TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/neutral_moebius_source_20261029/COORDINATE-FIELD-TEST.txt
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000001 | FIRST LOCAL ALGEBRA TEST: SPECTRAL COORDINATES ARE NOT THE QUANTUM CURRENT NET
000002 | 29 October 2026. Exact scoped obstruction, not an all-P1 no-go.
000003 | 
000004 | The existing original source has bounded local Weyl groups U_s,V_t with
000005 |     U_s V_t=exp(2ist)V_t U_s   for every real s,t.
000006 | The actual compactly supported current profiles and their normalization are
000007 | already given in original-admissible-source-closure-20261025/
000008 | P1-W8-LOCAL-MAP-AND-TWOPOINT-TEST.txt and the reviewed Atlas finding
000009 | finding:local-current-phase-and-conditional-cyclic-p1-w8-image.
000010 | This is an operator identity, not an equal-dimension comparison.
000011 | 
000012 | Consider the ordinary almost-commutative coordinate branch used as the target
000013 | in verification/v250_dirac_triple_contract.py:6-10, A_sp a represented
000014 | subalgebra of C(M,End(E)), with finite positive rank N at each point. A
000015 | finite direct-sum internal algebra is included through a finite matrix
000016 | representation. The original boundary paper calls this a realization choice.
000017 | It is not inferred for every admissible A_+ merely from its smooth center.
000018 | 
000019 | There is NO unital complexlinear star homomorphism of the full displayed
000020 | Weyl system into this coordinate algebra. Indeed evaluate at any point x.
000021 | The images U_s(x),V_t(x) are invertible unitary NxN matrices. Taking their
000022 | ordinary determinants gives
000023 |     det(U_s(x))det(V_t(x))
000024 |       =exp(2istN)det(V_t(x))det(U_s(x)),
000025 | so exp(2istN)=1 for ALL s,t. Set s=1,t=pi/(2N); then -1=1.
000026 | The same argument applies in any local trivialization of End(E). It does
000027 | not require differentiability of the Weyl groups or a normal map.
000028 | 
000029 | Thus the direct candidate iota(W(f))=a_f in A_sp already fails before any
000030 | state, reflection, Hessian or coupling comparison. Cauchy spinor sections
000031 | and coordinate multiplication are not that quantum field representation.
000032 | An actual quantization of the coordinate geometry can have infinitely many
000033 | field degrees of freedom; it is NOT excluded by this argument.
000034 | 
000035 | Scopes to preserve:
000036 | * Only this continuous local Weyl system and the finite matrix-fiber target.
000037 |   Discrete Pauli/clock algebras can have finite-dimensional representations.
000038 | * The original physical A_loc in full Seedop need not be A_sp and is not
000039 |   excluded. A field embedding into that genuinely quantum algebra is the
000040 |   correct sufficient local-source question.
000041 | * A W8-only subalgebra image is not excluded unless it is separately proved
000042 |   to contain the displayed Weyl system. Do not impose the stronger entire
000043 |   current-net map on a physical claim that needs only a smaller observable.
000044 | * No universal absence statement about all geometries, all A_+, P1/P2 or
000045 |   the existence of the full theory is obtained.
000046 | 
000047 | Independent original-source/analytic review: /root/original_kernel_search
000048 | confirmed the all-N determinant proof and the exact scopes, and found no
000049 | previous reviewed matrix-fiber version in the Atlas. The old scalar-phase
000050 | and internal Hodge/coordinate exclusions remain different results.
000051 | 
000052 | Practical next step: test a proposed source image in the original quantum
000053 | local algebra, with the exact Weyl phase if full currents are claimed, then
000054 | its complete reflected word functional and original time. A spectral
000055 | reconstruction theorem for coordinates alone cannot be substituted for this
000056 | field map. No new source action or quantization has been introduced here.