Scoped exclusion
Full operator skeleton does not select local insertion algebra
In the question: Historical: common source, state and event selection
Excludes only unique algebra reconstruction from these data in the declared product/domain setting. Not identical complete original tuples, full OS/P1/P2/minimality countermodels or a universal TFPT no-go. Additional algebra hypotheses need their own origin.
Read the exact result, assumptions and evidence
Result
On the same product skeleton A0=C∞(M)I and A1=C∞(M,Mn) acting on the left differ, with the same scalar center, identical D,J,Γ,B,R and fixed relative spectral/eta responses. Both obey order zero/one: JL_(b*)J^-1=R_b, [[D,L_a],R_b]=0. A1 mixes internal left indices, A0 does not. For n=2: fiber-span dimensions1/4, commutant dimensions16/4 and16 exactly vanishing left/right basis commutators. These operator/center/order conditions therefore do not reconstruct the multiplication algebra.
Required assumptions
- Declared product skeleton for algebra identifiability
Given a compact spin collar with a local selfadjoint elliptic geometric boundary problem stable under smooth multipliers, or closed double with H1 domain. On H=L²(M,S)⊗HS(Mn(C)),n≥2: D=D0⊗I, B=B0⊗I, J=J0⊗(X→X*), Γ=Γ0⊗I, R=R0⊗I, with zero finite Dirac term. Compare scalar and left matrix insertions on the same H. No arbitrary APS-domain invariance, complete OS source, unit winding or minimal P1/P2 branch is claimed.
- 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
- LOCAL_ALGEBRA_PROOF.txt lines 39–106
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-joint-source-origin-audit-20261016/LOCAL_ALGEBRA_PROOF.txt
caabb04e2449b2e12ff674690dbc8ee37feb0a043543cd667df8085eb93b9e26
finding:operator-skeleton-does-not-identify-insertion-algebra