Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
What has been tried, and what follows
Scoped exclusion
Generate a four-field term by geometry averaging in the retained quarter compiler
Marked Q rigidity removes the complex modulus;canonical conformal trace removes the remaining free boundary-state variation.
For a new attempt: Supply an actual additional original field insertion,connection variation,higher vertex or derived change of marked admission;do not optimize further conformal profiles.
Derive boundary and four-field response of the explicitly changed elliptic modulus family
Concrete modulus-to-state map and exact variance identity are determined. The fixed original compiler excludes the changed parameter;primitive law and source map are not replaced.
For a new attempt: First derive original measure support and actual marked source/sewing transport. Do not insert a chosen rho variance as the solution.
Construct given elliptic Quillen family before physical insertion comparison
Norm,operator,domain,null divisor,connection,both holonomies and local response are concrete. Common original P1 source map and actual Berry comparison remain open.
For a new attempt: Derive actual common P1 insertion/field transport with source reference against these concrete quantities;equal Chern integer is not a metric/connection proof.
Identify bare flat gauge ratio with minimal EM counting transfer
Actual ratios are1 and1-q;the zero-twist derivative additionally excludes the expressly described ansatz.
For a new attempt: Supply original operator/field insertion map instead of renaming parameters. Do not fitz(alpha),response exponent or reference to the target value.
Derive actual half period and graded GNS connection with source saturation
The existing free Green kernel already containsX;canonical parity-GNS partner realizes all modes. General standard doubling instead gives source-dependent affinityM. Its maximal saturation characterizes linear modular half action in the stated classes.
For a new attempt: Derive half-modular action on odd fields and the marked real sewing/carrier map from the actual original source. Do not merely rename geometric reflection as TomitaJ. For nonlinear action determine actual operator vertices;for established linear action the free source follows in the stated class.
Reuse source-selected spin and correct Pauli target
c,Q determine S0,beta. Spin-relative norm family and full complex N64/clock intertwiner for Wq are proved. Original source must still select one inverse point norm.
For a new attempt: Reuse proved S0-relative point-norm family. Source must select one inverse point norm in actual boundary operator. Do not repeat free spin selection,code/context search,or finite matrix census.
Derive native central quarter from ordinary theta determinant
chi=0 erases spin character before projectivization;alpha_D⁴=+I contradicts required alpha_native⁴=−I.
For a new attempt: Requires explicitly phase-preserving refinement or an additional line justified by existing markings. Repeating same matrix census or dimension matching does not change functor.