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A registered result in its source context

Original ledger classification: Synthesis/reduction [E]/[O] (one keystone theorem; QGEO.SYM corollary; QG.AMB decoupled)

Recorded statement: THE KEYSTONE UNIFICATION (2026-06-22): there is ONE open theorem (SEAM.EQUIV.01), QGEO.SYM.01 is its COROLLARY (a conformal-net axiom), and QG.AMB.01 is a decoupled general QG problem, NOT a TFPT gate -- collapsing the 'two open structural…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

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SEAM.EQUIV.UNIFY.01

Original ledger classification: Synthesis/reduction [E]/[O] (one keystone theorem; QGEO.SYM corollary; QG.AMB decoupled)

Original claim text

THE KEYSTONE UNIFICATION (2026-06-22): there is ONE open theorem (SEAM.EQUIV.01), QGEO.SYM.01 is its COROLLARY (a conformal-net axiom), and QG.AMB.01 is a decoupled general QG problem, NOT a TFPT gate -- collapsing the 'two open structural items' narrative to 'one solvable theorem + one decoupled foreign problem'. [E] QGEO.SYM.01 = COROLLARY: a chiral conformal net has a Moebius-covariant vacuum (the unique invariant positive-energy vector, a NET AXIOM); rotations U(1) < Moebius => the vacuum is rotation-invariant; the mu4 clock = rotation by pi/2 ((e^{i pi/2})^4=1) fixes it => omega o rho = omega. So SEAM.EQUIV.01 => QGEO.SYM.01 with NO extra premise (the v323 'rotation-invariant vacuum' is a net axiom); machine-pinned in Lean as qgeoSymIsCorollary. [E] THE ONE KEYSTONE THEOREM: SEAM.EQUIV.01 = a construction theorem (c=g_car+N_fam=8, det Cartan E8=1, gap 6 ln(3/2)>0 derived) with EXACTLY 1 open continuum lemma (rigorous continuum OS reconstruction + invertibility of the raw collar); 5 of 6 links cited/derived. [E] QG.AMB.01 DECOUPLED: margin Delta-31/(4pi^2)~1.648>0 (v76/v311/v330/v332) => no TFPT prediction depends on it; the general Euclidean-QG conformal-factor problem (GHP 1978), inherited not TFPT-specific. [E] COLLAPSED STATUS: open structural items 2 -> 1 (SEAM.EQUIV.01); QGEO.SYM.01 corollary; QG.AMB.01 decoupled; live residual = v_geo + G_net(=SEAM.EQUIV.01) + F_transfer. [O] the one residual = SEAM.EQUIV.01's continuum OS reconstruction (Lean-pinned FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). A synthesis/inventory module (like v275/v318); does NOT close SEAM.EQUIV.01.

Original classification detail

[E] the corollary reduction (QGEO.SYM.01 via the cited net-vacuum axiom) + the one-theorem framing + the QG.AMB decoupling/reclassification; [O] SEAM.EQUIV.01's one continuum lemma. A synthesis collapsing the status to one solvable theorem + one decoupled foreign problem; does NOT close SEAM.EQUIV.01.

Dependencies as recorded

SEAM.EQUIV.CHAIN.01; QGEO.BW.01; QGEO.SYM.01; QG.AMB.01; v308; v323; v329; v333; v76

Open the original ledger source, row 437

Location recorded in the ledger

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Navigation through a shared verification script

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Registered verification modules

  • v335_seam_equiv_unify.pyRegistered verification module · core
    Read the description recorded in the module registry

    The keystone unification: there is ONE open theorem (SEAM.EQUIV.01), QGEO.SYM.01 is its COROLLARY (a conformal-net axiom), and QG.AMB.01 is a decoupled general QG problem, NOT a TFPT gate. [E] QGEO.SYM.01 = COROLLARY: a chiral conformal net has a Moebius-covariant vacuum (the unique invariant positive-energy vector, a NET AXIOM); rotations U(1) < Moebius => rotation-invariant vacuum; the mu4 clock = rotation by pi/2 fixes it => omega o rho = omega. So SEAM.EQUIV.01 => QGEO.SYM.01 with NO extra premise (the v323 'rotation-invariant vacuum' is a net axiom); the two bedrock items collapse to ONE. [E] THE ONE KEYSTONE THEOREM: SEAM.EQUIV.01 = a construction theorem (c=8, det Cartan E8=1, gap 6 ln(3/2)>0 derived) with EXACTLY 1 open continuum lemma. [E] QG.AMB.01 DECOUPLED: margin Delta-31/(4pi^2)~1.648>0 => no TFPT prediction depends on it; the general Euclidean-QG conformal-factor problem (GHP 1978), inherited not TFPT-specific. [E] COLLAPSED STATUS: structural items 2->1; live residual = v_geo + G_net(=SEAM.EQUIV.01) + F_transfer. [O] the one residual = SEAM.EQUIV.01's continuum OS reconstruction (Lean-pinned). A synthesis/inventory; does NOT close SEAM.EQUIV.01.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.