Conditional result
Common five-slot transfer preserves E8 bracket but not automatically trace preservation
In the question: Automated construction of operator maps and sources
The same A is assumed on both correctly typed legs; no source origin of A, no identification of the two-mode carrier with C5, and no universal TP exclusion. Other family weights or channels remain possible; interaction formula assumes the specified finite generator decomposition.
Read the exact result, assumptions and evidence
Result
For A on C5, D=Lambda²A and original bilinear C_m:H→H*, D^T C_m D=sum_n adj(A)_(n,m)C_n, including singular A. Invertible A preserves the whole span and the concrete five-cycle the given equally weighted channel. A common scalar normalizes the simple equally weighted channel to trace preservation iff adj(A)adj(A)*=rI, equivalently AA*=sI for invertible A. A=diag(1,1,1,1,1/2) gives effects 1/2 and 1/4. An exact Duhamel integral of [V,a†] gives the free creator-relation defect for supplied H=dGamma(h)+V; the existing two-mode counterexample gives 1/256.
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
- EXTERIOR-TRANSFER-AND-E8-HODGE-20261102.txt lines 1–110
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/EXTERIOR-TRANSFER-AND-E8-HODGE-20261102.txt
577e80d7b36ab9305fe0a120a06a9dc20b7dfa35adb88283a6e68027fea36653
finding:common-five-slot-transfer-preserves-e8-bracket-not-automatic-tp