Track1ConformalSchlaefliEndpoint
plain-language theorem explainer
At lattice size N=5, the conformal Schläfli identity along a one-parameter family implies full weighted-deficit stationarity of the canonical periodic Freudenthal torus. Track 7 (Fork A handoff) cites this as the direct Schläfli-along-line endpoint, bypassing seven per-displacement-class stationarity leaves. The declaration is a pure implication Prop packaging two named targets; no independent proof lives here.
Claim. If the conformal Schläfli identity holds along the line at $N=5$ (equivalently $V(t)=0$ for every parameter $t$), then the canonical periodic weighted-deficit derivative is stationary at the flat configuration of the encoded Freudenthal torus with dimensions $5\times 5\times 5$.
background
Track 7 is the integration-lane receipt for parallel fork handoffs in the gravity master theorem. Fork A concerns Track 1.B stationarity reduction at $N=5$ on the canonical encoded periodic Freudenthal torus. The module records what new endpoints prove without upgrading the unconditional discovery claim.
The weighted-deficit derivative stationarity target packages second-order Schläfli stationarity at the already-discharged flat configuration of that torus. Separately, the conformal Schläfli-along-line target at $N=5$ asserts that the classical Schläfli differential identity, applied at every parameter and summed over tetrahedra, forces the volume (or deficit) variation $V(t)=0$ along the line.
Upstream, the $N=5$ specializations fix dimensions $5\times 5\times 5$ with the obvious positivity side conditions. The point of the packaging is that a single global identity can close the full stationarity input and skip the seven per-displacement-class leaves.
proof idea
Definitional packaging only: the Prop is the implication from the $N=5$ conformal Schläfli-along-line target to the $N=5$ instance of canonical periodic weighted-deficit derivative stationarity (dimensions $5,5,5$ with decide side conditions). No tactics or lemmas run inside the def body. The companion theorem that discharges the Prop applies the named reduction canonicalPeriodicWeightedDeficitDerivativeStationaryTargetAtN5_of_conformalSchlaefli.
why it matters
Fork A needs a clean Track 1.B stationarity handoff for the integrated one-statement and the Fork handoff certificate. This endpoint is the clearest next proof surface: establish the conformal Schläfli identity along the line (classical differential identity, summed over tetrahedra), and the full $N=5$ weighted-deficit stationarity input follows, bypassing seven displacement-class leaves.
Downstream, the companion holds-theorem, the Fork A/B/C/D/E/F integration one-statement, and the integration certificate all consume it as a named Prop. The module doc is explicit that Track 1 remains a reduction/interface package, not closure of open Schläfli leaves. In the broader RS gravity stack this sits under the structural master theorem path; it does not touch T5–T8 forcing, RCL, or the alpha band directly.
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