Track 1 remains a reduction/interface package, not a closure of the open Schläfli leaves.
Upstream endpoints already proved include the conformal Schläfli-along-line target at $N=5$, its localized expansion/reindexing half, the near-zero chain-rule and closed-form local cancellations, and the concrete Riemann-sum refinement that instantiates the master theorem's D2 input once product-filter data are supplied.
proof idea
Pure structure inhabitation: each field of the certificate is assigned the corresponding *_endpoint_holds theorem (or the inhabited many-body amplitude-linear certificate). No new mathematics is derived. Representative assignments include track2_many_body := track2_many_body_endpoint_holds, track1_conformal_schlaefli := track1_conformal_schlaefli_endpoint_holds (itself a one-line wrapper of the canonical periodic weighted-deficit derivative stationarity target at $N=5$), the near-zero chain-rule/closed-form/local/stationarity family, the mixed-axis stencil/coefficient/translation/soundness chain, and the Track 1.D tensor-shear scaffold plus TT-orthogonal surface reductions. The remaining elided fields follow the same pattern.
why it matters
Gives the single inhabited object that forkHandoffIntegrationCert_inhabited exposes as Nonempty ForkHandoffIntegrationCert, so downstream master-theorem wiring can depend on one name rather than dozens of leaf endpoints. Module doc is explicit: this does not upgrade the discovery claim; it only records what the new endpoints prove and keeps remaining Track 1 displacement-class leaves as the next dependency. In the Recognition gravity stack it sits after the structural master theorem and the physical residual / many-body / Page-curve / $w(z)$ forks, packaging their handoffs for verification Track 7 without claiming full Schläfli closure or a finished Einstein-equation derivation.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.