Conditional result
Unique relational singlet ray and multiple invariant densities
In the question: Common clock sectors, quartic geometry and operational reconstruction
Tensor sector and pure population are additional premises. Equal Lueders statistics do not prove entanglement.
Read the exact result, assumptions and evidence
Result
In given barH5⊗H5 the invariant vector rayOmega is unique. Jointlaw diagonal5/36, otherwise1/180; I25/25 has same marginals, jointlaw1/36. R=ΣbarE_a⊗E_a has spectrum(5/6)^1,(2/3)^5,0^19; maximizing selectsOmega only as an additional rule.
Required assumptions
- Relational quartic tensor sector without selected physical state
Consider conjugate(H5) tensor H5 with the actual diagonal G31 action as a finite kinematic category. Keep its unique invariant vector ray, its multiple invariant densities and correlations conditional on a chosen singlet separate. Mathematical construction does not derive the microscopic presence or population of this sector.
Original evidence
- RELATIONAL-CHANNEL.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/atlas-defect-synthesis-20261024/RELATIONAL-CHANNEL.txt
c145e53c52753ed4e4df545cdde062c3a6bc19fd9538c99962ec1c110bfaeeb4
- RELATIONAL-CHANNEL.txt lines 201–217
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/atlas-defect-synthesis-20261024/RELATIONAL-CHANNEL.txt
c145e53c52753ed4e4df545cdde062c3a6bc19fd9538c99962ec1c110bfaeeb4
- COVARIANT-INSTRUMENTS.txt lines 127–185
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/atlas-defect-synthesis-20261024/COVARIANT-INSTRUMENTS.txt
858d770e27f80aadb347194c4a9d1a8c869b12163d6cfe8433e4b12b1275ab10
finding:relational-quartic-singlet-and-invariant-density-separation