Track1ConformalSchlaefliNearZeroStationarityEndpoint
plain-language theorem explainer
Names the Track-1 near-zero Schläfli stationarity endpoint as the canonical periodic weighted-deficit derivative stationarity target on the encoded Freudenthal torus at lattice size N=5 in each direction. Gravity Track-7 handoff integration cites it as the Fork-A near-zero closure leaf. The body is a pure Prop abbreviation fixing the three extents and the NeZero/size side conditions by decide.
Claim. The near-zero Schläfli stationarity endpoint is the proposition that the canonical periodic weighted-deficit derivative is stationary on the encoded Freudenthal torus with extents $N_x=N_y=N_z=5$ (each strictly greater than 2).
background
Track 7 is the integration-lane receipt for parallel fork handoffs in the gravity master plan. Fork A covers Track 1.B stationarity reduction at $N=5$; this definition is one of the named endpoint Props that receipt consumes. It does not upgrade the discovery claim; it records what the new endpoints prove.
The upstream target packages canonical periodic Track 1.B second-order Schläfli stationarity at the flat configuration already discharged for the encoded Freudenthal torus. Concretely, it is weighted-deficit derivative stationarity for the kernel and hypotheses of that torus at given extents $N_x,N_y,N_z$ with each extent nonzero and strictly larger than 2.
The doc-comment states the mathematical content: the global near-zero expansion together with the local near-zero Schläfli identity close the full canonical $N=5$ weighted-deficit stationarity target. Sibling endpoints cover Schläfli reduction, displacement-class leaves, and seven-leaf stationarity packaging.
proof idea
Not a proof: a one-line Prop abbreviation. It instantiates the upstream canonical periodic weighted-deficit derivative stationarity target at $N_x=N_y=N_z=5$, discharging the three $2<N$ inequalities by decide. The actual stationarity content lives in the upstream definition and in the companion theorem that asserts this Prop via the near-zero Schläfli closure lemma.
why it matters
Gives Track 7 a stable name for the near-zero Schläfli stationarity leaf so the fork integration certificate and the single integrated handoff statement can list it without inlining torus parameters. Downstream, the holds theorem asserts the Prop from the near-zero Schläfli closure; ForkHandoffIntegrationCert and fork_A_B_C_D_E_F_handoffs_integrated_one_statement consume the Track-1 reduction/interface package (explicitly not a full closure of every open Schläfli leaf).
In the Recognition gravity stack this is bookkeeping on the discrete Regge/J-cost side of Track 1.B: stationarity of the weighted deficit on the periodic Freudenthal encoding at the canonical $N=5$ size used throughout the master theorem handoff. Remaining displacement-class leaves stay as the next dependency, matching the module's stated scope.
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