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Original ledger classification: Reduction [E]/[C]/[O] (gap-decoupled measure)

Recorded statement: THE PHYSICAL QG MEASURE AS A GAP-DECOUPLED, CLUSTERING OBJECT (2026-06-21, TOE attack point 4): the honest statement in place of an over-claimed 4D measure for QG.AMB.01/G_metric. [E] the seam transfer spectrum {1,(2/3)^6,(1/3)^6} gives…

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QGAMB.CLUSTER.01

Original ledger classification: Reduction [E]/[C]/[O] (gap-decoupled measure)

Original claim text

THE PHYSICAL QG MEASURE AS A GAP-DECOUPLED, CLUSTERING OBJECT (2026-06-21, TOE attack point 4): the honest statement in place of an over-claimed 4D measure for QG.AMB.01/G_metric. [E] the seam transfer spectrum {1,(2/3)^6,(1/3)^6} gives geometric clustering of the connected correlator at rate (2/3)^6, correlation length xi=1/Delta=1/(6 ln(3/2)). [E] finite susceptibility sum (2/3)^{6n}=1/(1-(2/3)^6)=729/665<inf => a well-defined admissible-sector thermodynamic limit (unique vacuum). [E] gap-decoupling (v76): Delta-31/(4pi^2)~1.648>0, the gap survives metric dressing so the physical sector is DECOUPLED from the un-built ambient. [E] NEG: an ungapped transfer (2nd eig->1) sends xi,chi->inf (no clustering). [C] spectral-action dictionary a2=EH, a4=R^2/72 (v36) + KMS beta=1 (v259). [O] the FULL ambient measure QG.AMB.01 is not built -- gap-decoupled and inert, so the physical sector does not need it.

Original classification detail

[E] the geometric clustering at rate (2/3)^6 + finite correlation length/susceptibility + the v76 decoupling margin + the ungapped negative control; [C] the spectral-action low-energy dictionary; [O] the full ambient measure (gap-decoupled, inert). Shows the physical sector is a convergent object; does NOT construct QG.AMB.01.

Dependencies as recorded

QG.AMB.01; GATE.METRIC.01; QG.GAPDEC.01; v36; v76; v259

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  • v311_gap_decoupled_measure.pyRegistered verification module · frontier
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    TOE attack 4 -- the physical QG measure as a gap-decoupled, exponentially-clustering object: the transfer spectrum {1,(2/3)^6,(1/3)^6} gives geometric clustering at rate (2/3)^6, correlation length 1/(6 ln(3/2)), finite susceptibility 729/665; the v76 margin 6 ln(3/2)-31/(4pi^2)~1.648>0 decouples the physical sector from the un-built ambient. Spectral-action a2=EH/a4=R^2/72 (v36) + KMS beta=1 (v259); QG.AMB.01 stays open (gap-decoupled, inert)

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