Allow strict-volume padding with one fewer borrowed digit

[petalas]

Summary

- Require R=q^k >= S_D(n) before compatible-row padding.
+ Require ceil(R/S_D(n))*S_D(n) < 2R, exactly S_D(n) < 2R.
+ Admit S/2 < R < S with an opt-in Count-tape row planner.

Proves the exact least fixed-width borrowing predicate at actual body depth. The gain over covering is at most one radix digit when both plans fit, and the wider contract can admit a formerly rejected fit. At the existing selected prime q=2^127-1, e=630087102387535114 and exact w=2, the minimum falls from 696331 to 696330.

Adds only research/strict-padding-borrowing/. PR3486 explicitly keeps R>=S; its unchanged proof is retained as a separate comparison receipt. Four canonical source inputs are pinned, including the complete frozen padding closure. No pending foreign Git object is required.

Evidence

• Before: the exact retained PR2786 planner rejects all 276 tested cases with S/2<R<S.
  After: the successor returns the least compatible row range under the same strict factor-two budget. All 1152 accepted/rejected Count-tape plans agree with direct arithmetic.
• Written unbounded proof, exact product bounds and a Lucas-Lehmer certificate support the selected-prime example. Bisection and a separate direct-stock exhaustive oracle agree on 8192 cases: 3058 one-digit improvements among jointly fitted cases and 32 newly fitted cases.
• Five complete synthetic rowwise-reversal fixtures check all 258 independent Boolean basis inputs. Seven bad-return modes, strict equality/alias/capacity boundaries, a preloaded-module rejection and seven actual optimized CLI corruptions pass. These endpoints do not execute selected C0.
• Repository Ruff/format checks and all four registered normal/optimized commands pass. At publication head 350ad76a718304552d2c82e2794de995fce819f5, all 20 committed-byte/source-history comparisons, export integrity and four actual Git-free export commands pass. All 21 exported files retain bytes, modes and inodes.

python3.12 -W error -B scripts/research_package.py --package research/strict-padding-borrowing
python3.12 -W error -B scripts/check_research_commit.py --package research/strict-padding-borrowing --check-source-history

Use an existing owned external TMPDIR for temporary fixtures. Base canonical main is 6f100d4bb5083f8c35d96fd95a539811c62f245c, priority revision 6; submission fetch found unchanged guidance. Fresh overlap covers 414 open PR bodies and 2338 Discussion records with complete pagination and no warnings. Arbitrary diffs, closed PR bodies and unpublished work are outside that coverage. Canonical claim.

Credit Nick Petalas/PR3486/3246, Tekalign/PR3264, Jose Manuel/PR2786/2808/2899, David Arias/PR2753, Ross Richardson/PR2420 and their retained BIT/geometry/hosting/assembly lineage. Their reserve and consumer results remain separately attributed.

The full borrowing selector is a host specification; the row adapter has a 4096-bit Count capacity. Selected C0/GL64 execution, fixed-role selector integration, uniform physical costs, source refinement, fresh fields, pointwise restoration, full-cover, precision/tape and outer-transfer obligations remain. No new cutoff, supplier, kappa or selected-frontier change is claimed. Independent human and formal proof-kernel review are unclaimed. Initial oracle-rank and cleanup-marker observation failures remain in the session evidence with their corrected receipts.

Merge Danger

Door: two-way

Sixteen isolated new package files; no shared runtime or frozen source changes.

Blast Radius: package