TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/mixed-current-origin-20261014/P1-GAUSS-AXIOM-DECISION.txt
Original file SHA-256: 92b2e8a3b8f08fe651ddb09c32fa4aeae410d0e2baf3ae7f894f134f953d3d75
Inclusive original lines: 1-106
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 | UR.SEAM.MIXED_CURRENT_ORIGIN.01 -- 23 October 2026
000002 | Decision on the fundamental local observable algebra
000003 | 
000004 | REQUESTED VERDICT:
000005 | AUFGRUND KONKRET BENANNTER DEFINITIONSLUECKE UNENTSCHEIDBAR.
000006 | 
000007 | This is the verdict on whether the particular new parity-Gauss net is
000008 | forced, admitted as an alternative, or forbidden by the primitive P1
000009 | source. It is NOT a claim of logical independence established by two
000010 | complete P1 models. No new extension, spinor field or gauge model is built.
000011 | 
000012 | [OMITTED: non-scientific conversation or execution metadata]
000013 | 
000014 | Suspend the search for spinor operators, dressings, endpoint limits and
000015 | further sector/gauge constructions. Compare only the actual original
000016 | definitions with the ALREADY constructed parity-Gauss representation.
000017 | E8, its128fields and their target monodromies are not premises in this test.
000018 | The existing finite compiler and conditional constructions keep their scope.
000019 | 
000020 | 2. The original premises, without silently enlarging P1
000021 | 
000022 | S1: documents/tfpt_1_architecture_e8/sections/001-source.tex:67-80.
000023 | The literal P1 postulate states: one oriented seam, a primitive reflection-
000024 | positive boundary kernel, unit winding [u_Sigma]=1, and self-linking
000025 | normalization c3=1/(8pi). Its organizing index/angle identity is explicitly
000026 | not a derivation of that normalization. P2 is a different premise.
000027 | 
000028 | These are the smallest explicit original P1 clauses available for the
000029 | requested implication. No clause in that statement identifies a represented
000030 | local Z2 gauge group, its link generators or its Gauss-invariant net.
000031 | This observation alone is not a logical nonderivability theorem.
000032 | 
000033 | S2: documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/
000034 | sections/001-section-primitive-core-and-carrier-interface-handoff.tex.
000035 | For the stronger later boundary-data formulation, the supplied tuple is
000036 |   T_boundary=(A_+,H_+,D_+,J,Gamma,B_Sigma).                   (2.1)
000037 | Lines65-85 impose a regular center/smooth compact oriented boundary
000038 | manifold, a compatible selfadjoint tangential B_Sigma, product collar
000039 | D_+=gamma_n(partial_n+B_Sigma), and reflection regularity.
000040 | Lines191-261 define the primitive seam-even/gap projector P_prim from
000041 | the indicated boundary polarization, domain and relative operator.
000042 | Lines302-316 define the relative spectral action, and expressly say that
000043 | P_adm A P_adm is NOT a definition of the local operator net.
000044 | This stronger tuple must not be silently identified with the scalar P1
000045 | postulate alone; granting it still does not supply the missing comparison.
000046 | 
000047 | S3: same file, lines319-343, defines the local net as follows:
000048 |   A_E(O) is generated by local field insertions supported in O;
000049 |   OS reconstruction gives A_M(O);
000050 |   H_adm=Ran(P_adm);
000051 |   A_adm(O)={A|H_adm: A in A_M(O), A and A* preserve H_adm}. (2.2)
000052 | This is a restriction of a SUPPLIED local source algebra. It does not
000053 | specify the field-insertion map of this particular QWZ/register/Gauss
000054 | model, and it does not turn a remote string into a local source insertion.
000055 | 
000056 | S4: same source directory, sections/
000057 | 002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex:103-144.
000058 | The thinner operational seed is explicitly
000059 |   S=(A_loc,tau_t,Theta,omega,[u_Sigma],D_coll).             (2.3)
000060 | A_loc is an INPUT quasilocal Euclidean net. Its state is required to be
000061 | reflection positive and clustering, relative action finite, seam class
000062 | nontrivial, and collar generator first-order elliptic/reflection regular.
000063 | The stated functor has direction
000064 |   supplied operational seed -> induced boundary datum.
000065 | It is not an inverse theorem selecting a unique A_loc from the displayed
000066 | scalar P1 data or from an operator spectrum.
000067 | 
000068 | S4:219-243 defines D_seed(S)=D(C_seed(S));269-305 asserts minimal boundary
000069 | packaging. Even GRANTING that asserted boundary uniqueness does not supply
000070 | a support-preserving inverse of C_seed or identify this Gauss net. A
000071 | pulled-back defect is constant on any fiber of C_seed by its definition;
000072 | using it to distinguish seeds in such a fiber would require a further
000073 | faithfulness/classification theorem. No such fiber or pair of complete
000074 | seeds is constructed here. The prior source audit already records the
000075 | limited scope of the minimal-stratum argument; it is not rerun as a new
000076 | general countermodel theorem.
000077 | 
000078 | S5: documents/archive--tfpt-45--source_extracts--04_qft_source/sections/
000079 | 002-section-closure-theorems-from-the-admissibility-complex.tex:12-100.
000080 | The later selector is P_adm=P_prim P_sing P_Theta, with
000081 | P_sing=(1+Z_c+Z_c^2)/3 and P_Theta=(1+Q_Theta)/2. These are the stated
000082 | carrier color-center and determinant data. They do NOT, by their names,
000083 | identify the local parity Gauss generators below. In particular i_C,
000084 | Gamma, Q_Theta, matter parity and local Gauss generators are not identified
000085 | without an actual represented operator map.
000086 | Lines256-284 and the following Schwinger/OS source define reconstruction
000087 | from supplied local source derivatives and positivity hypotheses; they
000088 | do not identify the missing microscopic source arguments with link fields.
000089 | 
000090 | 3. What exactly was added in the existing Gauss comparison
000091 | 
000092 | The existing REGISTER-GRADE-LIMITS-GAUSS-AND-DIRAC.txt:112-235 uses
000093 |   G_x=(-1)^{n_x} tau^x_{x-1} tau^x_x,
000094 |   G_x psi=psi for every x,
000095 |   P_G=product_x(1+G_x)/2,                                (3.1)
000096 | and declares a gauge-invariant local observable net. Link qubits are
000097 | redundant kinematic variables, not extra physical dimension on the
000098 | specified total-even old register/matter carrier.
000099 | Its explicit onto isometry E proves
000100 |   E*E=1, H_G E=E H_old, W E=E Z,
000101 |   tau^x_a E=E F_[0,a].                                  (3.2)
000102 | The original QWZ coefficients and common reference are retained.
000103 | 
000104 | Those equations establish a concrete global representation comparison;
000105 | they contain no identification of primitive OS H_adm with Ran(P_G), nor
000106 | of primitive supported insertions with the declared local gauge generators.