Conditional result
Normal spin lift and fermion response obey the same signed charge balance
In the question: Automated construction of operator maps and sources
New conditional common corollary of supplied family/lift,not P1 selection. Numbers become anomaly coefficients only under actual chiral1+1D field quantization; not an original Ward insertion calculation. Four A3 carriers are not four physical generations or a contradiction to original three-family construction. N×W index proves neither physical4D theory nor ΔB/L transitions. Dual-bundle formula Wm*=ΛoddE⊗⊕D^(−1−m) holds but supplies no actual OS domain/phase/RP map. Whole ordinary genuine heat pair of pure gauge conjugates Dg=MgD0Mg* is exactly zero; not transferred to Padm,marked insertions or unidentified original reflection-pair convention. Native clock,old Clifford/boundary states and whole positive sources retained. No stochastic rescan of settled loop classes. Local retention of the Yukawa seed in finite qM does not refute an upstream TFPT flavor derivation. Originals contain the hard holonomy formula; archived faulty D/P puncture display and existing analytic v117 C4/A4/S4 repair are already reviewed and reused,without claiming new D4 rigidity.
Read the exact result, assumptions and evidence
Result
Same supplied orbit family and existing September22 lift yield chW_m=64+(32+16Σm)x−16xy. For Σm=−2 normal family index has rank0 and ch=−16y. Split mA kernels are K+=2[Rodd⊗L+Reven⊗detV],K−=2[Reven+Rodd⊗Q],16modes each. Fully SM-equivariant Q is detV⊗L*,Y+.5; bare L* would haveY−.5. For commuting Spin10 charges q,signed quadratic mode sum is A_q=(Σm+2)Tr16q². Per-copy coefficients are Y:5/3+10m/3,T3:1+2m,SU3:1+2m and gravity8+16m. Same condition thus links algebraic natural lift to normal charge balance. Mathematical product index is−16d and weighted I_B=I_L=−4d. Conversely new origin identification of τ|winddet| with Dirichlet minimization fails exactly:gε=diag(exp(i[φ+εsinφ]),1) always costsτ but E=1+ε²/2. True HS loop energy has full Fourier equality class h exp(i sign(k)φP),but is an additional functional. Even one fixed hemisphere leaves all projector directions equivalent under unrestricted smooth other-disk gauges.
Required assumptions
- Given normal orbit family and four-copy natural spin lift
N=CP1_N and W=P(V) are distinct bases. Supplied SM color C=3_(Y−1/3) and V=2_(Y+1/2) carry E=C⊕(O_N1⊠L)⊕(O_N0⊠Q),Q=V/L=detV⊗L*. D=detE has normal degree1 and is SM neutral. For four integral m_j consider W_m=ΛevenE⊗⊕D^m_j; already proved natural joint lifts have Σm=−2. mA=(0,0,−1,−1) is only a supplied representative. Literal kernels use previously specified split vertical spin connection; virtual family classes persist under smooth variation. A1+1D anomaly interpretation needs actual quantization of these modes; N×W is not assumed physical spacetime.
- Given normal spin clutch,weak orbit family and U2 linearization
V=C² with actual SM action e^(it/2)U is supplied. N=CP1 normal spin sphere,W=P(V) separate weak orbit,L=O_W(-1) tautological,Q=V/L. Given degree-one clutch becomes explicit family g(w,φ)=e^(iφ)Pw+I-Pw,E=(O_N1⊠L)⊕(O_N0⊠Q),with split vertical connection and actual H1 domains. E8 application additionally retains named half-root λκ and mixed-carrier line j6. W is not assumed an already original physical parameter space; orbit/dual-section functor is tested as mathematical comparison.
- Actual full v252 gauge lift and original P2 comparison
Given the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed.
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Original evidence
- CLAUDE18-FERMION-INDEX-REVIEW.txt lines 1–148
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE18-FERMION-INDEX-REVIEW.txt
753096f719b3264f8d082f52c4128b433edf2f0dce45def8fc00c9419fbfbabc
- CLAUDE18-BOTT-COST-REVIEW.txt lines 1–104
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Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE18-BOTT-COST-REVIEW.txt
bf5fc5c50a88338917e40f37b0ec279c42a09add355adf2051c7e8c703a224b6
- CLAUDE18-CANDIDATE.txt lines 1–147
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Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE18-CANDIDATE.txt
7ab8de802d24df2eea6c2e6ca05d365cdc882f27867fb51c50d6f43dc6e22c04
- 012-subsection-bosonic-relative-index-and-higgs-selection.tex lines 84–94
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Original location and fingerprint
documents/archive--paper-latex--tfpt-42/sections/012-subsection-bosonic-relative-index-and-higgs-selection.tex
8140f7618b51292b8acf79fdc999cac9482842626ed07db4edb54dc91c9499d6
- PROOF.md lines 36–123
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Original location and fingerprint
experiments/theory-contracts/source-joint-spin-family-lift-20260922/PROOF.md
d3ae02543e90d840879808554816f923cc36cab52268a032d1ce29c2569f5bd2
- 008-source.tex lines 353–384
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Original location and fingerprint
documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/008-source.tex
aa2731355579b961ea9de47532cb0a4cb3db6e1c29e0f18965b517d1280d8d85
- C4-DESCENT-FINITE-MONODROMY.txt lines 1–180
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/C4-DESCENT-FINITE-MONODROMY.txt
b707e2d720a6dad3a74115b62f16d76077dfda3fe0d3eb8f0f8f76edaf5d7bd5
- C3-PAPER-INDEPENDENT-REVIEW.txt lines 1–36
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Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/C3-PAPER-INDEPENDENT-REVIEW.txt
a866494f4a88ab94cdc66bb97d824a6445fcb4e4a301c7807a373ba2fbc2c802
finding:normal-orbit-spin-family-index-and-signed-charge-balance