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: 11-91
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.

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/