TFPT scientific source excerpt Original repository path: experiments/theory-contracts/seam-positive-kernel-search-20261015/SOURCE-CHARGE-OBSTRUCTION-20261102.txt Original file SHA-256: 2765cb9284aee15fa6e84879fd6287e0a51b58778bfe0cd0c9e8e5c5dcdb7439 Inclusive original lines: 1-157 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 | R103. Source direction, central charge and the original field inventory 000002 | 2 November 2026. Scoped source application and search repair. 000003 | 000004 | 1. Actual question and original results retained 000005 | 000006 | The requested fundamental TFPT solution is not established by this report. 000007 | Keep the declared structured P1/P2 kernel and the existing common 000008 | Carrier/Padm -> S_adm/Z_rel -> OS/CAR -> Gamma chain. L20261102C-F retain 000009 | their explicit types: primitive spectral seed, bare integration action, 000010 | normalized conditional reader, full relative source and effective action 000011 | are related objects, not interchangeable names. 000012 | 000013 | The original E8 current calculation is already complete in its stipulated 000014 | realization, including192 signed mixed family transitions and64 diagonal 000015 | poles. Do not repeat it. R101/R102 and the original fourmark/three/five, 000016 | Clifford, clocks, flavor/Yukawa/alpha results remain in their stated scopes. 000017 | 000018 | This application concerns a proposed reverse route: can ordinary local 000019 | polynomials in the downstream matter fields themselves produce the 000020 | bosonic marked E8 spinor current under the SAME Spin10 action? 000021 | 000022 | 2. Exact all-word obstruction 000023 | 000024 | Let P be the physical Grassmann parity automorphism of the field algebra. 000025 | Let Z be the action of z^2=-1 in the kernel Spin10 -> SO10. These are 000026 | different named structures. Assume an actual common algebraic dictionary 000027 | with the following primitive field inventory: 000028 | 000029 | field P sign Z sign 000030 | Grassmann Spin10 spinor S+/- - - 000031 | bosonic tensor representation + + 000032 | 000033 | On S+ and its conjugate S-, z^2 acts as -I. On every representation that 000034 | descends to SO10 it acts as +I. Thus P and Z agree on all listed generators. 000035 | They agree on the whole generated *-algebra, since both preserve sums, 000036 | products and adjoints. Equivalently the tag homomorphism into Z2 x Z2 has 000037 | image contained in {(0,0),(1,1)}, at EVERY word length. 000038 | 000039 | If X is even, P(X)=X, hence Z(X)=X. A nonzero bosonic spinor current Y has 000040 | P(Y)=Y but Z(Y)=-Y. Consequently X cannot equal Y under an equivariant map. 000041 | 000042 | For bounded represented field algebras the fixed algebra of PZ is norm 000043 | closed. It is also weakly closed when the actions have the specified 000044 | normal/spatial implementations. For unbounded fields the same algebraic 000045 | claim concerns the stated common invariant domain; a new domain limit is 000046 | not assumed to exist merely from these tags. 000047 | 000048 | Equivariant derivatives, neutral insertions and multiplication by scalar 000049 | normalizations preserve the relation. Invariant normal ordering does too. 000050 | Relative reference/eta/Z0 factors cannot change the representation type 000051 | merely by being scalar factors. An actual change of domain, sector or 000052 | source field inventory must be supplied by its original map. 000053 | 000054 | This is an entire-class exclusion, not a finite search up to some word 000055 | length. It does NOT say that the full original P1 master has this inventory. 000056 | A genuine bosonic spinor/disorder field, or other off-diagonal primitive 000057 | tag, lies outside the hypothesis. Merely adding the target field does not 000058 | derive it from P1. A fermionic tensor primitive would also change the tag 000059 | inventory; it cannot be silently invented as a repair. 000060 | 000061 | 3. Actual carrier and root controls 000062 | 000063 | Carrier Source45 section006:192 gives S+ tensor family,16 times3=48. 000064 | v252_full_finite_triple.py:1-22,102-116 supplies particle/antiparticle96, 000065 | the actual Dirac/Yukawa/Majorana builder, J and finite gamma_F. The central 000066 | Spin action -I96 is transported from the spinor dictionary as an INPUT; 000067 | v252 alone does not construct all Spin10 generators. The checker verifies 000068 | its commutation with the actual D and antilinear J. Arbitrary fixed 000069 | Yukawas require no new full Spin10 dynamical invariance for this algebraic 000070 | central test. Do not equate gamma_F with physical field parity. 000071 | 000072 | The actual original v1_e8_glue.e8_roots returns112 integral roots and128 000073 | half-integral roots. With the original D5 marking, the latter split64+64 000074 | and carry the spinor central-square sign. The remaining112 roots plus8 000075 | Cartans give120. These are native source controls, not a reconstruction 000076 | of the physical P1 current from matter fields. 000077 | 000078 | The underlying current-type distinction was ALREADY proved: 000079 | finding:joint-spinor-not-source-coefficient, 000080 | seam-joint-conjugation-20261015/PROOF.txt:189-216. 000081 | The later CURRENT-LEVEL-CHECK.txt applies it to the actual v252 gauge 000082 | dictionary: ordinary complex S+ matter produces D5 level4 per generation, 000083 | not D5_1. The original ten real vector realization has level1. These are 000084 | reused results, not a newly discovered absence of every E8 construction. 000085 | 000086 | 4. Two decisive type tests for proposed shortcuts 000087 | 000088 | Clifford c(v) is an internal vector operator S+ -> S-, not a spinor field. 000089 | The scalar central action -I on S commutes with every End(S) operator, 000090 | including every Clifford polynomial. Internal exterior parity is not the 000091 | Grassmann parity of physical many-field insertions. A deck/reflection 000092 | factor with an unspecified intertwining action cannot fix this by name. 000093 | 000094 | For an invariant state omega and a charged field alpha_z(X)=iX, 000095 | omega(X)=omega(alpha_z(X))=i omega(X), so omega(X)=0. 000096 | In contrast omega(X*X) is neutral and may be strictly positive. The 000097 | appropriate nonzero-state test is the actual reflected OS two-point norm, 000098 | including its true adjoint/reflection and source support. RP alone gives 000099 | nonnegativity, not strict positivity or the module identification. 000100 | 000101 | 5. Existing positive theorem makes the actual source task smaller 000102 | 000103 | Reuse MATH.SEAM.ESERIES.SOURCE-RECONSTRUCTION.06, especially 000104 | e-series-source-reconstruction-20261024/SIMPLIFICATION.txt:8-110,118-164. 000105 | For a connected local unitary extension of U=V_D5 tensor V_A3 sharing 000106 | its conformal vector, a nonzero marked M_(1,1) already forces the entire 000107 | marked E8 extension, multiplicity one, vacuum correlations and conformal 000108 | dynamics. Its proof does not assume a separately chosen extension index 000109 | or exact module support. 000110 | 000111 | A useful immediate corollary of its complete four-support classification: 000112 | within THAT same class, any nonzero sector with odd D5 central class forces 000113 | one of the two oriented E8 extensions. The other supports {0} and 000114 | {0,(2,2)} have only even D5 labels. The marked orientation still needs its 000115 | original identification. This is reuse of the existing classification; 000116 | it does not derive U, the common conformal vector or source localization. 000117 | 000118 | Do not require full microscopic ALG-EXH merely to apply this smaller 000119 | conditional extension theorem. For the separate specified MMST collar, 000120 | the original later master has UGF and edge-projected TEL-a closed and 000121 | retains its stated local exhaustion hypothesis. That route is optional, 000122 | not a new universal prerequisite for the whole P1 source. 000123 | 000124 | The actual remaining source comparison is upstream of the matter readout: 000125 | identify a genuine original local insertion or sector map, then compare its 000126 | reflected norm, marked action, adjoint and time within the SAME given 000127 | source. Reconstructing the E8 current as an even polynomial of downstream 000128 | matter is excluded in the explicit inventory above. No demand is made 000129 | that every E8 current be a physical neutral3+1 observable. 000130 | 000131 | 6. Automatic search repair 000132 | 000133 | source_charge_checks.py implements the exact finite tag quotient and 000134 | native v252/v1 controls. Its assess_expression accepts only bounded JSON 000135 | expressions from the stated primitive/word grammar. It checks the actual 000136 | operator tags, rather than trusting the prose prediction. A proposed new 000137 | sector is explicitly unbound to the original source; its unknown tag is 000138 | overapproximated by all four tags. It never earns a physical proof flag. 000139 | This avoids falsely excluding a composite with a new fermionic tensor. 000140 | Clifford-vector-as-local-field is a type error and cannot count as a 000141 | matching candidate merely because unrelated check answers match. 000142 | This grammar is a scoped search class, not all possible original fields. 000143 | 000144 | The existing origin_hypothesis_search.py is extended with three fixed 000145 | checks and concrete expression assessment. No arbitrary generated code 000146 | or model-supplied command is executed. Nine curated controls now exist; 000147 | the new source catalogue runs its three relevant ones. 000148 | 000149 | The first actual two-round AI run matched all three boolean predictions 000150 | but continued to claim that the neutral scalar quarter current generates 000151 | the marked spinor. That claimed mechanism was not proved. The repaired 000152 | driver requires an explicit source expression and returns its separate 000153 | scientific source verdict. Matching booleans remain only scoped checks. 000154 | SEARCH-CHARGE-RUN-20261102.txt records the actual subsequent execution. 000155 | 000156 | No new Lean proof, original ledger promotion, physical measurement, 000157 | full TFPT solution or billions of enumerated candidates are claimed.