Independent verification: selected complex moments via integer root bounds

[arkfx]

The selected #626 complex supplier has strict native and conservative moment brackets at adjacent saving values separated by 10^-24. This adds a third arithmetic verification using dyadic exponent brackets and repeated integer square roots, without importing supplier, logarithm, exponential or binomial-series code. Status: independent finite verification; no new κ.

The checker recounts 72 invoice calls plus idle children, recovering 262,707 children, rank mass 520,704 and deficit 2,560. Exact rational intervals confirm all four endpoint decisions. Mathematical controls expose false acceptance after omitted idle children, physical-stock normalization, dropped surcharge, and a profile change preserving both count and rank mass. These are modified-model controls, not defects alleged against the selected assembly.

Reproduce offline with Python 3.11+ and the standard library:

python3 -I -B research/pr626-root-moment/verify.py
python3 -I -B research/pr626-root-moment/test_verify.py

Expected: PASS_PR626_ROOT_MOMENT and four tests OK. Normal and optimized Python agree. The package includes 1,743 exact integer-power comparisons, two unsafe-enclosure controls, six mathematical controls, five rejected inputs, actual implementation mutations and source/certificate corruption controls. A relocated package with only the five pinned inputs passes. python -B scripts/verify_selected_result.py and staged whitespace checks pass on Windows / CPython 3.12.3.

Only research/pr626-root-moment/ is added. It contains the checker, exact certificate, enclosure proof, source pins, validation and local sprint claim. No supplier, generator, upstream source or selected frontier changes. Repository-wide verification, cold supplier replay, the 47 outer inequalities, Lean and remote CI were not rerun. Construction-level correctness of the profile and surcharge model remains inherited, together with all-size/compiler/common-label/mutable-basis/hosting/precision/tape/analytic assumptions. This is not formal verification of the multiplication theorem or a practical speedup claim.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Selected #626 source: 660de893d27bb7abd1d5b01b1640207528a5c851; #622 construction: f69477f4f6d3c7eb1f740b166881bffed4ffa9f6. OS-random assignment seed 83, independent verification track. No pinned sprint issue exists, so the claim/result are local.

Overlap was refreshed through #704 (523 open PRs), with a final latest-arrival check before submission. #678 independently checks the bit moment with binomial enclosures; #667/#672 accelerate existing log/exp engines; #675 audits owner boundaries. This checks the complex native and conservative brackets by a different, series-free algebraic method and does not depend on those packages.

Credit to Chafik Boukhalfa/chafreaky (#626), Jeremy Kothe (#622/#623), icekylinx, DreamingOfClouds, Rohan Arun (#559), eumemic (#543), and the cumulative supplier lineage retained in the original notices. Prepared for arkfx with substantial OpenAI Codex assistance; Apache-2.0. No independent human peer review is claimed.

[Mister-Meeseeks]

100-PR batch review at 0f7dbb54948775c010b5e5bc8ab3cf92a52a9b25.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent dyadic repeated-square-root enclosure of the pinned moment, including fallback charge; profile validity is inherited.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.