4010 — Marked-Pole Closure Forces a Mixed K–Fiber Bicomplex
Status
Established in the tested finite-field source-jet models at primes (32009) and (32003), in residue charts (G_{12}) and (G_{31}).
Frozen objects
Start with the repaired simple-pole quotient (Q_{26}), obtained from the 36 simple-pole monomials by the ten relations internal to that sector.
Entry 4007 identified the first source-covariant-jet residual outside (Q_{26}):
[ (0,1,2,1,2,1;(0,0)). ]
No ambient truncation or fitted projection is allowed.
Finite falsifiers
First adjoin only that class, producing a rank-27 candidate. It is not jet-closed. At the sixth evaluated jet call:
- (G_{12}) requires ((0,2,2,1,1,1;(0,0)));
- (G_{31}) requires that class together with ((0,1,1,2,2,1;(0,0))) and ((0,1,2,2,1,1;(0,0))).
The result is identical at both primes.
Occurrence closure then forces the square-free degree-two layer in the five labelled pole factors: the (q)-pole and four marked poles. This layer has dimension
[ \binom52=10, ]
giving a rank-36 candidate over (Q_{26}).
The rank-36 candidate is still not jet-closed. At the fourteenth evaluated jet call the first forbidden residuals are
[ (2,1,2,1,1,1;(0,0)) ]
and, chart-dependently,
[ (2,1,2,1,1,1;(0,1)) quad ext{or}quad (2,1,2,1,1,1;(1,0)). ]
Thus the next required target changes three grades simultaneously:
- the (K)-pole order rises;
- a marked occurrence remains doubled;
- a fibre-degree direction appears and is exchanged between occurrence charts.
Narrow conclusion
The covariant-jet operation does not close on:
- the repaired simple-pole quotient;
- a one-class doubled-pole extension;
- the complete square-free degree-two marked-pole layer.
Therefore the missing constructor is not a finite marked-pole summand. It must couple marked occurrence grade, (K)-pole filtration, and fibre degree in one source-derived relative bicomplex.
This is the extension obstruction port. It is distinct from the descent obstruction port, which asks whether an operation coequalizes the ten-relation kernel pair.
No new carrier divisor is indicated.
Next falsifier
Derive the smallest source-defined trigraded target complex containing
[ ext{marked occurrence degree} oplus ext{(K)-pole filtration} oplus ext{fibre degree}, ]
including its chart transition and differential. Then test whether the covariant jet is a morphism of that complex. Do not form closure by iteratively adjoining ambient residual columns.
Artifacts
research/benincasa/checkers/check_rank27_doubled_pole_adapter_closure.pyresearch/benincasa/checkers/check_rank30_doubled_pole_occurrence_adapter_closure.pyresearch/benincasa/checkers/check_rank32_pairwise_doubled_pole_adapter_closure.pyresearch/benincasa/checkers/check_rank36_degree2_boolean_adapter_closure.pyresearch/benincasa/results/rank27-doubled-pole-adapter-*.jsonresearch/benincasa/results/rank30-doubled-pole-adapter-*.jsonresearch/benincasa/results/rank32-pairwise-doubled-pole-adapter-*.jsonresearch/benincasa/results/rank36-degree2-boolean-adapter-*.json
Sequence claim: seqclaim-8e7e1c1d9588d93d2e1b1fce.