Established in scope
Original admissibility needs image membership rather than a positive half or mere commutation
In the question: Common clock sectors, quartic geometry and operational reconstruction
Source-reviewed definitions and necessary image test,not a new proof of all original analytic reconstruction theorems. Failure of u* invariance for P+ excludes only an additional claim that u belongs to the same admissible star algebra; membership is not assumed. Odd fields and complete neutral response words remain distinct.
Read the exact result, assumptions and evidence
Result
Original later P_adm is primitive seam/Cauchy and gap selection with color and determinant upgrades. It is neither P+(B_a) nor the rank1 EM projector. Historical u=M_z is clutching,not already a local observable. Actual line membership is P_adm R0=R0; commutation alone is insufficient. An original local or reducing image isometry suffices; global Hilbert equivalence is unnecessary.
Required assumptions
- Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
- Original admissibility and graded-source interfaces
v42 defines P_adm through primitive seam/Cauchy,gap,color and determinant conditions; v31 closure assumes an RP CAR kernel without identifying it with the old circle. v42 exp(W_k[J]) is a formal parent integral; spectral action, positive geometric marginal and full graded source are not equated. The separate eta term of the master functional is retained. Seek an original local image, not global Hilbert equivalence.
Original evidence
- 003-subsection-primitive-relative-spectral-dynamics.tex lines 1–200
Source checked at this snapshot
Original location and fingerprint
documents/archive--paper-latex--tfpt-42/sections/003-subsection-primitive-relative-spectral-dynamics.tex
8683d7459140a06d5e03a06adefd05bf7e6538356e4e4da4397133aa991b8fe4
- ADMISSIBLE-SPACE-HISTORY.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/ADMISSIBLE-SPACE-HISTORY.txt
d89f814974cc444eee62765a5106293da42069c0388a321027f70895341e966c
- ADMISSIBLE-SPACE-HISTORY.txt lines 201–400
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/ADMISSIBLE-SPACE-HISTORY.txt
d89f814974cc444eee62765a5106293da42069c0388a321027f70895341e966c
- ADMISSIBLE-SPACE-HISTORY.txt lines 401–600
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/ADMISSIBLE-SPACE-HISTORY.txt
d89f814974cc444eee62765a5106293da42069c0388a321027f70895341e966c
- ADMISSIBLE-SPACE-HISTORY.txt lines 601–612
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/ADMISSIBLE-SPACE-HISTORY.txt
d89f814974cc444eee62765a5106293da42069c0388a321027f70895341e966c
- DIRECT-DEFECT-CLOSURE.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/DIRECT-DEFECT-CLOSURE.txt
84a79c74da8b18387a3d2d8a9928e4a437a608120b52a46c7ede6392cf1128ff
- DIRECT-DEFECT-CLOSURE.txt lines 201–226
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/DIRECT-DEFECT-CLOSURE.txt
84a79c74da8b18387a3d2d8a9928e4a437a608120b52a46c7ede6392cf1128ff
finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation