Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
Insufficient for the goal
A sufficient conditional route and complete source function exist. The actual generating P1 current embedding is not constructed in the reviewed original passages.
For a new attempt: Actually construct the original local kernel and Weyl operators with state,time,reflection and support; only then identify P1 W8 and target response.
Read the question and its evidenceScoped exclusion
The first response has an exactly nonzero tangential component outside the one-dimensional folded level1.
For a new attempt: Use the already existing full original c1 stress modes and all neutral intermediate states. The response then belongs to the existing source cycle;no extra generator is thereby needed.
Read the question and its evidenceReusable result
All grade components of the neutral W8 response are in the original stress span;the first has an exact22-word CAR construction. Prior microscopic and net-extension results retain their scope.
For a new attempt: For actual physical P1 identification still connect local fields,support,reflection and original collar/reference domains. Cyclicity or character equality is not a local operator map.
Read the question and its evidenceReusable result
The old winding arrow supplies the common CAR comparison within the existing cover source and generates exactly the local current net with both stress families.
For a new attempt: For complete physical P1 identification still connect source net,support,Theta,time,collar and reference from the originals;do not insert a newly fitted comparison matrix.
Read the question and its evidenceScoped exclusion
Independent factors retain the cubic Virasoro commutator term and do not yield a Heisenberg current algebra.
For a new attempt: Use the existing actual winding transport;then the positive local current theorem applies.
Read the question and its evidenceInsufficient for the goal
A fixed-domain involution is proved,but the explicit pi sigma1 term and divergent full PH polarization mismatch prevent the requested same-state/time identification in this class.
For a new attempt: Check the actual original P1 reflection and polarization type;do not present an additional flat connection or new sea as a derivation.
Read the question and its evidenceScoped exclusion
Neutral zero-branch word has complex OS norm. Repairing a single charged block by phase is insufficient.
For a new attempt: Use the existing whole NS cover or another originally derived positive kernel;then check its actual P1 identification.
Read the question and its evidenceReusable result
Both charges and all transverse modes are proved with correct source-order sign. Deck exchange explains the failing isolated sector.
For a new attempt: Supply P1 map and actual W8 state/time transport;do not introduce a new free kernel or fitted beta.
Read the question and its evidenceReusable result
Reuse previous proof in its named h,Q,kappa subgroup stratum. Full original D4 Real group has an additional equatorial pair. Actual seam pullback is ramified;boundary-tuple identity does not supply an unchecked physical seam morphism.
For a new attempt: Supply original P1 source morphism;do not search again for arbitrary free kernels or quarter phases.
Read the question and its evidenceScoped exclusion
Finite crosscap state is nonstationary under signed B;its filtering limit loses the loop quarter mark.
For a new attempt: Prove actual channel and state/time transport from original source,instead of renaming tree filtered vacuum.
Read the question and its evidenceReusable result
Exact original bosonization with quarter factor and separate connected-net theorem supplies existing neutral composites. Their existence requires no newly chosen elementary coupling.
For a new attempt: For physical derivation supply actual original P1 current image with state,time,Theta,regional admissibility and invariant admissible subspaces. Do not relabel larger connected net or dual commutant as additive eight-arc net.
Read the question and its evidenceInsufficient for the goal
Source-derived geometric return and canonical state construction are closed in stated scopes;physical P1 profile/history remains open.
For a new attempt: Supply actual original action/reference/intervention map and full native field interface.
Read the question and its evidence