Original ledger status
QGAMB.REDUNDANCY.01
QGAMB.REDUNDANCY.01
Track 2 (2026-06-23, next-plan v2): the AMBIENT REDUNDANCY statement -- the holographic route to Gravity-complete that SIDESTEPS building the general Euclidean QG measure (C7/QG.AMB.01). Instead of constructing the non-perturbative ambient measure (the conformal-factor swamp, v332/v334), assemble the established discriminators that prove the ambient sector carries NO physical d.o.f. relative to the holomorphic boundary algebra, so QG.AMB.01 is a non-fundamental CERTIFICATION object (like a coordinate choice in GR), not missing dynamics. [E] HOLOMORPHIC => DHR=Vec: #DHR primaries = |det Cartan| = 1 for E8 (ONE primary = vacuum, trivial braided category) vs 4 for SO(16)/D8 -- no nontrivial superselection charges => no hidden boundary sector a bulk could carry invisibly. [E] NO TORUS GSD: ground-state degeneracy on T^2 = #anyons = |det K| = 1 for E8 => a unique ground state => no topologically protected invisible bulk d.o.f. (the genus-1 obstruction of v344, redundancy reading). [E] FINITE PETZ RECOVERY: the seam transfer deviation subspace contracts at rate (2/3)^6=64/729<1 (v221) => bulk perturbations are boundary-recoverable at a finite gapped rate => Rec_Sigma bounded. [E] GAP-DECOUPLING MARGIN: Delta_eff=6 ln(3/2)-31/(4pi^2)~1.648>0 (v76/v337) => the un-built ambient sector is energetically separated from the admissible (boundary-reconstructible) sector. [C] RECONSTRUCTION MAP: Bisognano-Wichmann / Tomita-Takesaki gives the modular flow as the geometric boost (v258/v309/v323); with holomorphy this supplies Rec_Sigma: (bulk algebra)->A_Sigma^{mu4}. [C] THE REDUNDANCY STATEMENT: under SEAM.EQUIV.01 + BW, every gauge-invariant bulk observable is boundary-reconstructible (O_phys^bulk/Diff ~= A_Sigma^{mu4}) and ambient measures sharing the boundary state are physically equivalent => QG.AMB.01 carries no extra physical d.o.f. [O] RESIDUAL: the theorem consumes exactly TWO premises -- SEAM.EQUIV.01 (the boundary IS (E8)_1; the S3 lattice input, v366) and the BW intrinsicality of the raw collar (v329 NEG); it does NOT construct QG.AMB.01 but provides the ALTERNATIVE (holographic redundancy) route. Gravity-complete = Boundary-complete + Ambient-redundancy.
Recorded status: Ambient measure proved boundary-REDUNDANT (the holographic route); QG.AMB.01 reframed as a non-fundamental certification object [C]/[O] (conditional on SEAM.EQUIV.01 + BW)
Later scope correction: the DtN form estimate alone does not prove the transfer gap.
Dependencies, status detail and source
Canonical status: [E] det K=1 => DHR=Vec (no superselection) + no torus GSD + finite Petz recovery (2/3)^6 + gap margin Delta_eff~1.648>0; [C] the BW reconstruction map + the redundancy statement O_phys^bulk/Diff ~= A_Sigma^{mu4}; [O] the two premises (SEAM.EQUIV.01 + BW intrinsicality). The holographic route to Gravity-complete; does NOT construct the ambient measure.
Dependencies: QG.AMB.01; SEAM.EQUIV.01; v366; v329; v221; v76; v337; v258; v309; v323; v344; v83
Scripts: v369_qgamb_redundancy.py
Location: tfpt_research_contracts
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