TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ALL-SIX-INDUCED-DOMAIN-AND-ALGEBRA-REVIEW.txt
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000001 | INDEPENDENT ROOT REVIEW: ALL SIX ORIGINAL INPUTS, ACTUAL INDUCED DOMAINS
000002 | 30 October 2026. Original source, state, normal reader and parameters retained.
000003 | 
000004 | 1. The first map has been checked at its actual source.
000005 | ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt:40-146 gives
000006 | G_j=g(omega^j w,h_(-j)), G(cy)=G(y)Pc, Pc e_j=e_(j+1).
000007 | The induction chart of L_a therefore has column j carrying h_(a-j):
000008 | G_a=G Pc^(-a). This is an isomorphism of the INDUCED rank3 base objects.
000009 | It is not a claim that the distinct individual L_a on C are isomorphic.
000010 | The existing metric G^(-dagger)G^-1 and boundary norm are retained because
000011 | Pc is unitary. FUCHS-FRAME-INDEPENDENT-TRACE-REVIEW.txt:37-100 retains the
000012 | same interior continuation and NS domain, including all marked corners.
000013 | CANONICAL-BRANCHED-SPIN-PULLBACK.txt:42-49 gives c*sqrt(dz)=sqrt(dz).
000014 | Since c fixes z, its action changes neither the NS half-frequency nor
000015 | the given Hardy projection. At Phi=0, h=A_NS gamma_F is family blind;
000016 | the same statement holds for the given whole graph and V_h.
000017 | 
000018 | GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt:21-25 fixes R*h_a^q=h_(a+1)^p.
000019 | An output in L_b^p is consequently read against J applied to the L_(b-1)^q
000020 | induction chart. Thus E^(a)=E Pc^(-a), JE^(b-1)=(JE)Pc^(1-b), and
000021 |  Mscalar_ab=Pc^(b-1) Mcommon_ab Pc^(-a),
000022 |  Mcommon_ab=Pc^(1-b) Mscalar_ab Pc^a.
000023 | This has TWO different endpoint maps; replacing it by Ad(Pc) is wrong.
000024 | It carries the original J and normal factor, not a newly invented action.
000025 | It is proved here at the stated Phi=0 kinetic reader, not arbitrary Phi.
000026 | 
000027 | 2. Independent direct evaluation of every entry.
000028 | At w=0 the actual G calibration is h=(-omega,-omega,+omega).
000029 | On q_s use h_a=h_(a-s); on p_k use h_b=h_(b-k), with the SAME calibrated
000030 | values transported by R. q_s meets precisely p_(s+1) and p_(s+2).
000031 | The q eta sign is negative for s=a,a+1, the p sign for k=b,b+1.
000032 | A positive product cancels with the odd z factor; negative product adds.
000033 | This checks 42 exact zeros among the six times nine entries.
000034 | For each of the remaining12 entries root separately integrated
000035 |  zeta0 sqrt(1+w/omega^(a+2))sqrt(1-w/omega^(b+2)) dw/(1-w^3),
000036 |  zeta0=-h_(a-s) h_(b-k) omega^(-a-b), k=r+1,
000037 | on its ACTUAL ray: angle5pi/6+2pi s/3 for r=s, or7pi/6+2pi s/3
000038 | for r=s+1. Each square root starts at1. CCW orientation reverses the
000039 | reader sign for diagonal rays relative to the previously proved mu01.
000040 | At65digits all six matrices agree with their stated common-frame formula
000041 | to less than1.5e-65. The independent reverse representative at60digits
000042 | also agrees without invoking the asserted C3 relation.
000043 | 
000044 | Write alpha=I02, beta=I21, X=[2cosh(ell_NS/2)]^-1. Factoring4X/pi and
000045 | the ACTUAL P_gamma,+, the common answers are
000046 |  (mu01,mu12,mu20) -> (1,omega^2,omega) F,
000047 |  (mu10,mu21,mu02) -> (1,omega^2,omega) N,
000048 |  F=alpha E02+beta E21,
000049 |  N=-i(alpha E12+beta E20).
000050 | The exact reverse phase follows from omega conjugate(alpha)=-i alpha
000051 | and the same relation for beta. The old exact common phase and continued
000052 | period beta=-alpha+pi(1-sqrt2)C are retained, not fitted from numerics.
000053 | These are images of six original inputs at this reader. Their two
000054 | dimensional linear span does not make the six global twist sectors equal.
000055 | 
000056 | 3. Exact finite coefficient accessibility.
000057 | F and N, together, generate M3(C) whenever alpha beta is nonzero.
000058 | The squares alone do not. Set A=F^2/(alpha beta)=E01 and
000059 | B=-N^2/(alpha beta)=E10. Then P0=AB, P1=BA,
000060 |  E02=P0 F/alpha, E21=F P1/beta,
000061 |  E12=P1 N/(-i alpha), E20=N P0/(-i beta), E22=E20 E02.
000062 | All nine matrix units follow even without separately adjoining identity.
000063 | A separate exact linear commutant calculation has dimension1. These
000064 | identities hold for arbitrary nonzero alpha,beta, not selected decimals.
000065 | 
000066 | SCOPE
000067 | This closes the entire six-input finite moment calculation in the given
000068 | original induced NS/Hardy reader and its complex coefficient algebra.
000069 | It does not identify products of compressed readers with compression of
000070 | original field products, choose a physical linear combination/coupling,
000071 | derive a whole Yukawa tensor, or turn this algebra into physical time.
000072 | The already given full source still carries its products, both boundaries,
000073 | state and reflection. Its original common insertion/consumer is the next
000074 | source comparison. No new state, free phase, weight or clock was supplied.
000075 | 
000076 | INDEPENDENT REPLAY OUTPUTS
000077 | ROOT-ALL-SIX-ACTUAL-READER-CHECK.json:54 entries,42 exact zeros,12 periods.
000078 | ROOT-TWO-REVERSE-MU10-PERIODS-CHECK.json:two direct reverse integrals.
000079 | ROOT-SIX-READER-HOM-AND-M3-CHECK.json:32 exact algebra/domain-map checks.