TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/NATIVE-FIELD-TIME.txt
Original file SHA-256: 29752299e90efe398ead5d7f8dc2b9a42d4b715918fe190820b7836051867080
Inclusive original lines: 1-200
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 | L: ACTUAL OLDER NATIVE FIELD/TIME CALLERS AND THEIR WHOLE KERNEL
000002 | 3 November2026. relational_logic. Entry plan95, Atlas923b6826d0d1905a1d420d18.
000003 | Canonical sources read only. No R106/R107, 96-matrix or K spin replay.
000004 | 
000005 | RESULT
000006 | 
000007 | The old v330 source has enough ACTUAL data to evaluate its complete
000008 | three-state field/time kernel, not merely its printed two-point decay.
000009 | That calculation is given below for every time, every cylinder and every
000010 | word in its entire original field alphabet. Its four-point response
000011 | retains the third spectral channel that its two-point function misses.
000012 | This is an original existing source block, not an additional CAR model.
000013 | 
000014 | For a genuinely coupled quantum-link/CAR caller, the best reviewed native
000015 | implementation is still v990: its four CAR modes, six-state quantum link,
000016 | interacting H_W0, actual beta, sources, adjoints and time are all explicit.
000017 | Its whole timed source was ALREADY solved in the Atlas and is reused here,
000018 | not recalculated as another96-dimensional result. The later v1013 route
000019 | already supplies a full Hamiltonian-class local dynamics and states.
000020 | 
000021 | Neither of these reviewed native constructors reads the complete original
000022 | S_adm action and produces the missing original charged boundary embedding
000023 | or its full slab insertion. That is a statement about their actual code
000024 | callers and scopes, not an assertion that P1 lacks a source or a global
000025 | all-corpus absence. The existing structured P1/full G/H/J results stand.
000026 | 
000027 | 1. READ THE RELEVANT ATLAS BEFORE SELECTING AN EXECUTION
000028 | 
000029 | Live research_state retained R107 and L20261103K. In particular, the
000030 | primitive full-action insertion is not relabeled as the supplied DET
000031 | parent; no autonomous16-cell premise is introduced. The exact existing
000032 | finding actual-native-v990-full-timed-words-recover-kubo-response-distinct-
000033 | from-instantaneous-variance was read with its registered original sources.
000034 | It already contains the whole coupled96H timed source and its Kubo reader.
000035 | Repeating that run would not answer the new original-field ancestry task.
000036 | 
000037 | Code discovery first tried the codebase-memory graph. The full canonical
000038 | verification project is not indexed there; its available projects are
000039 | subprojects. Targeted Atlas sources and filename/literal discovery were
000040 | then used. All decisive source passages below were read through read_source
000041 | with their current hash validation.
000042 | 
000043 | The requested label v867 resolves in current project_scope.json:1351,3163
000044 | to v867_radau_conditioning(.py), not a Fock/source quantization module.
000045 | There is no current verification/v867_ file in the checked working tree.
000046 | This is a navigation correction, not a theory exclusion or claim about
000047 | all historical archives.
000048 | 
000049 | 2. COMPLETE ACTUAL v330 SOURCE, CLOSED WITHOUT A NEW MEASURE
000050 | 
000051 | Literal functions symmetric_transfer() and correlator(), lines45-63, give
000052 | 
000053 |  v=(1,1,1)/sqrt3,
000054 |  u2=(1,-1,0)/sqrt2, u3=(1,1,-2)/sqrt6,
000055 |  P0=vv^*, P2=u2u2^*, P3=u3u3^*,
000056 |  lambda2=64/729, lambda3=1/729,
000057 |  D=diag(1,-1,0), T=P0+lambda2 P2+lambda3 P3.
000058 | 
000059 | The exact full transfer is
000060 | 
000061 |                  [1651 1267 1456]
000062 |  T=(1/4374)      [1267 1651 1456].                     (1)
000063 |                  [1456 1456 1462]
000064 | 
000065 | Every entry is positive and every row sums to1. The SAME original
000066 | H_OS=-log T, not another dynamics, gives for all t>=0
000067 | 
000068 |  K(t)=P0+(64/729)^t P2+(1/729)^t P3,                   (2)
000069 |  H_OS=6log(3/2)P2+6log3 P3.
000070 | 
000071 | In the original state basis this generator is
000072 | 
000073 |         [ log(81/8) log(8/9) -2log3 ]
000074 |  H_OS= [ log(8/9) log(81/8) -2log3 ].                 (3)
000075 |         [ -2log3    -2log3     4log3 ]
000076 | 
000077 | These are the given transfer/OS time units. They are not identified with
000078 | an external physical spacetime scale or a new CAR modular generator.
000079 | 
000080 | The original stationary open-boundary source has ALL cylinder weights
000081 | 
000082 |  q(i0,...,iN)=(1/3) product_(j=1)^N T[i_(j-1),i_j].    (4)
000083 | 
000084 | Summing the last index uses exactly sum_j T[i,j]=1 and gives the preceding
000085 | cylinder. Thus these actual weights are exactly compatible; no additional
000086 | moment/UI condition or gap argument is needed to obtain consistency of
000087 | these SAME cylinders. Equation(4) determines this whole finite-alphabet
000088 | stationary process. It does not reset the master S_adm partition function:
000089 | the normalization belongs to the already normalized original T,v caller.
000090 | 
000091 | More generally, for any original diagonal field letters A_j=p_j(D),
000092 | all ordered source words are exactly
000093 | 
000094 |  q(A1(t1)...Ak(tk))
000095 |     =v^* A1 K(t2-t1) A2 ... K(tk-t_(k-1)) Ak v.        (5)
000096 | 
000097 | Because D has three distinct eigenvalues, polynomials in D exhaust the
000098 | ENTIRE original diagonal C^3 field algebra. Equation(5) is therefore
000099 | the whole original field source, not a chosen small correlator subset.
000100 | For arbitrary finite source pulses it resums to the same expression with
000101 | A_j=exp(J_j D)=diag(exp J_j,exp(-J_j),1), an entire finite generating
000102 | functional. No new Hamiltonian term or source state has been selected.
000103 | 
000104 | There is a compact all-order formula for the literal original D itself.
000105 | Put g_j=t_(j+1)-t_j>=0. Odd words vanish. For k=2m,
000106 | 
000107 |  q(D(t1)...D(t_(2m)))
000108 |   =(2/3) lambda2^(g1+g3+...+g_(2m-1))
000109 |        product_(r=1)^(m-1) [ (2+lambda3^g_(2r))/3 ].   (6)
000110 | 
000111 | Proof: in basis(v,u2,u3),
000112 |  Dv=sqrt(2/3)u2,
000113 |  Du2=sqrt(2/3)v+(1/sqrt3)u3,
000114 |  Du3=(1/sqrt3)u2.
000115 | The odd subspace is one-dimensional. Every paired passage through an
000116 | even-time gap contributes (2+lambda3^gap)/3; every odd gap contributes
000117 | lambda2^gap. The two endpoints contribute2/3. This proves(6) for all
000118 | word lengths, including coincident insertions, not only the tested cases.
000119 | 
000120 | In particular
000121 | 
000122 |  C2(t)=(2/3)lambda2^t,
000123 |  q(D(0) D(0) D(t) D(t))=4/9+(2/9)lambda3^t.           (7)
000124 | 
000125 | The actual four-point source therefore reads the missing third channel
000126 | directly; it is not a Wick/product replacement of the two-point source.
000127 | At t=1 the latter value is0.4447492760249964. At equal times D^4=D^2,
000128 | so it is2/3 as it must be. The two-sided D susceptibility is1586/1995;
000129 | that value follows from the literal D normalization, not the prose
000130 | header's different displayed susceptibility number.
000131 | 
000132 | Execution used ONLY the actual native v330 functions and these exact
000133 | closed formulas. Native T versus(1), row sums and its correlator were
000134 | checked; the complete word formula was independently checked against
000135 | native matrix products at lengths1,2,3,4,6,8, including coincident times.
000136 | Exit0; largest word discrepancy2.78e-16. Saved observed data:
000137 | work/original_field_L/NATIVE-T3-KERNEL.json.
000138 | This extends the executable all-word evaluation of this actual old source
000139 | block. It does not identify it with the full original charged field source.
000140 | 
000141 | 3. ACTUAL NATIVE QUANTUM-LINK FIELD/TIME MAP ALREADY AVAILABLE
000142 | 
000143 | v990:47-59,75-86,132-177 provides a more elaborate genuine CAR caller:
000144 | 
000145 |  H_space=C^6_link tensor Lambda(C^4),
000146 |  c_alpha=I_6 tensor Z^tensor(alpha) tensor sigma_-
000147 |                      tensor I^tensor(3-alpha),
000148 |  n_alpha=c_alpha^*c_alpha, X=X_6 tensor I_16, Z=Z_6 tensor I_16.
000149 | 
000150 | The four modes are two species(Q,e^c) on two sites. Its build_H_W uses
000151 | the noncommuting quantum-link X and charged hopping Z; thus it is not a
000152 | frozen-link partial trace. The actual original choices are
000153 | 
000154 |  lambda_e=1, hopping=.7, mass=.5, mu_Q=.5,
000155 |  theta0=.7, beta=.35,
000156 |  source letters O_Q=n0+n1, O_Z=(Z+Z^*)/2, O_C=n2+n3.
000157 | 
000158 | These values, field order, adjoints and H_W0 are all supplied before the
000159 | thermal source is evaluated. The source at constant J is literally
000160 | 
000161 |  W(J,theta)=log Tr exp[-beta H_W(theta)+sum_j J_j O_j].  (8)
000162 | 
000163 | Its full mixed field/link time law is alpha_t(A)=exp(itH_W0)Aexp(-itH_W0).
000164 | The whole ordered source with the SAME H_W0 and its actual thermal
000165 | normalizer is already given in the accepted Atlas finding cited below.
000166 | Its static Hessian is the integrated Kubo response, not instantaneous
000167 | variance. All external link degrees of freedom remain; the pure CAR
000168 | commutant is M_6 tensor I_16. These earlier full-kernel and retained-rest
000169 | results are reused, not claimed as a new origin derivation here.
000170 | 
000171 | The actual script imports tfpt_constants for checks/constants; it does
000172 | not call a primitive S_adm slab/action constructor to obtain its c_alpha
000173 | or build_H_W. Its own header explicitly types(8) as a1+1D two-site
000174 | center shadow, not the4D generating functional. This pinpoints the
000175 | ancestry boundary in this reviewed caller without inventing a new gap
000176 | in the already supplied finite source itself.
000177 | 
000178 | 4. OTHER TARGETED OLD CALLERS: WHAT THEY ACTUALLY SUPPLY
000179 | 
000180 | v174:1-88 executes combinatorial CAR-cone/exterior state counts and
000181 | central-charge arithmetic. It supplies no c_i matrices, source slab or
000182 | interacting time constructor. Its16 seam Majoranas and separate4-corner
000183 | complex-fermion Fock count are not the16-complex-mode DET factor.
000184 | No theoretical g-theorem reading is re-audited or promoted here.
000185 | 
000186 | v972:1-55 explicitly inherits v529's fixed FK seam-toy fence. It has a
000187 | Majorana reflection/interaction/cut calculation, actual operator algebra
000188 | generation and a finite OS/GNS shadow. Its own header distinguishes the
000189 | full even-algebra generation from its degree<=2/4 Gram census. It does not
000190 | read the complete original S_adm to select that interaction class or
000191 | produce its physical Weyl source map. The original positive FK results
000192 | remain valid in their declared toy/census class; they are not rerun.
000193 | 
000194 | v1008's native assembly is dimension1024 with four representative charge
000195 | species, a four-state clock, a physical edge and a DET4 mirror. Its
000196 | original source states explicitly that the seam column couples to the
000197 | PHYSICAL Q density. The Psi clock is an order-four simple-current
000198 | analogue. The same original says no full Spin(10), no dynamical links,
000199 | and no full real-space seam theorem. Thus its nonzero mixed response is
000200 | an existing coupling result, not a complete quantum-link realization of