Track1ForallDispStationarityPackagingEndpoint
plain-language theorem explainer
Packages the claim that every displacement class $d\in\mathrm{Fin}\,7$ has stationary weighted deficit-derivative sum into the seven-leaf stationarity bundle at $N=5$. Track 1.B / Fork A agents and Track 7 handoff consumers cite it as the uniform packaging interface. The declaration is a pure Prop abbreviation: forall over classes implies the structure bundle.
Claim. If, for every displacement index $d\in\{0,\ldots,6\}$, the canonical periodic weighted deficit-derivative partial sum for class $d$ on the $N=5$ Freudenthal torus is stationary at the origin (derivative zero for every vertex potential), then the seven-field stationarity bundle for all displacement classes holds.
background
This module is Track 7's fork-handoff integration lane. It records what parallel forks deliver without upgrading the discovery claim. Fork A is the Track 1.B stationarity reduction at $N=5$ on the canonical encoded periodic Freudenthal torus.
Upstream, each leaf CanonicalPeriodicDispWeightedDeficitDerivativeBaseStationaryTargetAtN5 d asserts: for every vertex potential $\xi$ on the $N=5$ torus skeleton, the partial weighted deficit-derivative sum over displacement class $d$ has derivative zero at the origin (HasDerivAt _ 0 0). The seven-target structure bundles those seven claims as named fields (disp0 through disp6), superseding the older disp0-only stationarity target.
The packaging endpoint is the clean interface between a single forall-quantified theorem and that structure bundle, flagged as the next target for the 1B-SCH agent.
proof idea
Definition only: the body is the implication
$(\forall d:\mathrm{Fin},7,;\mathrm{BaseStationary}(d))\to\mathrm{SevenBaseStationaryTargets}$.
No tactics. The companion theorem track1_forall_disp_stationarity_packaging_endpoint_holds discharges it by applying the existing constructor lemma canonicalPeriodicDispWeightedDeficitDerivativeSevenBaseStationaryTargetsAtN5_of_forall, which builds the structure from the forall hypothesis fieldwise.
why it matters
Gives Track 7 a uniform stationarity packaging fact rather than seven separate leaf citations. Downstream, track1_forall_disp_stationarity_packaging_endpoint_holds proves the endpoint; ForkHandoffIntegrationCert and fork_A_B_C_D_E_F_handoffs_integrated_one_statement consume the Track 1 reduction/interface package alongside many-body, residual/Bianchi, Page-capacity, $w(z)$, and falsifier-sensitivity handoffs.
Per the module doc, this does not close the open Schläfli/displacement leaves or assert the unconditional discovery theorem. It keeps remaining Track 1 displacement-class analytic content as the next dependency while letting Fork A report a single quantified packaging shape into the master handoff receipt.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.