Certify one selected BIT q-adic route and its carry failure mode

[petalas]

Summary

Add research/selected-bit-qadic-route/, taking the released field-split handoff from PR2120 and Discussion 2114.

selected PR589 port 8, embedded in GL64
  -> 77 exact rational column factors
  -> explicit low/high q-adic carry updates
  -> same right product, untouched ancestors and unused child stock

The written integer identity holds at every atom width. The executable is deliberately bounded. This is one row-index lowering, not the full all-size GL64 compiler, physical routing admission, a new stock coefficient or new kappa.

A concrete failure control shows why the missing interface matters. Dropping carries can preserve every low residue and restore the complete row after two applications, yet produce entry 19 instead of 14 modulo 25 on the exact selected route. This is a counterexample to those checks being sufficient, not a demonstrated selected-compiler bug.

Scientific base is canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Frozen sources, the selected frontier and all predecessor packages are untouched. Exact source/head pins, overlap coverage, scope change and open questions are in the package metadata.

Evidence

• Before: PR2084/2097/2120 retain the selected field/compiler realization as an assumption; the existing notes state affine routing without emitting this selected low/high carry program.
• After: the source-bound receipt contains 77 factors, every single-factor omission is detected, and 24 full 64-dimensional cases agree with a separate dense modular oracle. An exact proof covers all widths; finite fixtures are not presented as that proof.

Observed with standard-library CPython 3.12.15:

python3.12 scripts/research_package.py --package research/selected-bit-qadic-route
python3.12 -I -W error -B research/selected-bit-qadic-route/test_route.py
python3.12 -B -m unittest discover -s tests -p 'test_research_*.py'
make selected-record-check

Registered replay, 11 package tests normally and optimized, all 65 workflow tests, source pins, syntax checks and selected-record integrity pass locally. The tests include 1,493 exhaustive elementary cases, signed carries, noncommuting orientation, spectator isolation, source/citation corruption and public-CLI receipt/no-overwrite controls. No hosted-CI success, independent human review, formal kernel or full supplier cold replay is claimed.

Credit remains with Zhihao Chen's PR386/PR370 geometry lineage, DreamingOfClouds' PR545/PR589 pipeline on eumemic's base, Rohan Arun's selected assembly on Jeremy Kothe's PR1087, Adam Gall's PR2084 and PR2097, and the cutoff/stock predecessors named in the README. Their constructions and conditional bounds are not claimed as new. No predecessor Python is executed or vendored.

No Discussion claim was posted because the loaded engineering workflow prohibits human-directed Discussion posts; scope was recorded locally before implementation.

Merge danger

Door: two-way. Only a new opt-in research package is added.

Blast radius: local. Existing scientific inputs and production behavior do not change. The moving selected pointer is historical provenance, not a live replay input.

The GL64 physical realization, remaining owner routes and child-weight dependencies, complete invocation domains, leaf borrowing and paid physical/tape implementation remain open. The next useful step is one residual/hosted route certificate or one physically charged carry-controlled shift, not treating this row-index identity as a complete supplier.