Read the result in its research context.

Result

OriginalKMSarticle§4lines181–211,(4.6)/(4.7),incorrectlyinferssigma_global(A(I))=A(I)fromsubnetrotationcovariance. GlobalKMSmodulargroup=tau_-beta_smovesI. AnalyticevenCAR exteriorcommutator[n_f(t),a*(f_t)a(h)+a*(h)a(f_t)]=a*(f_t)a(h)-a*(h)a(f_t)!=0 refutesfixedI. Correct:E_(R_tI)tau_t=tau_tE_I; OR localphi_I=Phi|B(I),omega_I=phi_I|A(I) giveTakesakiE_Isigma_phiI=sigma_omegaI E_Iandlocalrestriction. Thislocalflowisnotglobalrotation.

Required assumptions

• Given holomorphic KMS inclusion with distinct local/global domains

  Testing the cited abstract theorem assumes already existing holomorphic conformal c8netB,mu_B1,A=B^Z4,irreducible localindex4 andinternalgauge commutingwithrotations. omega_beta is DEFINED as Gibbs(B)restriction. Distinguish globalGNS KMSmodulargroup,L0rotations andlocalmodulargroups ofrestrictedfaithfulstates. These premises do not constructmicroscopicBfromP1; originalH_source=8(L0+delta.p) isnot silentlyidentifiedwithL0orphysicalbeta_angle2pi.

• Fixed scalar Hardy model with quarter time

  H=L²(S¹), C projects onto n≥0, B_alpha=−i∂theta+alpha with alpha=1/4 or 3/4. C and B remain fixed for every candidate. Consider scalar unimodular multiplication operators: continuous symbols for isometry classification and H1 symbols for finite excitation energy. This source class is not derived from P1/P2.

• Do not identify source types

  Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

Original evidence

• ATLAS-KMS-LOCALITY-AND-SOURCE-WINDING.txt lines 43–73

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/mixed-current-origin-20261014/ATLAS-KMS-LOCALITY-AND-SOURCE-WINDING.txt

  a072b1a28c1e065ae3311df9a3e9cdbbeff6f4838a81e739e69490c6cc43618e

• 002-subsection-the-frozen-car-covariance.tex lines 181–211

  Source checked at this snapshot

  Original location and fingerprint

  documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/002-subsection-the-frozen-car-covariance.tex

  afb3b8aa137042aa4829e06b04c177fbb7f21661493ce2a5dbab66e2669c21ea

• 001-section-setting-and-correction-of-terminology.tex lines 163–190

  Source checked at this snapshot

  Original location and fingerprint

  documents/articles--2026-08-29--holomorphic_kms_extension_en/sections/001-section-setting-and-correction-of-terminology.tex

  68bd3c0ff07ad36144b286c908a2de2dfebbfa260c0892e334f795fe0c6ae063

• check_kms_locality_and_source_winding.py lines 20–33

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/mixed-current-origin-20261014/check_kms_locality_and_source_winding.py

  7c6e4579da19d55089a95f751e72a37af250e51360ee4b02fa499df7e2fba2a7

• check_kms_locality_and_source_winding.py lines 104–144

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/mixed-current-origin-20261014/check_kms_locality_and_source_winding.py

  7c6e4579da19d55089a95f751e72a37af250e51360ee4b02fa499df7e2fba2a7

• kms-locality-and-source-winding-results.json lines 1–82

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/mixed-current-origin-20261014/kms-locality-and-source-winding-results.json

  0d4ef01c6f44f021b87036353d9a8f8bd4850617bccbf8cf569387dc9931f955

• CLAUDE-KMS-AND-WINDING-REVIEW.txt lines 1–44

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/mixed-current-origin-20261014/CLAUDE-KMS-AND-WINDING-REVIEW.txt

  3c8a3e179a9a986441523c429fe905995f5d81d42129ec735f21ec32750f2642

finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs