Conditional result
Full admissibility needs vacuum image and actual transfer reduction
In the question: Common clock sectors, quartic geometry and operational reconstruction
Reuses established image-membership test and refines it at actual original projectors. Dirac gap,transfer ground energy and internal E8 weight are distinct operator quantities. Projector product names or commutation alone do not suffice. No general TFPT no-go.
Read the exact result, assumptions and evidence
Result
Original P_prim includes positive high-spectrum projector1_[eps²/4,∞)(D_prim†D_prim). An H8 vacuum mapped to a primitive Dirac zero mode would be removed. No original H8→H_prim/OS intertwinerW was found;neither retention nor exclusionOmega is established. QTheta Omega is also undefined onE8 module. OriginalD_adm commutators do not proveH8 commutation. If sourceW exists,Pprim WΩ=PTheta WΩ=WΩ andPadm reduces transportedH8,unique vacuum with gap at least3/2 or2 and exponential temporal semigroup clustering follow. OS reconstruction cannot prove this backwards because its theorem assumes clustering.
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.
- Stipulated E8 H8 module with original color-center selector
Retain stipulated E8 lattice extension with H8=8K_alpha,alpha=1/4 or3/4,actual rational Weyl dictionary M and original marked color center on first three carrier slots. Apply its P_sing after the carrier theorem. No intertwiner to the primitive P1/OS space is assumed.
Original evidence
- PADM-VACUUM-RETENTION-AUDIT.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/PADM-VACUUM-RETENTION-AUDIT.txt
4cbfdb96c2d8e7a75fe8c1423a91f98ff217e6e1fc13814cb86a7c08d3828d1f
- PADM-VACUUM-RETENTION-AUDIT.txt lines 201–229
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/PADM-VACUUM-RETENTION-AUDIT.txt
4cbfdb96c2d8e7a75fe8c1423a91f98ff217e6e1fc13814cb86a7c08d3828d1f
- CLUSTERING-ADMISSIBLE-SECTOR.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/CLUSTERING-ADMISSIBLE-SECTOR.txt
349e5a149d34078da67775e56f25e3aebf2c55111798a86d58322aa61cd380bc
- CLUSTERING-ADMISSIBLE-SECTOR.txt lines 201–258
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/CLUSTERING-ADMISSIBLE-SECTOR.txt
349e5a149d34078da67775e56f25e3aebf2c55111798a86d58322aa61cd380bc
finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction