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Original ledger classification: Exact [E] operator identities (sympy) + [C] the kinematic fence

Recorded statement: The internal SU(2), kinematic separation at twistor level (one module, 17 checks, <1 s; discovery probe su2_internal_kinematic_probe.py 17/17, verdict SU2-KINEMATIC-SEPARATED; the first executed slice of gamma kill test (6)). THE…

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Paper context: input 5 tfpt 3 e8 audit bootstrap

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WOIT.SU2.KIN.01

Original ledger classification: Exact [E] operator identities (sympy) + [C] the kinematic fence

Original claim text

The internal SU(2), kinematic separation at twistor level (one module, 17 checks, <1 s; discovery probe su2_internal_kinematic_probe.py 17/17, verdict SU2-KINEMATIC-SEPARATED; the first executed slice of gamma kill test (6)). THE QUATERNION SPLIT [E]: on C^4 = H^2 the right multiplications close the (opposite) quaternion algebra exactly, and Woit's Euclidean structure IS an internal direction: rho_tw = right-j VERBATIM (v519/v565 conventions). THE INTERNAL ALGEBRA [E]: right-sp(1) is a 3-dim real Lie algebra with exact su(2) brackets preserving EVERY fiber of PT -> S^4 (trivial on spacetime; control: left-j moves a generic fiber). THE SEPARATION [E, the kill-test datum]: the internal su(2) commutes EXACTLY with the full spacetime quaternion action and the two algebras intersect in {0} -- kill test (6)'s KINEMATIC branch does not fire. THE CLOCK FACTORIZATION [E]: RHO4 = left-u o right-u with u = e^{i pi/4} EXACTLY (must-fail: neither factor alone); the ALE deck is PURELY spacetime-side (DECK4 = left-i) and RHO4^2 = DECK4 o right-i. THE BREAKING [E]: the complex-linear part of the internal algebra is exactly span{right-i} -- the Euclidean/complex choice breaks the internal SU(2) to U(1), and the v519 mark torsor is exactly {right-mu o sigma_std : mu in mu4}. OS COMPATIBILITY [E]: sigma_std fixes right-j, inverts the internal charge, and inverts both clock factors simultaneously. THE READING [C]: kinematic twistor level only -- the dynamical half of kill test (6) stays open and formally live on A_hol; consistent with (not derived) the electroweak reading. WOIT.OS.TWISTOR.01 does not move.

Original classification detail

SU2-KINEMATIC-SEPARATED: rho_tw = right-j; internal su(2) fiber-preserving, commutes with spacetime, intersection {0} (kill test (6) kinematic branch does not fire); clock = left-u o right-u exact; deck = left-i; broken to U(1) with mark torsor = internal mu4; 17/17 checks

Dependencies as recorded

WOIT.GAMMA.TOY.01; WOIT.BETA3.DUALITY.01; WOIT.THETA.FREE.01; v519; v565; v608; v615

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  • v616_su2_internal_kinematic.pyRegistered verification module · core
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    WOIT.SU2.KIN.01: das interne SU(2), kinematische Separation auf Twistor-Ebene — die erste ausgeführte Scheibe des letzten unberührten γ-Kill-Tests (6): auf ℂ⁴ = ℍ² ist **Woits euklidische Struktur wörtlich die interne j-Richtung** (ρ_tw = right-j, v519/v565-Konventionen); das interne su(2) (right-Sp(1)) erhält JEDE Twistor-Faser (trivial auf der Raumzeit S⁴), kommutiert EXAKT mit der gesamten Raumzeit-Quaternionen-Wirkung, Schnitt = {0}: **SEPARATION — der kinematische Zweig von Kill-Test (6) feuert nicht**; **DIE CLOCK FAKTORISIERT: RHO4 = left-u ∘ right-u (u = e^{iπ/4}) EXAKT** — Raumzeit-Halbviertel mal interner Halbviertel-Phase; der ALE-Deck ist rein raumzeit-seitig (DECK4 = left-i), RHO4² = DECK4 ∘ right-i; die komplexe Wahl BRICHT das interne SU(2) auf U(1), und der v519-Mark-Torsor IST die μ₄-Untergruppe des internen U(1) (∘ σ_std); σ_std fixiert die euklidische Struktur und invertiert die interne Ladung; dynamische Hälfte bleibt offen auf A_hol [C] (17 checks, <1 s)

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