Established in scope
Quarter circle character does not select Gaussian defect connection
In the question: Automated construction of operator maps and sources
Given free scalar Gaussian defect line,fixed positive ell and constant α. Width4log2 is diagnostic,not physical scale. Projector connection is not asserted compulsory physical choice;no new time or exclusion of other originally specified connections. Original circle character remains correct. Whole coupled h time gives U_t=e^{ith}Ue^{-ith},not generally scalar2π closed clutch family. No native clock intertwiner or missing time in full operational Seed inferred.
Read the exact result, assumptions and evidence
Result
Existing scalar defect family Tφ=R−e^{iφ}U has periodic frame eφ,n=e^{iφn}y_n/||y||. Given circle action satisfies e^{itB}y(φ)=e^{itα}y(φ+t). Natural orthogonal-projector connection instead has〈eφ,∂φeφ〉=iμ and holonomy e^{-2πiμ},μ=〈n〉. Old allowed diagnostic control α=1/4,ell=4log2 gives μ=0.1855335532291087 and holonomy0.3940689714−0.9190808701i,not quarter phase. Exact rational partial sums and geometric tail bounds certify difference. Separately specified flat orbit transport still has circle phase+i;family equation does not select it as projector connection.
Required assumptions
- Relative unit seam on explicitly assigned collar faces
In existing product collar,test original relative unit gluing v1=Uv0 on an explicitly assigned pair of labeled faces. Scalar block has h e_n=(n+α)e_n and U e_n=e_(n+1),α=1/4 or3/4. Actual original Γ±-to-face assignment,orientation and three-cabled spin trace map are not assumed derived.
- Constant odd circle-source coefficient with existing sea and full boundary graph
In the existing Clifford chart on L2(S1,K) with finite K let h0=(-i∂theta+alpha)gamma,alpha=1/4 or3/4,gamma*=gamma,gamma²=I. Supply constant selfadjoint odd Phi,{gamma,Phi}=0,and V=-i gamma Phi,h=h0+V on common periodic H1. Compare given CAR sea projectors P_-(h0),P_-(h) and complete pure two-face projector G_ell(h),ell>0,including crossings. This is the existing source class with classical background, not physical selection from P1 or quantization of dynamic bosons.
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Original evidence
- DEFECT-TIME-PHASE-INDEPENDENT.txt lines 1–122
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DEFECT-TIME-PHASE-INDEPENDENT.txt
828d2d844d505b504da0466d9f6008c189df0d56a63be56e5ab9297e7c0b7d66
- CLAUDE25-CANDIDATE.txt lines 1–117
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE25-CANDIDATE.txt
5a7349f3040b85650865b152d4e8c13b54389e60a6fbb1435a6d6f9126bf2806
- F5-HARDY-SEAM-OPERATOR-REVIEW.txt lines 1–169
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/F5-HARDY-SEAM-OPERATOR-REVIEW.txt
6968c825edaf6454138c228949441a2d67ceae41a034037930f02aeebca8c017
finding:scalar-defect-circle-character-does-not-select-projector-holonomy