TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-PHASE-ACTION-STATE-TIME.txt
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Inclusive original lines: 1-131
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000001 | HIST20261103P. Correct phase action on the actual original collar and full time.
000002 | No new operator, state, clock, background or comparison model is selected.
000003 | 
000004 | 1. ACTUAL SOURCE AND THE IDENTIFICATION BEING TESTED
000005 | Use original-local-source-variable-background-20261102/SEED-FIELD.txt:27-93:
000006 |  gamma=gamma_F, gamma^2=I, Phi=Phi*, {gamma,Phi}=0,
000007 |  A=-i*d_x+a_conn(x), [a_conn,gamma]=0,
000008 |  h=A*gamma-i*gamma*Phi.
000009 | x is the original circle coordinate. It is not the axial phase theta of
000010 | the recovered Lorentz action. Keep the entire coefficient, including
000011 | all original Yukawa/Majorana blocks and both normal summands.
000012 | The supplied state has C(h)=(I+exp(2*ell*h))^(-1) and
000013 | X(h)=(2*cosh(ell*h))^(-1), with the original ell and domains.
000014 | 
000015 | A browser review treated exp(i*chi) as simultaneously removing a_conn
000016 | and rotating Phi because {gamma,Phi}=0. The first decisive test is the
000017 | ACTUAL group action, rather than the similar appearance of two phases.
000018 | 
000019 | 2. ORDINARY SCALAR PHASE: NO MASS ROTATION
000020 | For U_s=exp(i*chi(x))*I, exact product differentiation gives
000021 |  U_s^* A U_s=A+chi'(x)*I,
000022 |  U_s^* Phi U_s=Phi,
000023 |  U_s^* h U_s=h+chi'(x)*gamma.                         (1)
000024 | Thus a scalar phase shifts the ordinary connection by chi', and leaves
000025 | all mass, Yukawa and Majorana matrices unchanged. Anticommutation of
000026 | Phi with gamma cannot change its commutation with a scalar U_s.
000027 | Removing the local a_conn requires chi'=-a_conn in a scalar abelian
000028 | component, with its actual boundary twist retained. Matrix connections
000029 | require their actual ordered transport; (1) is not an arbitrary
000030 | nonabelian abelianization or removal of global circle holonomy.
000031 | 
000032 | 3. INTERNAL CHIRAL PHASE: DIFFERENT DERIVATIVE COEFFICIENT
000033 | For U_F=exp(i*chi(x)*gamma), again on the transported original domain,
000034 |  U_F^* A U_F=A+chi'(x)*gamma,
000035 |  Phi_F=U_F^* Phi U_F
000036 |       =cos(2*chi)*Phi-i*sin(2*chi)*gamma*Phi,
000037 |  U_F^* h U_F=A*gamma+chi'(x)*I-i*gamma*Phi_F.         (2)
000038 | The phase DOES rotate the full odd Phi in this case. Its derivative
000039 | adds chi'*I to h, not chi'*gamma. Equations (1) and (2) therefore do
000040 | not describe the same coupling or current. Since the actual nonzero
000041 | Phi anticommutes with gamma, gamma cannot equal I or -I on that whole
000042 | coupled space. No fixed invertible similarity changes I into gamma.
000043 | A projection to one grade would discard the nonzero Phi transitions.
000044 | This excludes that naive phase dictionary on the full original field.
000045 | It is not an exclusion of every possible original spacetime field map.
000046 | 
000047 | In particular gamma_F has not thereby been identified with spacetime
000048 | gamma5 of Spin(1,3), nor with the primitive doubled total grading.
000049 | The correct Lorentz phase theta=2*c*a and the matter shift S_hat remain
000050 | as derived in HISTORICAL-NORMALIZATION-INVARIANT-SOURCE-MAP.txt.
000051 | 
000052 | 4. THE GIVEN STATE AND TIME TRANSPORT EXACTLY
000053 | For either actual time-independent U, set
000054 |  h'=U^*hU, Dom(h')=U^*Dom(h).
000055 | Functional calculus gives, without choosing a different state,
000056 |  C(h')=U^*C(h)U, X(h')=U^*X(h)U,
000057 |  exp(-t*h')=U^*exp(-t*h)U.                           (3)
000058 | At an infinite signed h, the last exponential can be unbounded; (3)
000059 | then includes its transported functional-calculus domain. It is not a
000060 | claim that signed h is the positive physical time generator. Retain the
000061 | actual sea normalization and the whole scalar/body/reference factors.
000062 | The same block diagonal U on both faces transports the FULL graph
000063 | projection, including X. Source legs, C0, face orientation, reflection,
000064 | holonomy frame, reference and selectors transport with their actual
000065 | maps, as in REFERENCE-SOURCE-COMPLETION.txt:73-105.
000066 | Holding a periodic domain fixed when U is nonperiodic would violate
000067 | this identity; the endpoint twist is part of the original data.
000068 | 
000069 | For an r-dependent U in the actual charged first-order operator
000070 | K=d_r+h, direct differentiation instead gives
000071 |  U^* K U=d_r+U^*hU+U^*(d_r U),                       (4)
000072 |  R'(r1,r0)=U(r1)^* R(r1,r0) U(r0).
000073 | The last term in (4) cannot be dropped. It is anti-Hermitian for a
000074 | unitary U and real Euclidean r; one cannot call the remaining changed
000075 | frame a new selfadjoint time-independent h by notation. The endpoint
000076 | state and full ordered history transport, not a newly chosen vacuum.
000077 | In ordinary Lorentz Schrödinger time, the corresponding generator for
000078 | psi'=U(t)^*psi is H'=U^*HU-i*U^*(d_t U).
000079 | The Euclidean and Lorentz connection terms are not silently equated.
000080 | 
000081 | 5. FIELD-DEPENDENT ROTATIONS ALSO ACT ON THE BOSONIC MOMENTUM
000082 | At a compatible finite original regulator, suppose the actual change
000083 | is implemented on the whole given field Hilbert space by a unitary
000084 | W(b), where b is an already supplied canonical bosonic coordinate.
000085 | On the common smooth core, p_b=-i*d_b obeys the exact product rule
000086 |  W^* p_b W=p_b+A_b, A_b=-i*W^*(d_b W).               (5)
000087 | For the actual one-parameter finite Fock rotation
000088 | W=exp(i*q(b)*Q), with b-independent Hermitian Q, A_b=q'(b)*Q.
000089 | This is an operator-valued current, not its expectation value.
000090 | The full already supplied Hamiltonian transports as W^*H W; its
000091 | bosonic kinetic terms consequently contain p_b+A_b with the original
000092 | ordering. For a supplied quadratic kinetic term, expansion includes
000093 | the exact mixed momentum/current and current-square terms. Setting
000094 | A_b=0 would erase backreaction. This is the quantum-coordinate
000095 | counterpart of the recovered p_theta=F_theta^2*dot(theta)-j0/2.
000096 | It does not identify Q with the physical axial charge by similar
000097 | indices, or choose a new bosonic kinetic law.
000098 | 
000099 | The original R113 operator V_ji=Q_0[h_ji] can be noncommuting and
000100 | operator-valued. Therefore a substitution h -> U^*hU inside a numeric
000101 | matrix is not a conjugation of the whole H_B and all V_ji. Retain
000102 | W^*H_B W, every transformed V, source leg and Padm. No classical
000103 | average, independent thermal state or bare dGamma(h) is substituted.
000104 | 
000105 | 6. REGULATOR, MEASURE AND SPECTRUM SCOPE
000106 | The finite identities use the actual transported cutoff spaces. A
000107 | compression P_N U P_N need not be unitary when U mixes Fourier modes;
000108 | transport the regulator as well. At the full source level retain the
000109 | Pfaffian congruence, Berezin factor, all mass phases and the original
000110 | boundary/reference anomaly. Infinite-sea unitary implementation is not
000111 | assumed from the finite matrix identity alone.
000112 | If an actual whole selfadjoint source map is unitarily implemented,
000113 | its spectrum is preserved, not newly determined. It does not calculate
000114 | an uncomputed original H_B or prove physical positivity. Padm and its
000115 | memory terms transport too; PHP is not made a semigroup by this map.
000116 | 
000117 | RESULT
000118 | Established directly on the actual original coefficient: the two phase
000119 | actions are distinct, and the complete supplied state/time has the
000120 | explicit transport (3)-(5), including the bosonic momentum connection.
000121 | The false scalar-phase/mass-rotation identification is excluded.
000122 | No complete primitive S_adm, actual H_tr,pos or common interacting
000123 | spectrum is claimed. Existing full-source state/time results remain;
000124 | this continuation addresses genuinely moving field frames, not a
000125 | reopening of the already closed fixed-frame transport.
000126 | 
000127 | ORIGINAL SOURCE ANCHORS
000128 | SEED-FIELD.txt:27-93 in the cited original contract:
000129 | SHA256 db9d551297ad797c51b8fef682db85f13a08cbb289592e238289b17e59b66a0b.
000130 | REFERENCE-SOURCE-COMPLETION.txt:73-105 in that same contract:
000131 | SHA256 5ddc9c63c5f20f42befba6ae32fc57fdecb61c4b70dd9ab2d7b26fe667380cbb.