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A registered result in its source context

Original ledger classification: Geometric premise [O] (energy-commutator proof target; sharper, non-circular IFF sub-claim 2)

Recorded statement: THE ENERGY-COMMUTATOR CONTRACT (external-review proposal 2026-06-14; the NON-CIRCULAR sharpening of QGEO.ENERGY.01): the proposed premise is the operator identity [rho, Lambda_Sigma]=0 on the rank-8 Calderon polarisation -- rho the carrier…

Statement, assumptions and sources

Paper context: Research contracts

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QGEO.ENERGY.02

Original ledger classification: Geometric premise [O] (energy-commutator proof target; sharper, non-circular IFF sub-claim 2)

Original claim text

THE ENERGY-COMMUTATOR CONTRACT (external-review proposal 2026-06-14; the NON-CIRCULAR sharpening of QGEO.ENERGY.01): the proposed premise is the operator identity [rho, Lambda_Sigma]=0 on the rank-8 Calderon polarisation -- rho the carrier clock, Lambda_Sigma the Dirichlet-to-Neumann (Calderon) energy form of the RAW RP seam double. Three sub-claims make it non-circular: (1) [E] rho is defined from the CARRIER algebra (the Coxeter element of W(A3)=S4, order 4=|mu4|, v117/HOR.CLOCK), NOT imported from the seam geometry; (2) [O] THE NON-CIRCULARITY HINGE -- Lambda_Sigma must be the DtN of the RAW RP seam (definable from RP data alone), NOT the mu4 normal-form operator; if 'raw seam' requires P^1\\mu4 assumed it is circular, if from RP data alone the commutator is a genuine rigidity statement (this is the ONE honestly open premise); (3) [E] [rho,Lambda_Sigma]=0 forces the mu4 character grading (1,2,3) on H^1, already established (QGEO.COHOM.01, eigenforms z^{k-1}dz/(z^4-1), v177). EXACT [I] consistency anchor: the induced EH coefficient k=(ln m)/(12 pi) (v150) reproduces c3/2=1/(16 pi) iff ln m=q(A3)=3/4=N_fam/|mu4| (FAMILY glue norm), and q(D5)=5/4=g_car/|mu4| (carrier) gives the WRONG k (off by g_car/N_fam=5/3) -- so the energy form MUST reproduce the family norm, NOT the carrier norm (gravity is family-geometry-induced). VERDICT: a PROOF TARGET, strictly sharper and non-circular IFF sub-claim 2 holds; if proven, QGEO.SYM.01 turns from definitional bedrock into an ENERGY-RIGIDITY THEOREM. Not a proof -- the bedrock stays [O]. Python-only (the q(A3) rigidity is exact and Wolfram-mirrored)

Original classification detail

Geometric [O]: QGEO.ENERGY.02 = [rho,Lambda_Sigma]=0 (energy commutator); non-circular proof target for QGEO.SYM.01 IFF the raw-seam DtN (sub-claim 2) is RP-definable; exact rider: the EH coefficient selects q(A3)=3/4 (family), not q(D5)=5/4 (carrier)

Dependencies as recorded

QGEO.ENERGY.01; QGEO.SYM.01; QGEO.COHOM.01; HOR.CLOCK.01; v150_replica_eh_model.py; v192_qgeo_energy_clock.py

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Registered verification modules

  • v193_qgeo_energy_commutator.pyRegistered verification module · registry
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    QGEO.ENERGY.02: the energy-COMMUTATOR contract (non-circular sharpening of QGEO.ENERGY.01): [ρ,Λ_Σ]=0 on the rank-8 Calderón polarisation, ρ the carrier clock, Λ_Σ the DtN energy form of the RAW RP seam. Three sub-claims: (1) [E] ρ is carrier-defined (Coxeter of W(A3)=S4, order 4=|µ4|, v117), not imported from the seam; (2) [O] the non-circularity hinge — Λ_Σ must be the RAW RP-seam DtN, not the µ4 normal form (circular if it needs P¹∖µ4 assumed); (3) [E] [ρ,Λ_Σ]=0 forces the (1,2,3) grading on H¹ (QGEO.COHOM.01). Exact [I] rider: the induced EH coefficient k=(ln m)/(12π) reproduces c3/2 iff ln m=q(A3)=3/4 (FAMILY), not q(D5)=5/4 (carrier, off by 5/3) — gravity is family-geometry-induced. Proof target [O]; if proven, QGEO.SYM.01 becomes an energy-rigidity theorem.

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