[GamingPuzzled]

This adds a conditional parameter corollary of the reviewed PR #6030 construction: every fixed κ < 0.0031258115 is attainable under the same five framework assumptions. The explicit rational witness is κ = 3125811/10^9 = 0.003125811, exceeding #6030’s selected 0.003125804 by 7×10^-9 (approximately 0.00022394% in exponent saving).

This is a small parameter refinement of the unchanged physical word and complete paid/productive invoice. It does not satisfy the changed-profile criterion for a new hill-climbing mechanism, does not claim novelty or independent human review, and does not request a selected-frontier update. The package is offered as a reproducible proof/arithmetic contribution; the fixed-invoice ceiling and limited remaining headroom are stated explicitly.

The package includes the theorem and proof, exact rational certificate, pinned predecessor sources and attribution, a self-contained verifier, seven rejection/regression tests, and a validation receipt. It re-instantiates higher-moment completion/splitting, the finite compiler threshold and the complete nine-row outer ledger rather than substituting a raw moment root for a multiplication bound.

Validation on Python 3.12.15:

• Fresh full unchanged PR6030 source replay passed: scalar word, all 799 input columns, native maps/phases, adapters, physical caller, invoice and original arithmetic.
• Two exact interval engines, funded tails, explicit compiler threshold, BIT admission, all 54 strict and four functional outer predicates passed for the refined witness.
• Seven tests passed in normal and optimized Python; Ruff and strict mypy passed.

Reproduce the new arithmetic and tests:

python3.12 -B research/pr6030-parameter-refinement/verify.py
python3.12 -B -m unittest discover -s research/pr6030-parameter-refinement -p test_verify.py -v
python3.12 -O -B -m unittest discover -s research/pr6030-parameter-refinement -p test_verify.py -v

The predecessor is pinned at upstream commit a5bff3b. All five framework assumptions remain; the enormous uniform word and complete rounded multiplier are not materialized. DreamingOfClouds, Ali Romman, the cumulative P104 contributors and all retained compiler/native/BIT/analytic authors retain their source-specific credits. Prepared with substantial OpenAI Codex assistance.