Conditional result
Positive null-stable word kernel reconstructs cyclic representation
In the question: Future quotient and positive GNS reconstruction
Construction applies only with complete coherent K values and stated domain conditions; K from the original TFPT source has not been derived.
Read the exact result, assumptions and evidence
Result
Given a positive Gram kernel K with normalized reference, compatible composition/adjunction, and null-stable continuation, quotienting by null vectors and completing constructs H_K and the well-defined word action. Cyclic realizations of the same complete K values are unitarily equivalent on the common word domain; for unbounded operators, closures and self-adjointness remain additional requirements.
Required assumptions
- Positive word kernel with null stability
The GNS/Gram reconstruction requires a Hermitian positive kernel K, normalized reference, declared composition and adjunction, and stability of null relations under every allowed continuation; these are conditions on a supplied K source, not TFPT axioms proved from bare future answers.
Original evidence
- RESULTS.md lines 145–194
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/universalraum-primitive-source-audit-20260915/RESULTS.md
ae9880339326e402dee9783185defc0671bdec430a777d961d54e7636335aa80
- RESULTS.md lines 195–235
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/universalraum-primitive-source-audit-20260915/RESULTS.md
ae9880339326e402dee9783185defc0671bdec430a777d961d54e7636335aa80
finding:positive-word-kernel-reconstructs-cyclic-gns