[aliromman]

This construction raises complete conditional κ to 0.00314933, from 0.003128645 in PR #6167: +0.000020685, about 0.661%. The native word is unchanged. A binary tree of query suppliers replaces the paired path and changes the complete target/paid distribution. The selected frontier stays unchanged.

Review the proof, four-field checker, literal caller, complete receipt, and source pins.

The new four-field module combines two query suppliers, one paid thin query and two whole idle calls. It returns another query supplier and two independent Gaussian outputs. Root subtree sizes 4, 7 and 8 give 19 full native calls, 16 thin queries and 34 main fields per port. All helper inputs remain arbitrary and independent. The idle work, owned lifetimes, orientation wrappers and ordinary operations are charged.

Complete calculation	Result
Productive fields / paid calls	14,214 / 70,523
Rank-mass surplus	808
Raw crossing enclosure	(0.00314934401301, 0.00314934401302)
Tested saving / claimed κ	0.003149335 / 0.00314933

Evidence. The separate four-field Laurent checker and the emitted 34-field replay pass all 1,156 endpoint entries with distinct stage variables. The unchanged source replay checks all 799 input columns and 638,401 coefficients through a separate transpose. Native phase checks cover 7,904 new caller contacts and every main/idle target. Two rational moment engines agree; the new completion parameters, uniform compiler and all 54 strict plus four functional outer predicates pass. The retained BIT saving is 0.0034. Controls reject missing paid work, a missing central translation, wrong query orientation, the source completion cutoff and insufficient BIT saving.

Both registered modes passed on Python 3.12.13. Committed bytes, execute modes and the official export inventory passed. The full optimized replay also passed from a read-only export with no Git on PATH; hashes and modes stayed unchanged. A one-byte source mutation was rejected before import. The validation record identifies the tested scientific commit; the final commit changes only that record. Hosted CI passed both the planner and the registered scientific replay at head 9894015d6f380206f990ad5fd14bc49bbd26b0d0. The maintainer later archived this PR; that is not independent scientific acceptance or a selected-frontier update.

Reproduce with Python 3.12 and its standard library:

python3.12 -B scripts/research_package.py --package research/balanced-query-tree --check-only
python3.12 -B scripts/research_package.py --package research/balanced-query-tree

Expected scientific marker:

PASS_BALANCED_QUERY_TREE_KAPPA_00314933

Scope. This is an author-checked conditional construction. Five inherited assumptions remain: native all-column implementation, owned erasure, uniform compiler, precision/tape cost and analytic recovery. The uniform word and rounded multiplier are not materialized. Independent scientific acceptance, proof-kernel verification, global optimality and a practical speedup are not claimed. Full-history ancestry preflight is unavailable in the shallow checkout; exact source bytes and the immediate base are checked.

Provenance and credit. Base: canonical main 626e936, priority revision 8. All 18 consumed source files match PR #6167 at 564a076b113621a93edc4e39968ee4e4a8c9caf0 byte-for-byte. Cinna Davis @1337isnot1337 supplies the query-thinned path and thin-query interface in the PR #4470 lineage. Ali Romman @aliromman supplies the all-forward native binding in PR #5544 and the retained-operand source. DreamingOfClouds @DreamingOfClouds supplies the preceding local-word changes in PR #6144. All earlier native, helper, recursion, compiler, BIT and outer credits remain in NOTICE and the authenticated sources.

New query extension, tree caller and complete calculation: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. The scoped Discussion claim records the overlap checks and keeps the active local-word investigations separate.