Established in scope
Decoder forces product and temporal composition; all unitary erasure lifts classified
In the question: Historical: common source, state and event selection
Given original code/decoder and logical operation. No selection of H, logarithm branch, physical time normalization or actual intervention permission. Unitary class, not all CPTP instruments. Native group action differs from the decoder by an explicit gauge factor whose physical compensation remains open.
Read the exact result, assumptions and evidence
Result
The actual decoder D(A)=W(A tensor I4)W* is an injective corner *-homomorphism. Thus D(A)D(B)=D(AB), product preservation of unitary complement extensions and exp(-itD(H))=D(exp(-itH))+I-Pi follow without a new composition rule for given H. Every unitary lift with full branchwise erasure compatibility is necessarily and sufficiently R tensor V4, forced by the commutant rather than fitted. On C64 an arbitrary unitary44-complement block remains.
Required assumptions
- Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
- Original decoder and same native quarter polynomial
Fix original erasure decoder D(A)=W(A tensor I4)W* and its mark P220=P2 tensor I4. Substitute actual sigma20=sigma5 tensor bar(sigma4) and all four native reflection lifts of original tau5 into the existing R polynomial. This tests that continuation, not all coherent lifts.
- Unitary continuation with full branchwise erasure action
Consider unitaries T on the actual erasure carrier satisfying T(rho tensor I4/4)T*=RrhoR* tensor I4/4 for every logical state rho and a given logical unitary R. This is a declared compatibility class, not a physical instrument rule derived from P1.
Original evidence
- DECODER-COMPOSITION.md lines 8–105
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/DECODER-COMPOSITION.md
ac47935c73aefe05d746dcd61c2b3462b184dcfd9ec2a4916e32bad6c85d928f
finding:original-decoder-product-time-and-all-unitary-erasure-lifts