Established in scope
Original five source inputs are excitations, not the clustering vacuum for this time
In the question: Automated construction of operator maps and sources
Fixed original CAR time and admissible eight-arc word; the P1 seed does not specify the clustering direction. No exclusion of other P1 times or states, finite KMS interval, CAR vacuum, or excited insertions; no derivation of P1 localization, reflection or physics. The input basis is not orthonormal.
Read the exact result, assumptions and evidence
Result
All five original charge-zero inputs have K_alpha energy 4. The original J8 Gram is positive definite for both quarters with the stated exact determinant. A smooth quotient profile with nonzero first coefficient gives a bounded eight-arc Weyl word that reaches energy 3 from every nonzero vector in the input span. The connected Euclidean response based on K_alpha-4 grows on the infinite half-line; the same applies to positive states supported entirely in this span. The P0 vacuum channel J32 has the two exact R32 weights in the source. The R093 response remains an original vacuum word with the finite raising-current polynomials B_i.
Required assumptions
- 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
- ORIGINAL-FIVE-INPUT-STATE-AND-VACUUM-CLUSTER-20261102.txt lines 1–95
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-FIVE-INPUT-STATE-AND-VACUUM-CLUSTER-20261102.txt
daa072468c8e6be3b35285710869833a88e50b35edecbe16792aea9ad28a7dc4
- check_original_excitation_cluster_20261102.py lines 1–27
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_original_excitation_cluster_20261102.py
14e051950e7f29239f9475289989b5ce993d2157f2dae73c92f7864b93a8d7f7
finding:r094-original-five-excitations-distinct-from-clustering-vacuum