Particle charges and anomaly cancellation in one family
Original ledger classification: Identity [E] (spectrum+anomaly+RG) + [C]/[O] (S-matrix)
Recorded statement: THE CARRIER HALF-SPINOR IS ONE ANOMALY-FREE SM GENERATION + THE SM RG (2026-06-21, TOE attack point 3): connects the discrete compiler to constructive 4D QFT, closing the spectrum+anomaly+beta sub-question exactly. [E]…
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Paper context: Research contracts
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CAR.SM.ANOM.01
Original ledger classification: Identity [E] (spectrum+anomaly+RG) + [C]/[O] (S-matrix)
Original claim text
THE CARRIER HALF-SPINOR IS ONE ANOMALY-FREE SM GENERATION + THE SM RG (2026-06-21, TOE attack point 3): connects the discrete compiler to constructive 4D QFT, closing the spectrum+anomaly+beta sub-question exactly. [E] 16=Lambda^even(C^5)=1+10+5; SU(5) c SO(10): 10+5bar+1 = one SM generation (Q,u^c,d^c,L,e^c,nu^c), 16 Weyl states. [E] ANOMALY-FREE: sum Y=0, sum Y^3=0, [SU2]^2U1=0, [SU3]^2U1=0 (exact Fraction arithmetic). [E] one-loop RG from the carrier content (3 gen + 1 Higgs): (b1,b2,b3)=(41/10,-19/6,-7); b1 numerator 41 = the EM-budget integer (v3/v159), b3=-(11-2 n_f/3) with n_f=2 N_fam. [E] NEG: dropping nu^c leaves an incomplete 15!=16 multiplet; a 4th family shifts b1 off 41/10 (N_fam=3 pins the RG). [C]/[O] the full Epstein-Glaser interacting S-matrix (v269/v271/v273) and the Yukawa sector stay open. Closes the spectrum/anomaly/beta layer; not the interacting S-matrix.
Original classification detail
[E] the 16=1+10+5 decomposition + the four exact anomaly cancellations + the one-loop (b1,b2,b3)=(41/10,-19/6,-7) + the N_fam=3 RG-pinning negative controls; [C]/[O] the full EG interacting S-matrix + Yukawa. A genuine closure of the carrier->anomaly-free-SM+RG sub-question; does NOT close the interacting theory.
Dependencies as recorded
CAR.SM.01; QFT4D.SPERT.03; v273; v159
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- Research contracts
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- 2026-06-21 (TOE-roadmap solver round: the SEAM.EQUIV.01 keystone certificate, the modular bedrock, the carrier [formula in source] SM closure, the gap-decoupled measure, and the sharpened hypergraph substrate: v308– v312)Research changelog; TFPT — Introduction and reading guide
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- How to read this documenttfpt 1 architecture e8
- How to read this documentArchitecture, E8 and the electromagnetic fixed point
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- Front matter / supportStandard Model and flavor structure
- Research Contract 1 — [formula in source]tfpt research contracts
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- How to read this documenttfpt 1 architecture e8
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v310_carrier_sm_anomaly.pyRegistered verification module · registry
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TOE attack 3 -- the carrier half-spinor IS one anomaly-free SM generation with the SM RG: 16=Lambda^even(C^5)=1+10+5 -> SU(5)<SO(10) as 10+5bar+1 = one generation; gauge-anomaly-free (sum Y=0, sum Y^3=0, [SU2]^2U1=[SU3]^2U1=0, exact) and reproduces (b1,b2,b3)=(41/10,-19/6,-7); a 4th family shifts b1, so N_fam=3 pins the RG. Closes the spectrum+anomaly+beta sub-question; the full EG S-matrix + Yukawa stay open
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