track1_conformal_schlaefli_endpoint_holds
plain-language theorem explainer
The conformal Schläfli-along-line identity at lattice size N=5 implies full weighted-deficit derivative stationarity on the periodic cubic six-tet complex. Track 7 fork-handoff integration cites this as the direct Schläfli endpoint for Fork A (Track 1.B). The proof is a one-line application of the N=5 conformal-to-stationarity reduction already proved on the physical six-tet instance.
Claim. If the canonical periodic conformal Schläfli-along-line target holds at $N=5$ (the identity $V(t)=0$ for all deformation parameters $t$), then the canonical periodic weighted-deficit derivative stationarity target holds at $N=5$ (with matching period and weight indices).
background
Track 7 is the Gravity fork-handoff integration lane. It records what the parallel endpoints prove for Forks A–F without upgrading the discovery claim. Fork A is the Track 1.B stationarity reduction at $N=5$ on the periodic cubic six-tetrahedron lattice.
The endpoint proposition is an implication: assume the conformal Schläfli-along-line target at $N=5$, conclude the full weighted-deficit derivative stationarity target at the same $N$. The conformal target packages the classical Schläfli differential identity applied at every parameter and summed over tetrahedra, so the volume variation $V(t)$ vanishes identically along the conformal line. Weighted-deficit stationarity is the discrete Einstein/Regge critical-point condition used as Track 1.B input.
This route bypasses the seven per-displacement-class stationarity leaves. The physical six-tet cubic Dirichlet instance already supplies the bridge lemma that turns the conformal identity into the stationary weighted-deficit target.
proof idea
One-line term proof. The goal is exactly the proposition Track1ConformalSchlaefliEndpoint, i.e. the implication from the conformal Schläfli-along-line target at $N=5$ to weighted-deficit derivative stationarity at $N=5$. That implication is the already-proved lemma canonicalPeriodicWeightedDeficitDerivativeStationaryTargetAtN5_of_conformalSchlaefli on the physical six-tet cubic instance; the theorem is that lemma applied as a term.
why it matters
This is the direct Schläfli-along-line receipt consumed by Track 7. Downstream it feeds forkHandoffIntegrationCert and the one-statement integration theorem that packages Forks A–F (many-body channel lift, Schläfli-to-stationarity reductions, physical residual/Bianchi interface, Page-capacity transfer, $w(z)$ falsifier bands, and falsifier-sensitivity). The parent integration deliberately does not assert the unconditional discovery theorem.
Framework role: it closes the cleanest surface for Track 1.B stationarity input. Once the classical Schläfli identity is established along the conformal line and summed over tetrahedra, full $N=5$ weighted-deficit stationarity follows, skipping the seven displacement-class leaves. Remaining open work is proving the conformal along-line target itself and discharging the leftover Track 1 displacement-class leaves noted in the module doc.
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