Track1ConformalSchlaefliNearZeroLocalReductionEndpoint
plain-language theorem explainer
Packages the local near-zero Schläfli reduction for Track 1.B at the N=5 periodic Freudenthal torus: if the squared-edge chain rule and the closed-form Schläfli zero both hold near the flat configuration, then weighted-deficit derivative stationarity follows. Gravity Track 7 cites it as a Fork A handoff leaf. The body is a pure Prop abbreviation chaining three already-named targets.
Claim. The local near-zero Schläfli reduction endpoint asserts: if the canonical periodic local conformal Schläfli squared-edge chain-rule target holds at lattice size $N=5$, and the closed-form Schläfli zero target holds at the same deformed squared-edge tuple near flatness, then the canonical periodic weighted-deficit derivative stationarity target holds on the encoded Freudenthal torus with $N_x=N_y=N_z=5$.
background
Track 7 is the Gravity fork-handoff integration lane. It records what parallel forks prove without upgrading the unconditional discovery claim. Fork A covers Track 1.B Schläfli-to-stationarity reduction at $N=5$ on the canonical encoded periodic Freudenthal torus.
The weighted-deficit derivative stationarity target is the second-order Schläfli stationarity condition packaged at the flat configuration already discharged for that torus. The two hypotheses specialize the near-zero local conformal Schläfli program: a non-flat squared-edge chain rule, and a closed-form vanishing of the Schläfli contribution at the deformed squared-edge tuple, both fixed at $N=5$.
Sibling endpoints in the same module package other Track 1 leaves (disp-0 base vertex, disp-0 stationary, seven-stationarity, etc.). This one isolates the conformal near-zero local reduction.
proof idea
Definitional abbreviation only: the Prop is the implication from the $N=5$ squared-edge chain-rule target and the $N=5$ closed-form zero target into weighted-deficit derivative stationarity at $(5,5,5)$ with the three $2<N$ witnesses discharged by decide. No tactics. The companion theorem track1_conformal_schlaefli_near_zero_local_reduction_endpoint_holds later discharges it by applying the named reduction lemma that builds stationarity from those two near-zero inputs.
why it matters
Fork A needs a clean receipt that the remaining local near-zero Schläfli work reduces to two concrete targets rather than an open stationarity blob. This endpoint is that receipt. Downstream, ForkHandoffIntegrationCert and fork_A_B_C_D_E_F_handoffs_integrated_one_statement consume the Track 1 Schläfli reduction package (of which this is a leaf) alongside many-body, residual/Bianchi, Page-capacity, $w(z)$, and falsifier-sensitivity handoffs.
Per the module doc, Track 7 does not close discovery: displacement-class leaves stay open. The companion holds theorem quotes that the actual non-flat squared-edge chain rule is already proved for the canonical $N=5$ torus near flatness, so this interface is the integration seam, not a new analytic step. In RS gravity terms it sits inside the discrete Schläfli/Regge stationarity path that feeds the structural master certificate.
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