TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/DET16-ORIGIN-TEST.txt Original file SHA-256: 8fbb0d9da82e3a49c3ce1f6b0aa69a3034df059c6e891d2c3c0fbe3285dbf19b Inclusive original lines: 1-190 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 | R105. Original DET16 vertex origin: source decision and exact generator reader 000002 | 3 November 2026. Research application; no paper/ledger promotion. 000003 | 000004 | QUESTION AND SOURCE VERDICT 000005 | 000006 | The requested result is derivation of the same mirror vertex and all its 000007 | responses from the original TFPT source, not another successful evaluation 000008 | of a supplied parent. Preserve R104 and L20261102G/H/I in their full scope. 000009 | 000010 | The reviewed original provenance is explicit: 000011 | - v1002_spin10_mirror_projector.py:1-30,55-60,219-267 constructs the 000012 | determinant projector and supplies PHI=pi/7 as a probe parameter. 000013 | - spin10_det16_projector_probe.py:1-45 calls this an exploration testing 000014 | the number-violating vertex, not its derivation from the common source. 000015 | - det16_mirror_gap_theorem source001:42-77 defines the projector and calls 000016 | the finite identities inputs to that memorandum. 000017 | - thermodynamic_dynamics source001:57-111 defines the assembled class and 000018 | supplies the frozen term2(I-P) in its table. 000019 | - research_contracts source015:304-366 preserves Candidate typing and the 000020 | distinct scopes of later stability and filtered-wall results. 000021 | 000022 | Thus the literal Hamiltonian source contains DET16 BY ITS GIVEN TERM. 000023 | This selected derivation chain is not an independent S_adm/Z -> DET16 000024 | origin proof. It does not prove corpus-wide absence of another construction. 000025 | The common original source, geometrical transport, complete physical thermal 000026 | words, IR applications, and all solved compiler results are preserved. 000027 | 000028 | The actual Source45 QFT007:3-28 defines W_k using the complete S_adm and 000029 | its field tuple; it is not an explicit list of every fermionic vertex. 000030 | The lattice-action contract source017:153-238 contains a bilinear Dirac 000031 | term AND S_seam/top in a research demand; its later Hamiltonian decision 000032 | and thermodynamic class theorem remain part of the same passage. Neither 000033 | that demand nor one fixed bilinear fiber proves that all of S_adm has 000034 | fermion degree2. JOINT.txt:48-64 explicitly retains all additional original 000035 | vertices, full boson integration, determinant/Pfaffian and reference weights. 000036 | No global Wick rule or vanished primitive seam vertex is inferred. 000037 | 000038 | 1. COMPLETE TARGET GENERATOR ON THE ORIGINAL16 MODES 000039 | 000040 | Use the native CAR order, Omega=|0><0|, and 000041 | |phi>=(|0>+exp(i phi)|F>)/sqrt2. 000042 | Then the whole target is exactly 000043 | 000044 | H_DET=2I-P0-P16-exp(i phi)Omega*-exp(-i phi)Omega, 000045 | P0=product_i(1-n_i), P16=product_i n_i. (1) 000046 | 000047 | The off-diagonal transition alone is NOT the entire vertex. The diagonal 000048 | part is the unique squarefree polynomial 000049 | 000050 | I + sum_(m=1)^15 (-1)^(m+1) sum_(|A|=m) product_(i in A)n_i 000051 | -2 product_i n_i. (2) 000052 | 000053 | Its values are1 on N=0 and16, and2 on N=1,...,15. It contains occupation 000054 | degrees up to16, hence raw CAR degrees up to32. Each n_i has TWO letters. 000055 | This is a Hamiltonian polynomial, not automatically an unrenormalized 000056 | Euclidean action density. The exact source/transfer dictionary must carry 000057 | the distinction. The original v1002 unit-gap parent I-P and the v1013 000058 | coefficient2 parent have different clocks unless a supplied time map relates 000059 | them. No coefficient is fitted or derived by choosing a time unit here. 000060 | 000061 | The exact open heat transfer has 000062 | 000063 | =(1-exp(-2eps))exp(i phi)/2, 000064 | <0|T(eps)|0>=(1+exp(-2eps))/2, 000065 | =exp(-2eps). (3) 000066 | 000067 | The corresponding first derivatives are exp(i phi),-1,-2. These three 000068 | are NECESSARY tests, not sufficient to determine65536 squared matrix 000069 | entries. Exact whole-generator equality on the same carrier/domain and 000070 | same source insertions, state, time and reference gives equality of all 000071 | semigroup words. Alternatively every original unnormalized word/source jet 000072 | must agree; a single mismatch rejects the specific proposed identification. 000073 | 000074 | 2. DIRECT TOP-CHARGE READER, NO PHYSICAL U1 ASSUMPTION 000075 | 000076 | On a given16-mode Fock factor let N=sum n_i. Every matrix block has number 000077 | charge q=N_row-N_col in[-16,16]. For theta_l=2pi l/33, 000078 | 000079 | H_q=(1/33)sum_(l=0)^32 exp(-iq theta_l) 000080 | exp(i theta_l N)H exp(-i theta_l N). (4) 000081 | 000082 | The finite Fourier sum is exactly the charge projection because no two 000083 | of these33 integer charges differ by a nonzero multiple of33. In particular 000084 | the extreme block has one-dimensional input and output: 000085 | 000086 | H_16= Omega*. 000087 | For H_DET: H_16=-exp(i phi)Omega*. (5) 000088 | 000089 | With a rest Hilbert factor the coefficient is a REST OPERATOR, not 000090 | automatically a scalar; equality must retain its actual insertions/weight. 000091 | This gives the first concrete original coefficient to extract once the 000092 | same16-field/Padm/transfer map is provided. It replaces unstructured candidate 000093 | scans with a finite exact projection. It is not an evaluation of a source 000094 | whose actual16-field map has not been supplied. 000095 | 000096 | The diagnostic conjugations in(4) do NOT assume a physical U1 symmetry. 000097 | The original quarter average only selects q=0 modulo4, aliasing 000098 | q=-16,-12,-8,-4,0,4,8,12,16. Consequently C4 invariance permits the 000099 | determinant term but cannot choose its charge16 amplitude or its phase. 000100 | The diagnostic is not identified with the physical P1 clock. 000101 | 000102 | 3. WHOLE DYNAMIC-BOSON SHORT-TIME EXCLUSION IN ITS STATED CLASS 000103 | 000104 | Suppose H=sum B_a tensor M_a on these SAME16 CAR modes and an original 000105 | rest factor. Each M_a has number-charge bandwidth at most s; a raw CAR 000106 | degree bound r implies s<=r. The rest operators have no hidden action on 000107 | these16 modes and may fail to commute with one another. Finite regulators 000108 | are sufficient; otherwise state the common domains and required derivatives. 000109 | 000110 | Each H factor changes the selected occupation by at most s. Term by term, 000111 | 000112 | =0 whenever js<16. (6) 000113 | 000114 | This is an operator identity on the rest space. It survives every fixed 000115 | linear rest evaluation when the relevant derivatives/integrals are defined 000116 | and may be interchanged. It uses neither positivity, quasifree closure nor 000117 | conservation of particle number. Majorana pairs have s<=2 and are included. 000118 | For a bounded regulator ||H||<=M and s=2, 000119 | 000120 | |||| <= exp(eps M)(eps M)^8/8!. (7) 000121 | 000122 | All orders0..7 vanish. Order8 is only the EARLIEST POSSIBLE nonzero order; 000123 | it need not be nonzero. In contrast(3) has derivative exp(i phi) !=0. 000124 | Hence no exact equality of the same unfiltered open transfer near eps0 000125 | is possible in this class. A scalar reference quotient with a regular 000126 | nonzero value at0, or a regular common time map t(0)=0,t'(0)!=0, does not 000127 | turn zero first derivative into a nonzero off-diagonal first derivative. 000128 | Absolute diagonals/energy shifts still require original Z0/reference data. 000129 | 000130 | Full subsequent boson integration can make the fermion marginal non-Gaussian, 000131 | but cannot remove this zero if the open-kernel/rest-evaluation hypotheses 000132 | actually apply. A thermal interior correlator with e^-betaH already present 000133 | is NOT this unfiltered boundary transfer. A correlated or epsilon-dependent 000134 | boundary state, a different field map, effective high-charge Hamiltonian or 000135 | singular limit may leave this class; their actual derivation must be used. 000136 | 000137 | Projection requires particular care. P exp(-eps H)P and exp(-eps PHP) 000138 | are different constructions. If P fixes0 andF individually, their first 000139 | off-diagonal derivatives retain the zero in(6). For the compressed generator's 000140 | HIGHER powers, fixing those two boundary vectors alone does not preserve 000141 | the all-j bandwidth bound: P may mix intermediate occupation sectors. 000142 | That stronger statement needs filtration-preserving P, e.g. [P,N]=0. 000143 | No assertion of this property for the actual Padm is made here. 000144 | 000145 | This excludes a direct same-field low-charge identification, not the full 000146 | TFPT source, a topological effective interaction or the physical IR theory. 000147 | 000148 | 4. MINIMAL INSTANTON SUGGESTION CHECKED BEFORE ADOPTION 000149 | 000150 | The actual v1002 spin10_chiral_weights_doubled:624-629 gives16 even-minus 000151 | sign weights. For the root alpha=e1-e2, their coroot eigenvalues are 000152 | (w1-w2)/2: {-1:4,0:8,+1:4}. 000153 | Thus restriction to that root SU2 is four doublets plus eight singlets. 000154 | ONLY with a separately supplied4D Weyl index theorem and conventional 000155 | unit instanton charge does this give four chiral zero modes, not16. 000156 | This is not a new spacetime interpretation of internal indices. Charge4, 000157 | additional copies or another topology require an actual original source 000158 | map and still do not by counting supply(1)'s diagonals or coefficient2. 000159 | The primary lead Kikukawa, arXiv:1710.11618, is relevant to gauge-invariant 000160 | overlap measures with t Hooft insertions; its abstract retains a locality 000161 | issue. It is not being imported as a TFPT origin or a full4D closure. 000162 | 000163 | 5. EXECUTION AND CONSEQUENCE FOR FUNDAMENTAL WORK 000164 | 000165 | Native check_det16_origin.py runs with -B -OO and explicit raising checks. 000166 | Original65536D generator identity error0; Taylor operator errors through 000167 | order3 at most3.314e-17; native semigroup residual at most1.112e-16. 000168 | All65536 native diagonal entries match(2). Native charge support is exactly 000169 | {-16,0,16}; (5) error0. All33 Fourier charges tested with float residual 000170 | 3.308e-15. Actual root weights match section4. det16-origin-results.json 000171 | records hashes and scope. These are native operator controls; the all-class 000172 | short-time exclusion is analytic, not inferred from a finite sample. 000173 | 000174 | The requested complete origin is NOT established. Its first actual test 000175 | is the H_16 block produced by the original transfer construction on the 000176 | identified mirror fields, including real Padm action, seam/top terms, 000177 | gauge/rest operators, time, reflection, reference and all source legs. 000178 | Neither S_adm as an aggregate functional nor a nonzero16-point correlation 000179 | by itself is that Hamiltonian generator coefficient. Do NOT exponentiate 000180 | an action functional as though it already were H. 000181 | 000182 | The exact DET16 parent is one candidate, not a new universal F1 requirement. 000183 | Its exact origin may be proved, or a proposed exact map may be rejected. 000184 | An alternative original parent must be assessed on its actual whole source 000185 | and physical IR/chirality requirements. Symmetry, anomaly, equal ground 000186 | projector or scalar gap alone is not sufficient for common IR universality. 000187 | Do not introduce a freely chosen point contraction, instanton sector, 000188 | spectral flattening or fitted high-order term to make(1) true by definition. 000189 | Retain all52 completed F1 subtasks, full E8/clocks, memory/state/time/RP, 000190 | Yukawa/flavor/alpha and G/H/I. No new Lean or ledger/physical promotion.