TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/INDEPENDENT-HARDY-BMU-ALL-SIX-HOM-REVIEW.txt
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000001 | INDEPENDENT REVIEW OF THE ALL-SIX HARDY HOM FRAME AND COEFFICIENT ALGEBRA
000002 | 30 October 2026. Read-only review of the existing source calculation.
000003 | 
000004 | VERDICT
000005 | The two-end frame formula, the six common-frame matrices and the M3
000006 | coefficient-algebra conclusion are correctly typed in the stated scope.
000007 | I found no material mathematical error.
000008 | 
000009 | The result is restricted to the already given Phi=0, family-blind NS
000010 | Hardy source and its induced finite reader. It does not identify ordinary
000011 | matrix multiplication with multiplication of source fields, CAR operators
000012 | or physical insertions, and it does not make this response the whole
000013 | Yukawa matrix or a source-selection law.
000014 | 
000015 | 1. THE COMMON HOM FRAME IS FORCED BY BOTH ENDPOINTS
000016 | 
000017 | ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt fixes
000018 | 
000019 |   G=[g,c*g,c^2*g],             c:G -> G Pc,
000020 |   Pc=[[0,0,1],[1,0,0],[0,1,0]],
000021 | 
000022 | with column j carrying h_(-j). Therefore the input chart whose column zero
000023 | carries h_a is exactly
000024 | 
000025 |   G_a=G Pc^(-a).
000026 | 
000027 | This is a column transport in the existing differential frame. It is not
000028 | an independently chosen identification of three equal-dimensional fibers.
000029 | Since Pc is real orthogonal,
000030 | 
000031 |   G_a^(-*) G_a^(-1)=G^(-*) G^(-1).
000032 | 
000033 | For the fixed Phi=0 source, the tangential operator and V_h are family
000034 | blind. Hence the constant right factor preserves the transported H1_NS
000035 | domain, the Hardy projection, the graph isometry and the defect embedding:
000036 | 
000037 |   E^(a)=E Pc^(-a).
000038 | 
000039 | This step would not follow for an arbitrary fixed family-coupled Phi.
000040 | 
000041 | GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt fixes R*h_a^q=h_(a+1)^p. Thus p_b is
000042 | read by J E^(b-1), and a scalar cable matrix and a matrix in the one common
000043 | G frame obey
000044 | 
000045 |   Mscalar_ab=Pc^(b-1) Mcommon_ab Pc^(-a),
000046 |   Mcommon_ab=Pc^(1-b) Mscalar_ab Pc^a.
000047 | 
000048 | Both factors are necessary. Replacing this formula by a one-sided cycling
000049 | or by Ad(Pc) on one fixed matrix would lose the Hom(F_q,F_p) typing.
000050 | 
000051 | 2. SIX RESPONSES
000052 | 
000053 | The inspected replay records 54 entries: 12 signed continuous-root periods
000054 | and 42 support or eta-parity zeros. After the two-end frame transport its
000055 | six matrices are
000056 | 
000057 |   mu01 -> F,             mu12 -> omega^2 F,   mu20 -> omega F,
000058 |   mu10 -> N,             mu21 -> omega^2 N,   mu02 -> omega N,
000059 | 
000060 | where
000061 | 
000062 |   F=alpha E02+beta E21,
000063 |   N=-i(alpha E12+beta E20).
000064 | 
000065 | The maximum common-frame residual in the 65-digit result is
000066 | 5.30818374111834e-66. The two reverse periods were also independently
000067 | evaluated directly in ROOT-TWO-REVERSE-MU10-PERIODS-CHECK.json and agree
000068 | with -i times the corresponding old coefficients. Both alpha and beta are
000069 | nonzero; their ratio is the previously proved real nonunit value
000070 | I21/I02=-3.347597664025180155... . No phase fit enters this conclusion.
000071 | 
000072 | 3. EXACT COEFFICIENT ALGEBRA
000073 | 
000074 | For alpha beta nonzero set
000075 | 
000076 |   A=F^2/(alpha beta)=E01,
000077 |   B=-N^2/(alpha beta)=E10.
000078 | 
000079 | Then AB=E00 and BA=E11. With E22=I-E00-E11 one recovers
000080 | 
000081 |   E02=E00 F E22/alpha,       E21=E22 F E11/beta,
000082 |   E12=i E11 N E22/alpha,     E20=i E22 N E00/beta.
000083 | 
000084 | Their products give the remaining matrix units. Therefore the unital
000085 | coefficient algebra generated by F and N is M3(C), and its common complex
000086 | commutant is scalar.
000087 | 
000088 | The generating statement concerns F and N together. Their two squares
000089 | alone give only the embedded upper two-by-two block and do not generate
000090 | M3(C). HARDY-BMU-ALL-SIX-INPUT-READER.txt states the stronger conclusion
000091 | with the correct generators and does not make the squares-only error.
000092 | 
000093 | 4. EXACT SCOPE
000094 | 
000095 | The six matrices are responses to six already existing off-diagonal
000096 | induced inputs in the fixed finite reader. The M3 result is algebraic
000097 | accessibility inside their common coefficient chart. It is not a proof
000098 | that the original source supplies response words as composable physical
000099 | operations. Such a claim would require an original consumer that composes
000100 | the corresponding field or CAR insertions. The existing WEDGE, Clifford
000101 | and KO consumer applies linearly to each computed coefficient, which is
000102 | all that is used here.
000103 | 
000104 | FILES INSPECTED
000105 | 
000106 |   HARDY-BMU-ALL-SIX-INPUT-READER.txt
000107 |     SHA256 3f720735fa509cdb982309d9dbeb896250a9eb799d7081426892be3053acd6ff
000108 |   workspace HARDY-BMU-ALL-SIX-INPUT-READER.json
000109 |     SHA256 c3c6d6f6546d1e907cf7206ecb395a40daee5ec41de85aeff8c14518df7c2273
000110 |   workspace check_all_six_hardy_reader.py
000111 |     SHA256 803af8ae538995516b25a46d668a954e45f17f518102ecec9b2b7ff58901fb64
000112 |   ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt
000113 |   FUCHS-FRAME-INDEPENDENT-TRACE-REVIEW.txt
000114 |   GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt
000115 |   INDUCED-HARDY-DEFECT-BMU-FINITE-READER.txt
000116 |   HARDY-BMU-FIRST-NONZERO-ENTRY.txt
000117 |   HARDY-BMU-FULL-MU01-READER.txt
000118 |   F5-QP-REVERSE-HOM-KERNEL-REVIEW.txt
000119 |   ROOT-SIX-READER-HOM-AND-M3-CHECK.json
000120 |   ROOT-TWO-REVERSE-MU10-PERIODS-CHECK.json
000121 | 
000122 | No original, Atlas entry, ledger or previously pinned report was changed.