TFPT scientific source excerpt Original repository path: experiments/theory-contracts/paper-source-reconstruction-20261025/PAPER-PRIMITIVE-SOURCE-SELECTION.txt Original file SHA-256: c3b3449113e952b4db209b35d2584c5bab3f131f6852250f8febb5d94eac268d 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. Conversation metadata and personal execution details are omitted where indicated. 000001 | PAPER PRIMITIVE SOURCE SELECTION 000002 | ================================ 000003 | 000004 | 25 October 2026. Targeted original-source audit. No Atlas, ledger or paper 000005 | source was changed. 000006 | 000007 | Verdict 000008 | ------- 000009 | 000010 | CONDITIONAL POSITIVE, WITH THE FIRST EXTRA PREMISE IDENTIFIED. 000011 | 000012 | The full operational seed is much stronger than the scalar P1 statement. It 000013 | already contains 000014 | 000015 | S=(A_loc,tau_t,Theta,omega,[u_Sigma],D_coll). 000016 | 000017 | Therefore, once a complete seed object is fixed, its local net, state, time, 000018 | reflection, seam class and collar operator are not still waiting to be chosen 000019 | from c3. This is the useful positive correction: a QWZ Hamiltonian may serve 000020 | as a regulator representative of that already supplied source. Its numerical 000021 | mass and holonomy parameters need not become new fundamental P1 constants. 000022 | 000023 | The current papers do not yet prove that the fixed QWZ strip is such a 000024 | representative. The first additional premise is the full graded one-particle 000025 | source and time identification 000026 | 000027 | the local seed contains a(f), a(f)^* and the full CAR relations, 000028 | 000029 | the one-particle boundary generator induced by D_coll 000030 | intertwines the free CAR one-particle generator K, 000031 | 000032 | alpha_t(a(f))=a(exp(i t K)f), 000033 | 000034 | together with the already isolated local, time and reflection covariant 000035 | embedding of the quotient CAR net into the operational seed. On the same 000036 | reconstructed representation, H>=0 and H Omega=0 then force 000037 | 000038 | omega restricted to CAR = omega_P, 000039 | P=1_(-infinity,0)(K). 000040 | 000041 | Thus the quasifree state is a consequence, not a second premise. The direct 000042 | proof and the essential full-CAR qualification are recorded in 000043 | GROUND-STATE-SOURCE-REDUCTION.txt. Without the operator and time 000044 | identification, neither unit spectral flow nor APS/Calderon nor the Quillen 000045 | determinant line selects that state. 000046 | 000047 | This distinguishes two statements which had been conflated: 000048 | 000049 | * fixed K -> one pure gauge-invariant quasifree ground-state symbol P; 000050 | * gap + chirality + reflection + SF=1 -> a unique K. 000051 | 000052 | The first is valid. The second is not established by the cited paper or by 000053 | v464. 000054 | 000055 | 1. What the original operational seed actually supplies 000056 | ------------------------------------------------------- 000057 | 000058 | The current archived source defines Seedop objects at 000059 | 000060 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/ 000061 | sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex 000062 | lines 103--143. 000063 | 000064 | Lines 105--119 put A_loc, tau_t, Theta, omega, [u_Sigma] and D_coll in the 000065 | object itself. D_coll is required to be first-order elliptic and reflection 000066 | regular. Lines 122--143 then construct the forward collar-completion functor 000067 | from a complete seed. Thus this theorem does not reconstruct a seed or a 000068 | quasifree covariance from SF=1. 000069 | 000070 | The same source, lines 269--306, claims a defect-minimal boundary datum. Its 000071 | proof obtains existence of a minimum from well-foundedness and identifies the 000072 | first positive defect as |SF|=1. It does not classify all minimizers or prove 000073 | that the minimized stratum has one unitary-equivalence class. The sentence at 000074 | lines 304--305 invokes the boundary reconstruction after the full datum has 000075 | already been supplied. Hence it cannot turn SF=1 into a unique D_coll. 000076 | 000077 | The one-sided boundary theorem is nevertheless useful. In 000078 | 000079 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/ 000080 | sections/001-section-primitive-core-and-carrier-interface-handoff.tex 000081 | lines 65--170, 000082 | 000083 | the fully specified D_+=gamma_n(partial_n+B_Sigma) has a Calderon projector 000084 | P_C, and iC=2P_C-1 gives its Cauchy-data polarization. This is canonical 000085 | relative to the complete elliptic boundary problem. It does not say that P_C 000086 | is the covariance of omega, that A_loc is a CAR net, or that D_+ was selected 000087 | by the seam class. 000088 | 000089 | The provisional APS role is stated even more explicitly in 000090 | 000091 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/ 000092 | sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex 000093 | lines 33--42 ("APS roles on the admissible branch"). 000094 | 000095 | APS_dom^prov is an analytic starting representative. The later Calderon 000096 | upgrade produces APS_dom only after the doubled operator D_b is known. APS 000097 | therefore fixes a boundary realization for a supplied operator; it does not 000098 | choose the operator or its CAR state from SF=1. 000099 | 000100 | 2. P1, spectral flow and Quillen carry less information 000101 | -------------------------------------------------------- 000102 | 000103 | The registered P1 source is 000104 | 000105 | paper-source:7b58a2b8767cacd98fa2feb4 000106 | documents/tfpt_1_architecture_e8/sections/004-source.tex:201--243. 000107 | 000108 | It fixes the one-sided Gauss--Bonnet normalization c3=1/(8 pi). It does not 000109 | specify A_loc, a one-particle Hilbert space, K, P, omega or a field insertion. 000110 | The paragraph immediately preceding the P1 box calls the identification 000111 | "single scalar two-point kernel = quasifree seam state" a premise merge which 000112 | is recorded, not claimed. 000113 | 000114 | Likewise SF=1 is an integer homotopy invariant of an operator family. It gives 000115 | net eigenvalue crossing, but not the eigenvalues, eigenvectors, localization 000116 | kernel or negative-energy projector of one representative. The operational 000117 | source itself consequently carries D_coll in addition to [u_Sigma]. 000118 | 000119 | The relative APS source states exactly what its package remembers: 000120 | 000121 | documents/archive--paper-latex--tfpt-42/sections/ 000122 | 041-section-relative-aps-and-superconnection-setup.tex:1--12. 000123 | 000124 | It starts with a declared pair (D,D_ref), seam boundary conditions and an eta 000125 | term for residual asymmetry. These are data about an already declared operator 000126 | pair. They do not invert the index and recover a unique pair. 000127 | 000128 | The Quillen material does not add the missing inverse. The original 000129 | determinant-line discussion at 000130 | 000131 | documents/tfpt_1_architecture_e8/sections/007-source.tex:70--99 000132 | 000133 | packages a U(1) determinant variation, counterterm and seam response. It is a 000134 | functional of an operator family after that family has been supplied. The text 000135 | also keeps the exact seam Quillen functional as ALPHA.QUILLEN.EXACT.01. A 000136 | determinant line records determinant curvature, phase and index information; 000137 | it does not determine the full spectral projector P or the local two-point 000138 | kernel. Thus APS plus Quillen plus SF=1 cannot replace the full CAR operator 000139 | and time identification. Once that identification is available, positive 000140 | energy removes the previously listed independent state premise. 000141 | 000142 | 3. The v463/v464 rigidity claim under the smallest decisive test 000143 | ---------------------------------------------------------------- 000144 | 000145 | The changelog statement is registered as 000146 | 000147 | paper-source:209c76fdd7ea6b363778966e 000148 | documents/changelog/sections/010-source.tex:272--308. 000149 | 000150 | It says v464 reduces the realization to one-particle data. That reduction is 000151 | correct: a quasifree CAR state is determined by its symbol P. The stronger 000152 | claim that the original invariants fix P does not survive inspection of the 000153 | actual checker 000154 | 000155 | verification/v464_seam_oneparticle_rigidity.py. 000156 | 000157 | The smallest test is simply to trace the checker's inputs and operator: 000158 | 000159 | * it accepts no D_coll, B_Sigma, P_C, SF class or QWZ Hamiltonian; 000160 | * lines 60--69 choose the separate critical chain h(k)=sin(k) and define 000161 | P_N by the occupation rule sin(k)<0; 000162 | * lines 103--111 verify only that this chosen 0/1 occupation matrix is a 000163 | Hermitian projection; 000164 | * the exact dispersion has zeros at k=0 and k=pi, so this chosen chain is 000165 | not the gapped K whose uniqueness the prose asserts; 000166 | * lines 136--150 compute a Hilbert--Schmidt norm on one fixed finite window. 000167 | Local-window finiteness is not the global Shale--Stinespring condition 000168 | P-Q Hilbert--Schmidt. 000169 | 000170 | Most decisively, v464 cites v426 for the assertion that K is fixed by gap, 000171 | chirality and reflection. But 000172 | 000173 | verification/v426_seam_lto_rp_kms.py:1--35,56--117 000174 | 000175 | constructs one finite-dimensional K satisfying reflection oddness, mu4 000176 | commutation and a gap. It labels the result "constructively satisfiable" and 000177 | states twice that it does not prove the continuum realization. It contains no 000178 | classification or uniqueness theorem for K. 000179 | 000180 | The earlier kernel checker is honest about the same boundary: 000181 | 000182 | verification/v113_quasifree_kernel.py:33--46,161--170 000183 | 000184 | proves that one supplied polarization determines one quasifree vacuum, while 000185 | marking the premise that the seam state is quasifree as recorded, not claimed. 000186 | 000187 | Therefore v464 establishes properties of one chosen symbol and illustrates 000188 | the Araki reduction. It does not prove that D_coll or SF=1 canonically selects 000189 | that symbol. The v463 holomorphic c=8 endpoint classification is unaffected; 000190 | it classifies the endpoint after the source realization has been furnished. 000191 | 000192 | 4. What remains positive for the QWZ source 000193 | ------------------------------------------- 000194 | 000195 | The microscopic theorem 000196 | 000197 | paper-source:7296b452273b7022082ac2e2 000198 | tex-artefacts/toe_research_20260909.tex:16--96 000199 | 000200 | is a valid source theorem for its declared regulator. It fixes the width-eight,