TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/BLOCKING-PATH.txt
Original file SHA-256: bb2b6ac13400c4267819de29189f00d006545fdff8c0acb80e4036757bbe05e3
Inclusive original lines: 1-200
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 | THE ACTUAL WEIGHTED BLOCKING AND INTEGRATION PATH
000002 | L20261102H, 2 November2026. Original-source continuation.
000003 | Entry Atlas e99ef15ca0af3a2090099835, plan87. Canonical unchanged.
000004 | 
000005 | RESULT
000006 | 
000007 | Two positive existing constructions must be used together in their actual
000008 | scopes, rather than requiring a bare spectral formula to survive every
000009 | elimination unchanged.
000010 | 
000011 | 1. The actual stationary transfer in v330 already defines an exactly
000012 |    compatible complete cylinder family for its given transfer fields.
000013 |    Its weighted marginal identity follows directly from the given
000014 |    stochastic T and stationary boundary vector, not from a variance test.
000015 | 2. The original whole-source caller has an exact unnormalized fiber
000016 |    integration with all exterior source legs and a tower rule. It carries
000017 |    the effective weight, determinant/reference factors and all induced
000018 |    higher interactions. For a fixed complete original source this gives
000019 |    the required weighted marginal equality exactly.
000020 | 
000021 | The old geometric theorem's D_Vn is called blocked and compatible, not
000022 | defined there as PDP. It is also not explicitly defined there as a Schur
000023 | or logarithmic effective operator. Do not substitute either reading by
000024 | guess. The existing full-source integration is the correct positive
000025 | operation when actual variables are eliminated. It does not require the
000026 | result to be the same bare Tr f(D_Vn^2) ansatz.
000027 | 
000028 | The full common field tuple remains the original phi of S_adm, including
000029 | its actual geometry/scalaron, gauge, common Higgs H, matter, constraints
000030 | and ghost components where those enter that caller. The v330 three-state
000031 | transfer labels are not silently identified with this entire tuple.
000032 | The existing G geometric/IR map and full U transport remain intact.
000033 | 
000034 | 1. A CONCRETE EXACTLY COMPATIBLE PRODUCER IS ALREADY IN v330
000035 | 
000036 | Freshly hash-read complete original:
000037 |  source:f15dfc8c547c01da89f1:1-136,
000038 |  verification/v330_qgamb_admissible_measure.py,
000039 |  SHA256 21cbeb2b96d9ee581da3a9c45be400d77d232730ba37bbb19cb4cec07fb5e5be.
000040 | 
000041 | symmetric_transfer42-53 supplies one fixed T, with the stated eigenvalues
000042 | 1,64/729,1/729 and v1=(1,1,1)/sqrt(3). Its actual matrix is exactly
000043 | 
000044 |  T=1/4374 * [[1651,1267,1456],
000045 |             [1267,1651,1456],
000046 |             [1456,1456,1462]].
000047 | 
000048 | Thus T_ij>0, T1=1, and pi_i=1/3 is stationary. No boundary state is
000049 | chosen anew: correlator56-61 already uses THIS stationary v1 on both
000050 | ends. Its full diagonal-field cylinder functional is therefore
000051 | 
000052 |  mu_n(i0,...,in)=(1/3) product_(j=0)^(n-1) T_(ij,i(j+1)).   (1)
000053 | 
000054 | On the actual finite counting space I_n, take the given stationary
000055 | endpoint-weighted w_n=(v1)_i0 (v1)_in product T. Its Z_n is1. Summing
000056 | the final site uses sum_j T_ij=1, and summing the initial site uses
000057 | pi T=pi. Hence for every bounded retained word F and m>=n,
000058 | 
000059 |  I_m(w_m F composed with p_mn)/Z_m=I_n(w_n F)/Z_n.          (2)
000060 | 
000061 | Retaining sites separated by b steps sums their intermediate fields
000062 | exactly to T^b. These effective transitions remain determined by the
000063 | same original T and satisfy (2). The semigroup identity T^(b+c)=T^b T^c
000064 | is the exact blocking composition. All bounded cylinder moments follow;
000065 | no new three-state model, fitted coupling or separate reference measure
000066 | has been introduced. This is an application of the already established
000067 | fixed-transfer result to the actual source file, not a fresh gap theorem.
000068 | 
000069 | This direct construction is stronger for this finite-alphabet family
000070 | than inferring projectivity from the script's susceptibility/variance
000071 | test. No new audit of that test is required to construct (1).
000072 | The normalization of (1) is the normalization already used by this
000073 | stationary transfer caller. It is not an assertion Z_ref=1 for the
000074 | different full geometric/matter generating functional.
000075 | 
000076 | The explicit local fields read in this script are the three transfer
000077 | labels and the diagonal observable diag(1,-1,0). Its full physical
000078 | application uses the original stated admissible-sector identification.
000079 | Equation(1) alone neither creates continuous H/g variables nor identifies
000080 | a different actual full-field algebra by a count of its dimensions.
000081 | 
000082 | 2. THE ORIGINAL WHOLE-SOURCE INTEGRATION ALREADY RETAINS EFFECTIVE WEIGHTS
000083 | 
000084 | The original QFT007:5-29 defines
000085 |  exp W_k[J]=integral_Hadm Dphi exp(-S_adm[phi]-V_k[phi]+J.phi),
000086 |  V_k=phi R_k phi/2,
000087 | followed by its stated Legendre/regulator procedure. The same original
000088 | QFT007:115-142 retains every S_adm^(n) as an interaction vertex in Gamma.
000089 | Thus this caller does not impose closure on one unchanged bare spectral
000090 | shape after integration.
000091 | 
000092 | Exact original:
000093 |  paper-source:f588a78cad85dd5237213db3:1-45,115-145,
000094 |  documents/archive--tfpt-45--source_extracts--04_qft_source/sections/
000095 |  007-subsection-renormalized-physical-and-scheme-readout-laye.tex,
000096 |  SHA256 9c1c587cbd61fc4034649d778d16f1ee0e8c1e1189885babb3d8148a6fe72d7c.
000097 | 
000098 | The existing complete original-source proof spells out the actual
000099 | operation at FULL-SOURCE-REGULATOR-PROOF.txt:60-89:
000100 | for an ORIGINAL supplied factorization, with its actual Jacobian,
000101 |  rho(dp,dq)=m_P(dp) r(p,dq),
000102 |  K_R(p;J_q)=integral_fiber(p) r(p,dq)
000103 |                          exp(-V_R(p,q)+J_q.q),
000104 |  Z_R[J_p,J_q]=integral m_P(dp) exp(J_p.p)K_R(p;J_q).       (3)
000105 | 
000106 | The entire exterior source J_q remains. Sequential integration obeys
000107 | the tower identity. With Berezin/signed weights the same operation is
000108 | the original ordered unnormalized fiber integration, not an invented
000109 | positive conditional probability. These formulas are already proven
000110 | with all source legs, higher vertices, scalar and reference retained.
000111 | 
000112 | Freshly read exact sources:
000113 |  research-source:7816b374a7515b08d57a537b:1-102,
000114 |  research-source:11363fc8655cdd14c912d9ce:177-232,
000115 |  FULL-SOURCE-REGULATOR-PROOF.txt,
000116 |  SHA256 589a9054dd0af97934ff572ad3a5e1b18d8a0e3ed9cfb848f450b509dbf48df0.
000117 | Its exact graded implementation retains arbitrary even densities, not
000118 | only quadratic ones. No new software or implementation is needed here.
000119 | 
000120 | 3. APPLY THAT ACTUAL OPERATION TO THE REQUESTED WEIGHTED IDENTITY
000121 | 
000122 | For an actual fine source m and its actual retained readout p_mn,
000123 | disintegrate its given integration operation over the SAME original
000124 | coarse base I_n, including its original Jacobian/orientation. Define
000125 | the induced weight by the original fiber operation,
000126 | 
000127 |  w_eff,n<-m(x)=integral_fiber(x) w_m(x,y) r_mn(x,dy).       (4)
000128 | 
000129 | Then for every integrable retained word F,
000130 |  I_n(w_eff,n<-m F)=I_m(w_m F composed with p_mn).
000131 | In particular Z_eff,n<-m=Z_m, and dividing gives exactly the requested
000132 | normalized identity. Keeping all discarded source legs gives the whole
000133 | version(3), so the statement is not only a two-point or Gaussian check.
000134 | Successive applications of(4) compose by the tower rule.
000135 | 
000136 | The existing R080 identity is precisely the condition that a separately
000137 | specified w_n already equals this effective weight up to its normalization:
000138 |  E_nu_m[w_m | p_mn=x]=(Z_m/Z_n)w_n(x).
000139 | We reuse that result. No old uniform-kernel/infinite-mass countercase is
000140 | repeated. On a nonprobability base use its actual disintegration as in(3),
000141 | rather than assuming a new flat probability base.
000142 | 
000143 | The same operation is applied SEPARATELY to the actual admissible and
000144 | reference full weights, on their actual common basis where supplied.
000145 | Thus their unnormalized integrals and the original ratio Z_adm/Z_ref
000146 | are retained; the exterior determinant/eta/reference factors are not
000147 | absorbed into an arbitrarily reset coarse normalization. At zero fibers
000148 | or complex weights keep the full kernel(4). S_eff=-log w_eff is only a
000149 | notation on a legitimate nonzero branch, not an extra measure rule.
000150 | 
000151 | Important distinction: fixed fine source m with fields eliminated is
000152 | not the same operation as changing the outer physical volume m itself.
000153 | For different outer volumes, w_eff,n<-m can depend on their boundaries.
000154 | Exact compatibility of those induced weights across all outer volumes
000155 | is not implied by (4) alone. A limit state supplies consistent restrictions
000156 | after its actual limit is taken; the independently reviewed v1013 route
000157 | uses that legitimate alternative instead of exact finite Gibbs projectivity.
000158 | Original full-moment projectivity and its local-integrability consequences,
000159 | where already proved, are retained and are not requested anew.
000160 | 
000161 | 4. ACTUAL FERMION BLOCKING: EFFECTIVE OPERATOR PLUS EXTERIOR FACTOR
000162 | 
000163 | The existing implementation joint_source.schur_source99-113 returns
000164 | BOTH the effective kinetic matrix and the interior determinant:
000165 |  K_eff=K_bb-K_bi K_ii^-1 K_ib,
000166 |  scalar=det K_ii.
000167 | The actual original proof derives the pair by ordered Berezin integration:
000168 |  det K=det K_ii det K_eff, (K^-1)_bb=K_eff^-1.
000169 | With discarded fermion source legs retained, the effective source also
000170 | contains bar_eta_i K_ii^-1 eta_i and the corresponding shifted retained
000171 | legs. Thus even the Gaussian operation is more than compression K_bb.
000172 | At singular K_ii retain the original unnormalized complementary-minor
000173 | polynomial; the inverse chart does not authorize deleting zero modes.
000174 | 
000175 | Graph-first function discovery and exact code snippet were read at
000176 |  experiments/theory-contracts/seam-collar-multifield-20261016/
000177 |  joint_source.py:99-113.
000178 | Hash-read original proof:
000179 |  research-source:6e712a71a2fb68462ed31a33:271-326,
000180 |  seam-collar-multifield-20261016/PROOF.txt,
000181 |  SHA256 3537a2b080df0bb8b5d30c73da7dd83dc8e1ae5a6cfea4bb48a8b99f0080dfce.
000182 | The proof states its kinetic/pairing assumptions and keeps the distinction
000183 | between a mode partition and the original geometric boundary cut.
000184 | 
000185 | Later exact original carrier/complement formulas preserve the same data:
000186 |  A=I-zC, Q=I-F,
000187 |  S_F=A_FF-A_FQ A_QQ^-1 A_QF,
000188 |  det_rel(A',A)=det(S'_F S_F^-1)det_rel(A'_QQ,A_QQ).
000189 | Both the Schur term and the exterior relative determinant come from the
000190 | SAME given source. They introduce no new kernel or state.
000191 |  research-source:411120cbda538239f28969b7:194-220,
000192 |  KMS-AND-CARRIER-TRANSPORT.txt,
000193 |  SHA256 9efcfb0d68e16db842aab97b7171b2d667e7b065cb4c6ab8138102acc4c8fb68;
000194 |  research-source:f9cac57a5ac6adf6ca4739a2:568-646,
000195 |  GRADED-DETERMINANT-SOURCE.txt,
000196 |  SHA256 9cadaa53b70ebb666109f9cc7a02c07292a6faacf03eae79bf3d235682bf6952.
000197 | 
000198 | In the existing conditional CAR chart there is a related exact STATE
000199 | restriction: C_b=P C P and h_eff=log((I-C_b)C_b^-1)/(2ell), with the
000200 | actual given face/scale convention. This is the reduced quasi-free