A registered result in its source context
Original ledger classification: Identity/Lattice [I]/[L] (symbol homogeneity + rigidity count + |Z2| arithmetic) + [P] (the gapped flow reaching the fixed point)
Recorded statement: FREENESS AS THE RIGID BOUNDARY FIXED POINT (simplicity-first reframing of premise A; the free-bulk postulate becomes a fixed-point property): (1) UNIVERSAL DtN SYMBOL [I]/[L] - the Dirichlet-to-Neumann (Calderon) operator of ANY 2nd-order…
Statement, assumptions and sources
Paper context: Origin Theory
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GATE.METRIC.14
Original ledger classification: Identity/Lattice [I]/[L] (symbol homogeneity + rigidity count + |Z2| arithmetic) + [P] (the gapped flow reaching the fixed point)
Original claim text
FREENESS AS THE RIGID BOUNDARY FIXED POINT (simplicity-first reframing of premise A; the free-bulk postulate becomes a fixed-point property): (1) UNIVERSAL DtN SYMBOL [I]/[L] - the Dirichlet-to-Neumann (Calderon) operator of ANY 2nd-order elliptic bulk is an order-1 pseudodifferential operator with principal symbol |xi|_g (Lee-Uhlmann 1989) = |k| on a flat boundary mode, homogeneous degree 1; any bulk interaction shifts only the lower-order (degree<=0) symbol => irrelevant in the UV/scaling limit, so the free chiral dispersion omega_k=|k| is bulk-detail-INDEPENDENT, not a fine-tuned input; (2) HOLOMORPHIC c=8 IS RIGID [I] - in a chiral/holomorphic theory every field has weight (h, hbar=0); an exactly-marginal deformation needs (1,1); with hbar=0 no (1,1) field exists => 0-dimensional marginal space => the fixed point is ISOLATED, no continuous knob along which a non-Gaussian interaction could turn on; (3) UNIQUE = (E8)_1 [I]/[L] - the only holomorphic c=8 chiral theory is the E8 lattice net (unique even unimodular rank-8 lattice, v83) = free-fermion/lattice theory => the rigid isolated fixed point IS (E8)_1, free; (4) THE |Z2| TRIPLE ROLE [I] - the same |Z2| halves the one-sided S^2 Gauss-Bonnet (c3=1/(|Z2|*2pi*chi(S^2))=1/(8pi)), labels the sheet, AND is the GSO/Ramond projection giving mu=1 (248=120_NS+128_R, v148): one object, three roles, so the geometry fixing c3 is the projection making the net holomorphic. CONSEQUENCE [P]: premise (A) is reframed from 'the seam is free' (a fine-tuned postulate) to 'the gapped (Delta=6 log(3/2)>0) boundary RG flow reaches the holomorphic fixed point'; given that, freeness is FORCED by rigidity (2) + uniqueness (3), the universal symbol (1) supplies the free UV dispersion and the |Z2| (4) supplies holomorphy - a strictly smaller, structural residual, not 'prove Gaussianity'. Not a finite proof, but the residual is now milder and simpler
Original classification detail
Identity/Lattice [I]/[L]: freeness = the rigid holomorphic c=8 fixed point; premise (A) reduced to reaching it
Dependencies as recorded
GATE.METRIC.13; GATE.METRIC.12; SEAM.EHMODEL.02; v59; v83; v148; v155; v156
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- Origin Theory
- Red-team audit
- Research contracts
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- 2026-06-13 (premise A reframed: freeness is a rigid boundary fixed point, v157)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- 2026-06-13 (seam Fock-space readings v174: CAR cone, Witten index, g-theorem)Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-13 (premise A: the destination fixed point is provably stable, v158)Research changelog; TFPT — Introduction and reading guide
- 2026-06-13 (premise A maximal honest closure: A2 by assembly, R1 = GATE.QGEO, zero independent open gates, v165)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
- Front matter / supportResearch contracts
Registered verification modules
- v157_rigid_fixed_point.pyRegistered verification module · registry
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freeness as a rigid fixed point (simplicity-first reframing of premise A): (i) the DtN/Calderón symbol is universally |k| (Lee-Uhlmann, bulk-detail-independent — the free dispersion is not a premise); (ii) a holomorphic c=8 theory has NO marginal (1,1) field (all fields h̄=0) ⇒ rigid, isolated, no room for an interaction; (iii) the same |Z2| that halves 8π in c3 IS the Ramond projection giving μ=1 (holomorphic); (iv) holomorphic c=8 unique = (E8)1 = free. Premise (A) shrinks from 'prove Gaussianity' to 'the gapped flow reaches the holomorphic fixed point'
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