TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-U6-TRIALITY-SECTOR-SELECTION-REVIEW.txt
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Inclusive original lines: 1-153
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | ORIGINAL U6: JOINT TRIALITY/SHEET CHARACTER AND PHYSICAL SECTOR SELECTION
000002 | Independent narrow source/code review, 30 October 2026.
000003 | No original/pinned-file change, Atlas write, new search class or suite run.
000004 | 
000005 | VERDICT
000006 | The originals ALREADY DECLARE the quark/lepton leading CP readings rho and
000007 | rho^4, hence the common triality omega^2 and opposite sheet signs. Once
000008 | that readout assignment is assumed, the actual positive product U6 has
000009 | unique rank-one joint projectors. No further Fourier-phase choice is needed.
000010 | 
000011 | What v233 does NOT do is derive this assignment as an action on the original
000012 | local fields or on their source insertions. Its code inserts exponents1,4
000013 | and checks their arithmetic. The strongest later 'phase origin' and
000014 | 'Galois-forced' checkers inspected also insert the same values. The genuine
000015 | mixed-spin realization of U6 remains positive and is not undone by this
000016 | source-use distinction.
000017 | 
000018 | 1. THE CODEGRAPH AND ACTUAL v233 DATA FLOW
000019 | 
000020 | The graph-first query for verification/v233_cp_triality_phase.py returned
000021 | 'project not found or not indexed' for the parent repository. The known
000022 | original files were then read directly; no alternative project was invented.
000023 | 
000024 | verification/v233_cp_triality_phase.py:
000025 |  43: imports only check,summary,reset,N_fam from project constants;
000026 |  50-52: explicitly defines scalar rho,omega and sheet=-1;
000027 |  54-64: checks mu6 factorization and the three supplied cusp weights;
000028 |  66-79: explicitly assigns q_fam,q_sheet=1%3,(-1)^1 and
000029 |         l_fam,l_sheet=4%3,(-1)^4, then checks equal family/opposite sheet;
000030 |  81-89: checks an order-three factor of the order-thirty arithmetic;
000031 |  91-97: scalar negative controls and N_fam=3.
000032 | There is NO U6 matrix, v252 input, physical field, source insertion,
000033 | Yukawa/Majorana operator, source state, time or quark/lepton representation
000034 | map in this checker. In particular the q/l variable names at68-69 are
000035 | not obtained from the actual SM source labels.
000036 | Its own status35-39 explicitly retains the physical CP derivation as [C].
000037 | SHA256 43b34998aa882f2207fc1ebaa74b67cf157a5c8de977a62afa363d8f0284b94c.
000038 | 
000039 | The first six-cycle matrix in v231_cp_mu6_phases.py:68-72 is the valid
000040 | regular shift. But its quark/lepton phases are already inserted at55-66;
000041 | the only U6 test is its characteristic polynomial. Its scope33-38 retains
000042 | physical CP as conditional. SHA256
000043 | 9e3567f184de3b5ec14f21df3c969d89bf3953d69edc288c29a3b564ccad3b26.
000044 | All these arithmetic checks would give the same results if the proposed
000045 | physical source intertwiners were absent or attached to different sectors:
000046 | those intertwiners are not inputs to any checked expression.
000047 | 
000048 | 2. ACTUAL ORIGINAL PHASE RULE VERSUS OPERATOR INSERTION
000049 | 
000050 | The original v29 phase grammar explicitly separates the issues:
000051 |  documents/archive--paper-latex--tfpt-v29/sections/
000052 |  003-subsection-flavor-and-the-phase-grammar.tex:3-29.
000053 | It proves the global SM quotient but calls the physical realization of the
000054 | six-point CP grammar conjectural. SHA256
000055 | 245bd862d8189b6c805964c83b0e56b374f890991d67a10c388da24e3740ccfc.
000056 | 
000057 | documents/tfpt_5_redteam/sections/002-section-outcome.tex:234-249 states
000058 | rho^1 for the quark leading phase and rho^4 for the lepton phase, together
000059 | with v231/v233 factorization. It ALSO retains physical derivation as [C].
000060 | These existing recorded readouts must be preserved; they are not missing
000061 | numbers that need rediscovery. The question is their source-operator origin.
000062 | 
000063 | The actual later source consumer is different from a Fourier projector:
000064 |  archive--tfpt-45--source_extracts--03_em_flavor_source/sections/
000065 |  003-subsection-discrete-phase-operator-and-transport-grammar.tex:3-13,61-84,
000066 |  defines U6 and reads CKM as arg tr Pi_triangle(nabla_F^star).
000067 | Its structural kernel at90-124 uses Pstr D_f^*D_f Pstr. Neither place
000068 | equates U6^4 with a universal family-center insertion, or U6^3 with the
000069 | quark/lepton source grading. The checked positive-kernel limitation is
000070 | already finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable;
000071 | ORIGINAL-HOLONOMY-E0-SOURCE-REVIEW.txt:499-579 is reused, not rederived.
000072 | 
000073 | 3. THE STRONGER OLD CLOSURE CANDIDATES DO NOT SUPPLY THAT MISSING MAP
000074 | 
000075 | v316_galois_readout.py:56-61 explicitly inherits v231/v233's conditional
000076 | physical phases. v320_galois_cp_relation.py:48-63 inserts ckm=pi/3 and
000077 | pmns=4pi/3 before checking their difference and multiple. It establishes
000078 | the exact relation for those specified branches and its falsifiable readout;
000079 | it does not calculate which field receives the two characters.
000080 | 
000081 | The strongest apparent alternative was checked rather than overlooked:
000082 | v405_seam_equiv_omega.py:1-12,34-46 calls SEAM.EQUIV.02 a named conditional
000083 | contract, not a closure. Its phase test92-100 inserts delta_pmns=4pi/3.
000084 | v406_pmns_phase_origin.py:53-75 likewise sets delta=4pi/3 and verifies
000085 | delta=4*(pi/3). No CM field-to-insertion intertwiner occurs in that test.
000086 | These are valid conditional CM/readout consistency statements, not the
000087 | desired independently evaluated source rule. In the original text,
000088 | tfpt_2_standard_model/sections/006-section-neutrinos.tex:50-59 states the
000089 | keystone reading conditionally, while112-120 still distinguishes assembled
000090 | phase from an M_nu/D_F operator output. Both passages must be retained.
000091 | 
000092 | 4. EXACT CONSEQUENCE ON THE NOW GENUINELY REALIZED U6
000093 | 
000094 | Reuse MIXED-SPIN-PRODUCT-U6-SOURCE-REVIEW.txt. On V_ab, a!=b, the actual
000095 | product pullback sends (a,b)->(b+1,a+1). Thus its third power exchanges
000096 | (a,b) and(b,a), and its fourth power translates both labels by+1.
000097 | These are actual source-geometric actions. They do not label the sectors
000098 | as quarks or leptons. The q_a point name is not the quark field label.
000099 | 
000100 | Put T=U6^4 and S=U6^3. Then T^3=S^2=I, TS=ST and U6=TS.
000101 | The already specified joint character gives, without another phase choice,
000102 |  P_F=(I+omega T+omega^2 T^2)/3,
000103 |  P_q=P_F(I-S)/2, P_l=P_F(I+S)/2.
000104 | On the regular six-cycle these are orthogonal rank-one projections and
000105 |  U6 P_q=rho P_q, U6 P_l=rho^4 P_l.
000106 | This is a correct conditional selection theorem, not an extra hypothesis
000107 | that Fourier eigenvalues exist. The remaining premise is the original
000108 | physical sector assignment to T=omega^2 and S=-1/+1.
000109 | 
000110 | The existing SPIN-PRODUCT-CAR-U6-TRANSPORT-REVIEW.txt also matters here:
000111 | raw ordered CAR pairs carry -U6, whereas ordinary geometric products carry
000112 | U6. Their fourth powers agree but their cubes have opposite signs. The
000113 | already proved alternating orbit intertwiner carries this difference
000114 | exactly; it introduces no new fitted phase. Dropping that map would flip
000115 | the sheet labels when passing to the actual ordered pair insertion.
000116 | 
000117 | 5. THE ACTUAL P2 LABELS GIVE A PRECISE NEXT COMPARISON
000118 | 
000119 | [OMITTED: non-scientific conversation or execution metadata]
000120 | [OMITTED: non-scientific conversation or execution metadata]
000121 | [OMITTED: non-scientific conversation or execution metadata]
000122 | [OMITTED: non-scientific conversation or execution metadata]
000123 | [OMITTED: non-scientific conversation or execution metadata]
000124 | [OMITTED: non-scientific conversation or execution metadata]
000125 | [OMITTED: non-scientific conversation or execution metadata]
000126 | 
000127 | There is even a concrete color-based grading on this GIVEN matter module.
000128 | With the standard C2(3)=C2(bar3)=4/3 normalization, set
000129 |  S_col=I-(3/2)C2(SU3_color).
000130 | It is -I on every quark piece and +I on every lepton piece. No charge fit
000131 | is needed. IF the supplied family-center action Z_F=omega^2 I3 is used
000132 | on the positive chiral family module, Z_F S_col has exactly rho/rho^4.
000133 | This constructs the possible target reader from already proved labels.
000134 | It does not identify the geometric S,T with these two target operators.
000135 | The conjugate chiral module carries the conjugate family-center character.
000136 | 
000137 | The original carrier seam involution is not an automatic replacement:
000138 | tau=diag(-I3,+I2) on E has Lambda_even(tau)=-1 on BOTH Q and L,
000139 | and +1 on BOTH u^c and e^c. This smallest weight test rules out that
000140 | particular substitution for S_col; it excludes no other physical source map.
000141 | Similarly color triality and family triality are different actions.
000142 | A scalar phase on a matter field is also not yet the rephasing-invariant
000143 | CKM or PMNS phase; the original triangle/Yukawa consumer must be retained.
000144 | 
000145 | The smallest decisive source test can now be written without unknown
000146 | Fourier phases: for the actual relevant insertion/readout map J require
000147 |  J U6^4=Z_F J, J U6^3=S_col J,
000148 | with the proved signed geometric-to-CAR comparison, all original charge
000149 | labels, and its given source products/state/time. The original sources
000150 | inspected supply no such J. Its construction, not another cyclotomic
000151 | factorization or eigenvalue scan, is the next necessary origin step.
000152 | This is a bounded source-review conclusion, not a universal no-go or a
000153 | request to choose a new state in the already complete operative Seed.