Literal Q Even-Degree No-Go and the Odd Boundary-Crossing Connector
Superseded by entries 275--276. The degree-two premise below applies only to the sheet-summed full-log carrier. Entry 275 derives two labelled hemispheres, each with primitive relative -coefficient one. Therefore the historical conclusion that the admitted source has image must not be cited as a current obstruction. The separate endpoint connector torsor remains, as recorded in entry 276.
Exact obstruction
Entry266 computes that the coherently oriented full-log carrier reaches the primitive K6 top with coefficient two. Entry176 supplies an abstract local central exceptional coefficient +1, but its constructed support lies in the road/boundary subcomplex F_B. Under the literal entry143 quotient to Q, every such support-preserving correction is zero.
The presently typed generic row is therefore
[2, 0],
not [2,1]. Its Smith factor is 2 and its cokernel is Z/2. No integral source coordinate maps to the primitive value qSigma with coefficient one.
This is the earliest global obstruction after the complete finite occurrence, Boolean, Tor, Cech, edge, and facet matrices of entries266, 339--343. It occurs at the boundary-crossing Q projection.
Minimal additional datum
Adjoin a connector whose literal Q coefficient is m. The augmented row is
[2, m].
Its cokernel vanishes exactly when m is odd. The minimal primitive choices are m=+1 or m=-1, with the sign fixed by the established orientation.
Thus the missing datum is not another local cap coefficient: that coefficient is already +1. It is a support-typed proper/log-excess boundary-crossing map transporting the central exceptional generator from F_B through E into the literal generic Q top with independently proved odd coefficient.
Until this arrow is constructed, using the abstract +1 as the Q column is circular. The pointed endpoint/Q mapping fiber and physical parity remain undefined.
Evidence
- research/voevodsky/check_literal_q_even_degree_obstruction.rs
- entries 143, 176, 266-268.
{
"status": "superseded_historical_sheet_summed_no_go",
"superseded_by": [275, 276],
"carrier_Q_coefficient": 2,
"existing_central_Q_coefficient": 0,
"current_row": [2, 0],
"current_smith_factors": [2],
"current_cokernel": "Z/2",
"primitive_qSigma_reachable": false,
"abstract_local_exceptional_coefficient": 1,
"abstract_coefficient_has_literal_Q_support_map": false,
"repair_row": "[2,m]",
"repair_iff_m_odd": true,
"minimal_primitive_connector_coefficients": [-1, 1],
"mapping_fiber_instantiated": false,
"physical_p_defined": false,
"physical_bockstein_defined": false,
"D8_Jordan_tested": false,
"graph_admission_claimed": false
}