Only if the same marked family connection is irreducible and beta preserves it in parallel; without this added premise the 2+2 packet is not excluded. A noncommuting common source-derived connection remains open.
Read the exact result, assumptions and evidence
Result
Under the explicitly additional premise that beta preserves the fixed marked irreducible SU(3) family connection, its commutant is scalar and beta must have the 3+1 form diag(b,b,b,-3b). Thus a beta packet with eigenvalue multiplicities 2+2 is excluded under that premise only; no original parallelity rule follows.
Required assumptions
Common parallelity to irreducible family connection
Only for the commutant conclusion, assume additionally that the marked SU(3) family connection is irreducible and beta preserves it in the same marked frame. This is not an accepted P1/P2 axiom and must be derived from the source.
Applies to connecting discrete/topological classes to a concretely acting common carrier; it does not claim that the holonomy class asserted by the original theorem is undefined.
Read the exact result, assumptions and evidence
Result
The theorem lists [nabla_F*] and Chern classes in its singleton. The audited lift formula constructs the carrier action only once A_E is supplied; the original connection on the common carrier and Phi therefore remain to be specified as a source step.
Required assumptions
P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
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.
The theorem listing singleton [nabla_F*] and Chern classes is recorded as a discrete/conjugacy-class statement; the common operator realization is kept separate and the lift formula is explicitly marked as conditional on A_E.
The 2+2 exclusion holds only with the added premise of parallelity to the marked irreducible family connection. Whether the common original source induces this connection and marking belongs to the target problem’s open source selection.
Original historical attempts linked to this question
These are original research records. Their reported verdicts are distinct from the reviewed results above.
source boundary lift selection 20260922
Does the original boundary completion select a common charged lift, and which joint lifts preserve an independently fixed marked family connection?
Recorded verdict: PARTIAL
Historical inventory; not independently reviewed by this export.