TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-MODULAR-SOURCE-IDENTITY.txt
Original file SHA-256: c78d87c93543c4e4f5fe03d88440d340aeb28943ad21bd7990182317725c31c6
Inclusive original lines: 1-77
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.

000001 | HIST20261103M. Recovered modular/recovery history and actual source types.
000002 | Anonymized original-source review, 3 November2026.
000003 | 
000004 | Actually reviewed original code:
000005 | verification/v238_modular_lindblad_dynamics.py, lines1-180,
000006 | SHA256 7938425550d9ad7f199e875f22c52609f4eeeb25b9f51df9a49af508a3576645.
000007 | verification/v240_gns_os_reconstruction.py, complete143lines,
000008 | SHA256 9c2f5a46007479b3e2557d9406392a5067f28228c97e04f979925ce9cd854480.
000009 | Graph discovery preceded code reading. No module result is newly claimed
000010 | executed. The following small exact algebra was independently evaluated.
000011 | 
000012 | R238 actually sets u2=(1,-1,0)/sqrt2,u3=(1,1,-2)/sqrt6,
000013 | J=ones(3)/3,T=J+(64/729)u2u2^T+(1/729)u3u3^T,L=logT.
000014 | The eigenvalues of -L are exactly0,6log(3/2),6log3.
000015 | L is genuinely a classical Markov generator here: L12=log(9/8)>0,
000016 | L13=L23=2log3>0, and row/column sums vanish. This is retained.
000017 | 
000018 | The same caller sets Lambda=diag(1,2,3) and calls G=iLambda+L a GKSL split.
000019 | Its checks establish only antihermiticity of iLambda and symmetric
000020 | nonpositivity of L. They do not define a generator map on M3 observables.
000021 | If the3-vector is interpreted as the actual diagonal algebra C^3,
000022 | G(1,1,1)^T=i(1,2,3)^T, so that literal action is not unital and does not
000023 | preserve real observables. A Hamiltonian acts on an observable algebra by
000024 | a commutator, not by an arbitrary one-sided phase multiplication.
000025 | A3x3 amplitude generator is also not, by that fact alone, a generator on
000026 | all9matrix coordinates. No additional Lindblad embedding is inserted.
000027 | Primary mathematical definition: Lindblad, Commun.Math.Phys48(1976),
000028 | 119-130, Theorem2 and introduction's conditions Phi_t(I)=I and complete
000029 | positivity; DOI10.1007/BF01608499. The original article was checked.
000030 | 
000031 | R240 supplies M3 and rho=diag(1/2,3/10,1/5), with GNS inner product
000032 | Tr(rho A*B), dimension9, modular generator i[logrho,.]. These finite
000033 | GNS facts for the supplied faithful state are retained. It separately
000034 | constructs the same3x3 -logT as in R238. It does not construct a common
000035 | field map that makes this3x3 transfer the action on the full9dimGNS space.
000036 | 
000037 | The smallest exact same-diagonal-state test gives, with p=diag(rho),
000038 | Tp=(3742/10935,710/2187,3643/10935),
000039 | Tp-p=(-3451/21870,539/21870,1456/10935) !=0.
000040 | Thus if that actual diagonal channel is meant, the separately supplied
000041 | GNS state is not its stationary state. Changing channel or basis requires
000042 | an actual transported map, not an equal gap. Also the chosen Lambda's
000043 | arithmetic-progression spectrum differs from logrho modulo a constant
000044 | and an overall nonzero scale: log(1/2)+log(1/5)-2log(3/10)=log(10/9)!=0.
000045 | R238 permits other diagonal Lambda as a family, but choosing another
000046 | family member is not proof of equality of these concrete two callers.
000047 | 
000048 | Scope of exclusion: the literal assertion that these two displayed
000049 | callers already give one full original source/state/time or a verified
000050 | quantum GKSL generator. Positive -logT, its finite gap, the GNS theorem
000051 | for the supplied state and valid classical Markov L are not withdrawn.
000052 | No universal obstruction to a genuine quantum/continuum embedding is
000053 | claimed. The current P1 source already includes its state and time;
000054 | this historical comparison does not demand a new arbitrary state there.
000055 | 
000056 | Later existing manuscripts explicitly work under additional hypotheses:
000057 | 1. Holomorphic KMS extension article, setting section: proper INTERNAL
000058 | Z4 gauge action preserving every local interval algebra and commuting
000059 | with rotations. It explicitly distinguishes vacuum-vector ground state
000060 | from vacuum-sector rotational Gibbs state and assumes the scaling-limit
000061 | identification for its frozen finite CAR interpretation. Such a gauge
000062 | action is not automatically the original geometric quarter rotation.
000063 | Only the setting/frozen-covariance/qualification text was consulted here;
000064 | no new independent proof of every quoted classification theorem is made.
000065 | 2. Thermodynamic-dynamics article, equilibrium and combined theorem
000066 | section: existence of limit dynamics and ground/KMS states is stated for
000067 | a supplied frozen finite-local-space Hamiltonian class, without claiming
000068 | unique state, gap survival or interacting continuum/IR closure. Preserve
000069 | this existing conditional dynamics route; it does not select S_adm.
000070 | These articles are retained for continuity, not used to relabel a new
000071 | chosen Gibbs state as the whole original interacting TFPT vacuum.
000072 | 
000073 | The P25-L kinetic/time response, Q25/S25 source checks, later seam/E8,
000074 | clocks, flavor, alpha and full96 source results remain in their scopes.
000075 | A common positive spectrum must be obtained from the same original
000076 | field action, reference, state and physical time; equal numerical gaps
000077 | or reusing the same matrix logarithm do not establish that identity.