TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/ORIGINAL-HADM-FIELD-MAP.txt Original file SHA-256: 8a8cbf5d59055ccb060e6947d0c34449db9ccf6a95463104e9e8150a733fc52c Inclusive original lines: 1-180 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 | R107. Original source to sixteen mirror fields: derivation and source boundary 000002 | 3 November 2026. Entry: plan93, Atlas d85a2c73c21006679e506283. 000003 | 000004 | VERDICT 000005 | The primitive H_adm has NOT been evaluated on the native v1002 mirror fields. 000006 | No supplied DET parent was run or relabeled as that primitive generator. 000007 | The present result is an exact conditional reconstruction from the original 000008 | time derivation, plus a literal original-carrier calculation. It identifies 000009 | the unresolved field arrow precisely; it does not close that arrow. 000010 | No absence theorem for the entire corpus, no physical F1/IR completion. 000011 | 000012 | 1. ORIGINAL SOURCE DIRECTIONS ACTUALLY REVIEWED 000013 | 000014 | Source45 Boundary002:103-143 defines the operational seed 000015 | (A_loc,tau_t,Theta,omega,[u_Sigma],D_coll). 000016 | The time action tau_t and state are included as genuine structured data. 000017 | The displayed functor goes Seed -> spectral bordism, not the other way. 000018 | The completion/minimality map is not automatically an inverse reconstruction 000019 | of every local source word from a finite carrier representation. 000020 | 000021 | Source42 Primitive003:1-35,217-290 gives the one-sided operator datum, 000022 | the finite carrier restriction, the relative spectral seed and the physical 000023 | local net by invariant restriction. Almost-commutative factorization is 000024 | expressly a realization choice. Its Lorentzian corollary:398-403 gives 000025 | alpha_t(O)=exp(it H_adm) O exp(-it H_adm) after the declared closure. 000026 | Source42 Completion027:229-355 defines a master with Z_rel already as an 000027 | argument and splits its continuous stationarity conditions. This is not 000028 | a new explicit mirror source polynomial or an instruction H=master. 000029 | 000030 | Source45 QFT007:3-26 defines Z from the common S_adm and regulator; 000031 | :115-145 retains all higher action derivatives, not just a Gaussian part. 000032 | QFT005:144-160 differentiates W=log Z for truncated Schwinger functions. 000033 | Full reflected word moments use Z/Z[0] (or the equivalent sum over all 000034 | graded connected partitions), not one connected derivative alone. 000035 | QFT008:215-254 constructs the OS quotient, vacuum [1], and exp(-s H_adm) 000036 | from the full admissible Schwinger family under its stated hypotheses. 000037 | 000038 | The other transfer route was also checked: Source45 QFT004:110-156 000039 | specifies blocked C6 kernels, diagonal weights and the retained word 000040 | basis. :241-284 builds a parent from the Perron line and local penalties. 000041 | QFT005:2-40 writes parent domination with positive additional terms as 000042 | a hypothesis. These statements do not supply the action of that transfer 000043 | on the native v1002 c_i by naming its Perron vector or its gap. 000044 | The technical companion006:171-210 repeats the same OS construction; 000045 | it is not a second concrete mirror-field assignment. 000046 | 000047 | Navigation coverage: a literal H_adm spelling scan of documents/*.tex 000048 | recursively found39 matching files,27 with a nearby16/mirror/fermion/time/ 000049 | CAR keyword. This is discovery coverage only; it neither proves complete 000050 | semantic coverage nor absence of a differently named map. Decisive passages 000051 | above were read, not inferred from search summaries. Existing G/H/I/J, 000052 | R104-R106 and all source/state/time/reflection results are retained. 000053 | 000054 | 2. WHICH SIXTEEN OBJECTS THE ORIGINAL ACTUALLY IDENTIFIES 000055 | 000056 | Source45 Carrier002:188-301 gives Splus=Lambda_even(C5), dimension16, 000057 | with the explicit six Standard Model representation sectors and charges. 000058 | These are internal one-particle species components. Native v1002 constructs 000059 | the distinct CAR16 algebra on F=Lambda(Splus), dim F=65536 per cluster. 000060 | This second exterior construction is legitimate quantization. It does not 000061 | by itself assign each native cell annihilator to a concrete original 000062 | spacetime field, smearing, mirror polarization or charged field extension. 000063 | The coefficient vector 1 in Lambda^0(C5) is the neutrino species direction; 000064 | it is not the empty vector of the subsequent sixteen-mode Fock space. 000065 | 000066 | The required source arrow is a genuine unital CAR representation 000067 | iota: CAR16 -> original reconstructed field algebra, 000068 | with C_i=iota(c_i), its actual adjoints, smearing/transport, source legs, 000069 | reflection and time. In a linear field realization it would have the 000070 | form C_i=Psi(f_i) with the actual canonical CAR inner product and actual 000071 | mirror/carrier map. This notation supplies no choice of f_i. 000072 | Individual charged fields need not preserve the Gauss physical sector. 000073 | Their valid charged extension/intertwiners or invariant whole words must 000074 | be obtained from the original theory, not assumed to lie in A^G. 000075 | 000076 | 3. EXACT GENERATOR MAP WITHOUT AN AUTONOMOUS CELL ASSUMPTION 000077 | 000078 | Work at a finite bounded regulator first. More generally require a common 000079 | common form/core domain invariant under all matrix units and their 000080 | adjoints, on which the H products and time derivatives exist; unbounded 000081 | identities are interpreted on that core or as forms. Assume the actual 000082 | iota above is established; 000083 | this premise is NOT asserted for the original P1/mirror identification. 000084 | Let delta(A)=d/dt alpha_t(A)|0=i[H,A], with H=H_adm. 000085 | 000086 | Set P0=product_i(1-C_i^* C_i). For an ordered subset I let C_I^* be the 000087 | ordered creation word and C_I its adjoint, and define 000088 | E_IJ=C_I^* P0 C_J. 000089 | The exact CAR give E_IJ E_KL=delta_JK E_IL and sum_I E_II=1. 000090 | A unital finite matrix algebra representation gives Hspace=F tensor R, 000091 | E_IJ=|I>, as an OPERATOR on R, not a chosen number. 000093 | 000094 | Summing the ordinary commutator identity gives 000095 | sum_IJ delta(E_IJ) E_JI 000096 | = i [d H - 1_F tensor Tr_F H], d=65536. 000097 | Therefore 000098 | (1/(i d)) sum_IJ delta(E_IJ) E_JI 000099 | = H - 1_F tensor (Tr_F H/d). (1) 000100 | Proof: sum_IJ H E_IJ E_JI=d H; sum_IJ E_IJ H E_JI= 000101 | 1_F tensor sum_J H_JJ. No cyclic partial-trace shortcut is needed. 000102 | Every offdiagonal H_IJ, including H_F0, is thus determined by delta on 000103 | the actual field algebra; an unknown pure rest generator cannot hide it. 000104 | Equation(1) is an analytic identity, not an executed4^16-term computation. 000105 | No assertion alpha_t(CAR16) subset CAR16, or QHP=0, is used. 000106 | 000107 | There is a much shorter exact reader for the determinant coefficient. 000108 | Use the native ordered basis, C_i|F>=epsilon_i|F_without_i>, epsilon_i=+-1. 000109 | Then C_i P0=0 and 0, xi=P0 Omega/sqrt(p0) is an empty-sector SOURCE VECTOR. 000126 | If p0=0, unitality sum_J omega(E_JJ)=1 ensures some J with pJ>0. 000127 | Then xi=E_0J Omega/sqrt(pJ) satisfies P0 xi=xi. This is an insertion in 000128 | the SAME original source, not a new physical ground state or measure. 000129 | The vectors xi_I=E_I0 xi are orthonormal. Their actual complete OS word 000130 | kernel satisfies ; its negative derivative at0+ is 000131 | when those vectors are in the generator/form domain. 000132 | For arbitrary source words remove the OS nullspace and normalize the 000133 | Gram support before interpreting a matrix as H. These are rest-state 000134 | matrix elements, not a proof that H_F0 is scalar on all R. 000135 | The charged field/source admissibility condition of section2 still applies. 000136 | For comparison with real time, delta(C)=-i d_s[exp(-sH)C exp(sH)]|0; 000137 | inverse heat is only a suitable domain/form expression, not a bounded 000138 | unitary Heisenberg evolution or a shortcut around the full OS kernel. 000139 | 000140 | 5. ORIGINAL96 CARRIER CALCULATION ACTUALLY EXECUTED 000141 | 000142 | v252_full_finite_triple.py:63-116 defines P_g as all16 particle species 000143 | of family g inside the full96. It gives D_F=[[S,T],[T*,conj S]], 000144 | T_(nu_R,g;nu_R,h)=MR[g,h], with each Yukawa coupling L to R. 000145 | Let Q_g=1-P_g. Directly summing the actual matrix entries gives 000146 | 000147 | sum_g ||Q_g D_F P_g||_HS^2 000148 | = ||MR||_HS^2 + 2 sum_f n_f sum_(g!=h) |Y_f[g,h]|^2, (3) 000149 | n_u=n_d=3, n_e=n_nu=1. 000150 | 000151 | Only particle COLUMNS are selected: the Majorana contribution is T*, 000152 | not both T and T*. The MR3x3 norm coefficient is1, not2. 000153 | Root executed full_D for all90 real/imaginary coefficient directions 000154 | of its five actual3x3 inputs and formed the whole real coefficient Gram 000155 | with integer entries. Offdiagonal Gram0 and diagonal error0: weights 000156 | 6,6,2,2 for offdiagonal Yu,Yd,Ye,Ynu;0 for diagonalY;1 for each MR. 000157 | This covers the whole symbolic input class, not a physical random fit. 000158 | The saved original-carrier16-result.json records the actual execution. 000159 | 000160 | For example, the original nu_R,g column leaves its family with squared 000161 | norm sum_(h!=g)|Ynu[h,g]|^2 + sum_h|MR[g,h]|^2. 000162 | The naive one-family compression therefore loses actual original terms 000163 | whenever this expression is nonzero. D_F is an INTERNAL one-particle 000164 | operator, not H_adm on a mirror Fock cluster. Equation(3) is neither a 000165 | physical mass prediction nor an obstruction to an open coupled16-field 000166 | embedding. The existing whole P/Q source readers retain these couplings. 000167 | 000168 | 6. EXACT STATUS OF THE REQUEST 000169 | 000170 | [OMITTED: non-scientific conversation or execution metadata] 000171 | [OMITTED: non-scientific conversation or execution metadata] 000172 | [OMITTED: non-scientific conversation or execution metadata] 000173 | [OMITTED: non-scientific conversation or execution metadata] 000174 | [OMITTED: non-scientific conversation or execution metadata] 000175 | [OMITTED: non-scientific conversation or execution metadata] 000176 | [OMITTED: non-scientific conversation or execution metadata] 000177 | [OMITTED: non-scientific conversation or execution metadata] 000178 | [OMITTED: non-scientific conversation or execution metadata] 000179 | [OMITTED: non-scientific conversation or execution metadata] 000180 | [OMITTED: non-scientific conversation or execution metadata]