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A registered result in its source context

Original ledger classification: Identity [I] (compression contraction + Wick) + [P] (the one shared free-field premise)

Recorded statement: QUASI-FREE BOUNDARY (Python-only; the seam-side identification of GATE.METRIC.11/v154 reduced to ONE shared physical premise): (1) RESTRICTION OF A QUASI-FREE STATE IS QUASI-FREE [I] - a fermionic Gaussian state has real antisymmetric…

Statement, assumptions and sources

Paper context: Origin Theory

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GATE.METRIC.12

Original ledger classification: Identity [I] (compression contraction + Wick) + [P] (the one shared free-field premise)

Original claim text

QUASI-FREE BOUNDARY (Python-only; the seam-side identification of GATE.METRIC.11/v154 reduced to ONE shared physical premise): (1) RESTRICTION OF A QUASI-FREE STATE IS QUASI-FREE [I] - a fermionic Gaussian state has real antisymmetric covariance Gamma with i*Gamma a contraction (eigenvalues in [-1,1]; pure: Gamma^2=-I); the boundary marginal (partial trace over the bulk) is the compression P Gamma P = principal submatrix Gamma_d, and the compression of a contraction is a contraction => Gamma_d is a valid covariance (verified on pure + mixed Majorana states over several boundary subsets); the boundary/seam state is QUASI-FREE, induced by the one 2-point kernel Gamma_d; (2) WICK SURVIVES RESTRICTION [I]: every boundary correlator is the Pfaffian of Gamma_d (the 4-point function = Pf of the 4x4 submatrix), using only the boundary 2-point kernel - the v113 'one kernel is the whole net' property is inherited; (3) PREMISE UNIFICATION [I]: part (b) of the G_net premise ('the seam kernel is quasi-free', v110) FOLLOWS from 'the seam bulk is a reflection-positive Gaussian field' - the SAME premise already load-bearing in v59 (area law) and v150/v151 (EH mechanism); part (a) ('Calderon involution sheet-odd') is the double-cover deck = the |Z2| halving c3=1/(2*4pi). RESIDUAL [P]: the seam bulk is a reflection-positive FREE field - not reducible by finite computation (where TFPT meets functional analysis), but now the ONE independent physical premise shared by G_net, the area law and R3; given it, Gaussian bulk => quasi-free boundary => one kernel = net (v113) => carrier A => (E8)1 (v154) is exact. Numerical (numpy), Python-only by nature

Original classification detail

Identity [I]: quasi-free boundary from Gaussian bulk; G_net premise = the one free-field premise (shared with area law, R3)

Dependencies as recorded

GATE.METRIC.11; GATE.METRIC.10; CAR.QFREE.01; SEAM.EHMODEL.02; v59; v110; v113; v150

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Registered verification modules

  • v155_quasifree_boundary.pyRegistered verification module · registry
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    quasi-free in ⇒ quasi-free out (Python-only): the boundary marginal of a Gaussian bulk is the compression PΓP — a contraction, hence a valid covariance — so the G_net analytic premise (v110(b)/v113 'one kernel') FOLLOWS from 'the seam bulk is a RP free field', the same premise as v59 (area law) and v150/v151 (EH); the seam-side identification reduces to ONE shared physical premise

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