CrocSwap / integer-mult-bounds

# A sharper exponent for integer multiplication
**Community research maintained by Douglas Colkitt — conditional on the original
OpenAI #109 framework.**
**Donating inference or asking an agent to contribute? Start with
autoresearch.md** for task selection, current priorities and
how to avoid duplicating other agents' work. Agents should also read
AGENTS.md and CONTRIBUTING.md.
Coordinate claims, findings and handoffs on the
discussion board,
starting with the coordination guide.
New to the construction? Read the bottleneck brief.
Workflow feedback is welcome in discussion #1200.
## Current reviewed result: rare-pattern T16 owner exchanges
**Rohan Arun's #1094** gives
$$
T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
\kappa=\frac{836330098538459}{500000000000000000}=0.001672660197076918.
$$
This is about **0.02823% more exponent saving** than the #1042 checkpoint, not measured runtime. It follows alternating packing improvements by **Jeremy Kothe and Rohan Arun**, on Jeremy's mutable-leaver construction, Rohan's #987 slot search, **Hao Yan's #858 controller**, and the credited frame/ownership work of **Chafik Boukhalfa, icekylinx, Jonathan Capalbo** and the retained lineage. The bit supplier remains **DreamingOfClouds' #589 on eumemic's #555**.
All twelve packing candidates pass complete strict local admission, controller/invoice checks, both exact moment engines and all 47 assembly inequalities. Independent owner and pricing auditors by **Josie Elliston and Sagar Thakrar** also check the final candidate. Complete prior construction/bit evidence is explicitly reused and source-bound in the local review. All-size/compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery and analytic obligations remain conditional. This is **not a complete Lean multiplication theorem**. Hosted Linux CI is separate.
Forty-PR review and attribution ·
Selected record ·
Exact assembly ·
Integration receipt ·
PR ledger · Contributors
Post-selection research and verification rounds are indexed in
current status. Use the
PR ledger for each contribution's reviewed head,
integration status and remaining obligations.
 [code] 
The batch includes separate U10, rank-seven-end and E4 gap-filling constructions, finite bit circuits, exact decoder bounds, independent numerical and SAT-proof audits, and verification tools. These contributions retain individual credit even when they do not advance the selected κ. #1048 remains open with an exact counterexample and certification corrections documented in the review.
The preceding circuit/verification batch
and U8/T21 review remain available,
including their independent evidence-admission, precision, formalization and
parallel-tooling contributions.
The previous fifteen-PR review
retains independent reconstruction, owner-optimality and verification-tooling
work. Alluri's #681 consolidation
and its six component contributors remain credited for historical circuit-count
savings, independently