docs(research): WAN chain K-lever benchmark, R(K) round law, receipt protocol

[463464q435q43]

PR: WAN chain K-lever benchmark, zero-parameter round law, and a receipt protocol (docs-only)

Target: leyten/shard master (based on 182e93b, applies clean).
Branch: mosaic/wan-chain-k-benchmark · Files: docs/research/wan-chain-k-benchmark.md (new, docs only — no code).

Motivation

Three things we measured on our own scattered-EU M2.5 ring (6× RTX 5090, 274.8 ms loop, this
repo's engine at 182e93b, pristine/config-only) that belong in upstream's research docs:

1. The K lever. §4.2 of the paper concludes only α (drafter) or T (transport) moves the
   draftable number. K — the chain round length, fixed at 8 in research/m25_ctx_table.py — is a
   third lever, lossless by construction, and it is large: 181.5 → 294.9 ± 25.4 tok/s on a 420-tok
   verbatim copy (K 8→48, d8), 647.7 → 710.2 ± 20.1 on a ~1k-token sustained continuation
   (K 64→128), every run byte-identical to plain greedy. Both throughput knees are located and
   bracketed from both sides (420-tok cell peaks at K=64; long cell at K=128 — K=192/256 read
   below their interleaved K=128 control, with byte identity still perfect at K=256: the knee is
   round-time growth, not acceptance or proposal-quality collapse).
2. A zero-parameter round law. On verbatim-saturated cells the round count is deterministic:
   R(K) = warmup + ceil(C/K) — reproduces all 8 ladder rungs on the 420-tok cell and hit FOUR
   pre-registered predictions exactly on the long cell (R=14@K96, R=11@K128, R=9@K192, R=7@K256,
   g = 1008/R exact each time). Verified at every tested K from 8 through 256, including past the
   knee — the law prices rounds, not speed. Round time follows committed tokens (draft-size
   slope ≈ 0): the "commit-attribution" model won two independent pre-registered model brackets
   against alternatives.
3. A benchmarking protocol. Pre-registration before data, byte-identity as a class boundary,
   regime binding, config-stated comparator sentences, interleaved A/B for engine deltas. Five of
   our banked receipts are pre-registered negatives — the discipline is what makes the wins
   trustworthy. The doc proposes this as a convention for docs/receipts/.

The doc cites the paper by its Zenodo concept DOI 10.5281/zenodo.21178430 (the README
badge's DOI; the current version 1.2 resolves at 10.5281/zenodo.21180635 — both land on
the same record, verified 2026-07-07).

The doc also contains our comparator sentences vs the paper's promoted numbers, written
class-fair (both configs, both loop RTTs, in one sentence) — including the interactive cell where
the comparison favors upstream (10.87 ± 0.79 on our 274.8 ms loop vs 10.7–12.6 promoted on
~105 ms). We'd rather these sentences live where the compared party can review them.

Why upstream might want this

• It answers a question the paper leaves open (the K dependence of the pipelined chain) with a
  located optimum and a predictive law that went 6-for-6 on pre-registered round-count
  predictions across the full tested range.
• The fairness discipline (quote "87" not "87.2"; never cross-quote length classes; name both
  configs) protects upstream's numbers as much as ours.
• No code, no maintenance burden; every row is final and receipt-backed (no pending slots).

Verification

Receipt names are cited inline throughout the doc; raw per-run JSONs, prompts, signed receipts,
and the exact m25_run_arm.py configs are retained on our side and can be furnished on request.
Every claimed row includes n, CI, g (exact), engine sha, and its regime.

License / transfer

Contributed under Apache-2.0 like the rest of the repo. Mosaic Intelligence retains authorship
credit for the measurements; upstream is free to edit, condense, or fold the protocol section
into its own conventions.

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Prepared 2026-07-07 by the authors (Mosaic Intelligence).