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A registered result in its source context

Original ledger classification: Identity [I] (operator-dimension count) + [P] (basin/convergence of the gapped flow)

Recorded statement: THE FREE CHIRAL c=8 FIXED POINT IS STABLE (exact operator-dimension count; the finite core of premise (A)'s reaches-the-fixed-point residual): (1) DIMENSIONS [I] - in the 16-Majorana chiral theory psi has weight h=1/2, the fermion-bilinear…

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Paper context: Origin Theory

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GATE.METRIC.15

Original ledger classification: Identity [I] (operator-dimension count) + [P] (basin/convergence of the gapped flow)

Original claim text

THE FREE CHIRAL c=8 FIXED POINT IS STABLE (exact operator-dimension count; the finite core of premise (A)'s reaches-the-fixed-point residual): (1) DIMENSIONS [I] - in the 16-Majorana chiral theory psi has weight h=1/2, the fermion-bilinear current :psi_i psi_j: has h=1, the quartic :psi psi psi psi: has h=2, the 2k-fermi operator h=k; a 1d boundary perturbation is relevant/marginal/irrelevant as h </=/> 1; (2) NO RELEVANT INTERACTION [I] - bosonic (even fermion number) chiral operators have INTEGER h, lowest h=1, so the relevant window 0<h<1 is EMPTY; (3) CURRENTS DO NOT DEFORM [I] - the h=1 operators are the 248 currents (120 NS + 128 R, v148), chiral (hbar=0), not (1,1)-marginal bulk deformations (v157); integrating a chiral current is a symmetry; (4) LOWEST INTERACTION IRRELEVANT [I] - the quartic h=2>1 (irrelevant), all higher 2k-fermi h=k>=2; (5) STABILITY [I] - no relevant deformation + no marginal interaction + only irrelevant interactions => the free chiral c=8 fixed point is ISOLATED and STABLE (the exact operator-content version of v157 rigidity). RESIDUAL [P]: only that the gapped (Delta=6 log(3/2)>0) boundary flow lands in the BASIN of this fixed point - the destination is now a proven stable fixed point, so (A) reduces from 'prove Gaussianity' to a standard basin-of-attraction statement (conformal-perturbation convergence, not a finite computation)

Original classification detail

Identity [I]: free chiral c=8 fixed point provably stable; (A) reduced to basin-of-attraction

Dependencies as recorded

GATE.METRIC.14; GATE.METRIC.13; v56; v59; v148; v157

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Registered verification modules

  • v158_fixed_point_stable.pyRegistered verification module · registry
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    the free chiral c=8 fixed point is STABLE (exact dimension count, finite core of A): chiral Majorana h=1/2, bilinear current h=1, quartic h=2; the relevant window (0,1) for bosonic ops is EMPTY, the h=1 currents are chiral (not (1,1)-marginal, v157), the lowest interaction (quartic) is h=2 > 1 irrelevant ⇒ isolated stable fixed point; (A) reduces to a basin-of-attraction statement

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