A registered result in its source context
Original ledger classification: Theorem [E] (factorization through the gap => ambient-measure independence)
Recorded statement: THE DECOUPLING THEOREM (consolidated, citable, 2026-06-22): every TFPT dimensionless readout factors through the gapped admissible sector and is INDEPENDENT of the ambient QG measure -- the theorem that makes the QG.AMB.01 reclassification…
Statement, assumptions and sources
Paper context: Frontier and open physical interfaces
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DECOUPLING.THEOREM.01
Original ledger classification: Theorem [E] (factorization through the gap => ambient-measure independence)
Original claim text
THE DECOUPLING THEOREM (consolidated, citable, 2026-06-22): every TFPT dimensionless readout factors through the gapped admissible sector and is INDEPENDENT of the ambient QG measure -- the theorem that makes the QG.AMB.01 reclassification (v335) honest. [E] GAP MARGIN: Delta - 2*dim(E8)*c3^2 = 6 ln(3/2) - 496/(64 pi^2) = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0 (the ambient back-reaction scale 2*248*c3^2 = 31/(4 pi^2) exactly). [E] FACTORIZATION: every readout (mass ratios, mixings, alpha^-1, R+R^2) is a function of the admissible gapped transfer spectrum {1,(2/3)^6,(1/3)^6} + the discrete kernel alone; the ambient couples only above the gap. [E] THE THEOREM: margin>0 => exponential clustering (lambda_2=(2/3)^6) with finite susceptibility chi=1/(1-(2/3)^6)=729/665, so the ambient contribution is gap-suppressed => no readout depends on the ambient measure => QG.AMB.01 decoupled. [E] NEG CONTROL: gap closed (lambda_2->1) => chi diverges => fails (non-vacuous). [E] COROLLARY: zero frozen kill tests depend on the ambient measure. Consolidates v76/v311/v330/v332; does NOT construct the ambient measure (that is QG.AMB.01).
Original classification detail
[E] the margin, the factorization through the gapped sector, and the gap-suppression are exact/machine-checked; the decoupling is rigorous GIVEN the factorization. Does NOT construct the ambient measure -- proves TFPT does not need it.
Dependencies as recorded
QG.AMB.01; v76; v311; v330; v332; v335
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- Frontier and open physical interfaces
Sections that explicitly cite this claim
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- 2026-06-22 (next-steps round: the one open lemma literature-anchored, the Decoupling Theorem, the holomorphy discriminator hardened in Lean, and the [formula in source] budget: v336, v337, v338, FORM.CARTAN.DET.01)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- 2026-06-25 (No-Ambient-Dependency: no frozen readout is computed from QG.AMB.01: v423)Research changelog; TFPT — Introduction and reading guide
- 2026-06-23 (Directions 3 \& 7 — the two hard functional-analysis residuals ADVANCED: the QG measure as one-loop fluctuations around the parameter-free saddle ( v365), and the seam collar verified IN MMST's free-fermion class so the scaling limit is [formula in source] ( v366))Research changelog; TFPT — Introduction and reading guide
- 2026-06-24 (Typed correction budget: v388 the gap correction is keyed to the mechanism class, not a uniform band)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- 2026-07-13 ( v476 — the AP2 compression conjecture of the entropic-action bridge made well-posed on an exactly solvable model: the literal operator-side reading is ill-posed on a pure bulk, the state-side reading is forced, the mismatch is exactly quadratic in the cross-cut correlations and gap-suppressed; AP2 stays , no status moves)Research changelog; TFPT — Introduction and reading guide
- 2026-06-23 (Bird's-eye synthesis: two new structural patterns — v383 the universal spectral-gap principle and v384 the residual is certification, not construction)Research changelog; TFPT — Introduction and reading guide
- Research Contract 2 — [formula in source]tfpt research contracts
- 2026-06-24 (Correction error-bars: v393 the typed budget as actual first-correction magnitudes)Research changelog; TFPT — Introduction and reading guide
All 14 linked sections
- Front matter / support
- Front matter / support
- 2026-06-23 (Track 2 of the forward plan v2 — the AMBIENT REDUNDANCY statement ( v369): the holographic route to Gravity-complete that sidesteps building the general Euclidean QG measure)
- 2026-06-23 (Direction 5, the matter–gravity backreaction: the carrier's gravitational anomaly is forced [formula in source] , and the matter vacuum-energy backreaction is finite ( [formula in source] the forced [formula in source] from [formula in source] , not [formula in source] ) — the loop closes; no new SM-quantum-number read-out (declined): v361)
- Research Contract 2 — [formula in source]
- Full quantum gravity — induced from the boundary kernel
Registered verification modules
- v337_decoupling_theorem.pyRegistered verification module · frontier
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THE DECOUPLING THEOREM (consolidated, citable): every TFPT dimensionless readout factors through the gapped admissible sector and is INDEPENDENT of the ambient QG measure -- the theorem that makes the QG.AMB.01 reclassification (v335) honest. [E] GAP MARGIN: Delta - 2*dim(E8)*c3^2 = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0. [E] FACTORIZATION: every readout (mass ratios, mixings, alpha^-1, R+R^2) is a function of the admissible gapped transfer spectrum {1,(2/3)^6,(1/3)^6} + the discrete kernel alone. [E] THE THEOREM: margin>0 => exponential clustering (lambda_2=(2/3)^6), finite susceptibility chi=729/665, so the ambient contribution is gap-suppressed => no readout depends on the ambient measure => QG.AMB.01 decoupled. [E] NEG CONTROL: gap closed => chi diverges => fails (non-vacuous). [E] COROLLARY: zero frozen kill tests depend on the ambient measure. Consolidates v76/v311/v330/v332; does NOT construct the ambient measure.
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