TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/mixed-current-origin-20261014/ATLAS-KMS-LOCALITY-AND-SOURCE-WINDING.txt
Original file SHA-256: a072b1a28c1e065ae3311df9a3e9cdbbeff6f4838a81e739e69490c6cc43618e
Inclusive original lines: 43-73
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000043 | 3. A local-domain error in the printed modular chain, and its repair
000044 | 
000045 | In section4 the paper infers from rotational covariance of the SUBNET that
000046 |   sigma_s^(Phi_beta^B)(pi(A(I)))=pi(A(I))
000047 | and writes a fixed-interval modular identity(4.7). This inference is false.
000048 | For the GLOBAL KMS GNS algebra the valid relation is sigma_s=tau_(-beta s).
000049 | Rotations move I: tau_t(A(I))=A(R_t I), not A(I) for a fixed proper interval.
000050 | 
000051 | An explicit bounded EVEN original-CAR witness suffices. Choose normalized
000052 | f inside I and t with f_t supported outside I. Choose orthogonal h with
000053 | support in the same exterior region. Put
000054 |   n_f=a*(f)a(f), B=a*(f_t)a(h)+a*(h)a(f_t).
000055 | Then n_f is local even in I, B local even in I-complement, and
000056 |   [tau_t(n_f),B]=a*(f_t)a(h)-a*(h)a(f_t) !=0.
000057 | If tau_t(n_f) belonged to A(I), even locality would force this to vanish.
000058 | This is an analytic CAR/translation witness, not a numerical scaling claim.
000059 | The actual full QWZ finite Hamiltonian similarly moves local number operators
000060 | outside a fixed region; the checker evaluates its exact quadratic CAR action.
000061 | 
000062 | There are TWO valid repairs, with different domains:
000063 | (i) GLOBAL modular/physical rotation covariance has a moving interval:
000064 |   E_(R_t I) tau_t(x)=tau_t E_I(x), x in B(I).
000065 | (ii) For LOCAL faithful states phi_I=Phi_beta^B|B(I), omega_I=phi_I|A(I),
000066 |   phi_I composed E_I=phi_I. Takesaki on B(I),A(I),phi_I then gives
000067 |   sigma_s^(phi_I)(A(I))=A(I),
000068 |   sigma_s^(omega_I)=sigma_s^(phi_I)|A(I),
000069 |   E_I sigma_s^(phi_I)=sigma_s^(omega_I) E_I.
000070 | This local modular group is NOT identified with global rotations. No new
000071 | physical time, one-sided chiral measure or charged generator follows.
000072 | Expectation/invariant-state uniqueness remain intact; only the printed
000073 | fixed-I physical-rotation identification is excluded. No paper edited.