# Root-merge 2/5: AMM fee-challenge findings

## Scope and conclusion

This merge combines all 25 supplied results. The results do not establish a confirmed
`>=2000`-seed fresh comparison against STACK from seed 5,000,000 onward. Most measured
gains are against V10 or VanillaStrategy, and the strongest later V10-relative results
are only about +0.16. Therefore no result here should be presented as a board move or as
the requested final STACK candidate. The only directly STACK-paired measurement in this
set is the RS1/V10 implementation run (b20-a,b20-b), but those files report component
edges and gas rather than the requested final `paired{n,mean_diff,se,worst}` object.

The goal figures supplied by the brief remain: STACK board 519.71 (29th), 10th 524.66,
1st 528.40, so roughly +5.0 paired gain is needed; STACK hash
`2eaafc7960e520b8a7fd322ec8afaff8fa677c730228a961efb509cc30b25719`; STACK's stated
historical peak is 214k/250,000 afterSwap gas with zero OOG. These are brief figures,
not measurements made by this merge.

## Results that were actually measured

All claims below are attributed to the supplied result name. “V10-relative” means the
candidate ran alone against VanillaStrategy under the stated harness; it is not a
STACK comparison.

### Retail-state / flow and size families

* **b15-a (e04-retail-state/a):** a latent retail-flow state (weighted first/later
  prints, count/size moments, and bounded missing-flow correction) was implemented. Its
  zero-mix control reproduced V10 bit-for-bit. The best provisional C arm had only
  `+0.033 +/- 0.072` on a 64-seed partial recheck; the planned 256-seed recheck and
  512-seed held-out run were not completed. Its component deltas were retail
  `-1.4463 +/- 0.0857`, arb `+1.4794 +/- 0.0558`; gas max afterSwap 210,819, OOG 0.
  The supplied source was not independently re-established in the result, and the
  result itself labels the pick provisional. (b15-a)
* **b15-b:** the same family was completed against V10. The frozen arm has hash
  `df2817ba4ec233a456eb45909faa4a706efe0fabd1734a908fe52545f4d07577`, parameters
  `[2,0.16509179839500446,0.9909893448132306,0.6684959838546022,1.5946627692375024,80.0]`,
  512-seed held-out mean `+0.09383374943510048`, SE `0.01577346341497711`, retail
  `+0.03595198876958994`, arb `+0.05788176066550904`, and afterSwap max 201,968,
  OOG 0. It was not run on confirmation seeds. (b15-b)
* **b22-a and b22-b:** independent 512-seed tuning blocks replicated the flow/size
  pattern. The full RS1 arm (same hash and parameters) scored respectively
  `+0.07913846581963269 +/- 0.016787684079370598` and
  `+0.08260855527069544 +/- 0.02615383820069299` versus V10. In b22-a, count-only
  was `-0.20274102129727734`, while count+size was `+0.14431946144132557`; in b22-b
  these were `-0.15511866235911387` and `+0.14684892673332106`. Thus the retained
  signal is size information, not count-only flow. The strong fee-dependent correction
  hurt relative to correction-off (b22-a `-0.06584 +/- 0.01338`; b22-b
  `-0.06463 +/- 0.01319`). All reported arms had OOG 0; afterSwap maxima were about
  202k and initialization maxima about 243,099. (b22-a,b22-b)
* **b21-a:** a broader seven-dimensional RS1-style CMA search froze hash
  `f24b6ca198b744c380842c3a17964a6dc21f311bb04984b26733afa3fee8eaf2`. On 512 held-out
  seeds it scored `+0.16177968946971466 +/- 0.02586702741272507` versus V10 and
  `+0.08053785508635214 +/- 0.021225587576043266` versus RS1. Component delta versus
  V10 was retail `+1.4925384987239503` and arb `-1.3307588092542348`; afterSwap max
  202,468, OOG 0. It is still far below the goal-sized +5 and is not a STACK result.
  (b21-a)
* **b21-c:** a separate rate/size/mix/cap search froze hash
  `c25f2a922e76febb6bd73e223867c285076403285aca2ee96ae04597a67d0f44`. Held-out
  V10-relative mean was `+0.1334077650864739 +/- 0.022577637940322682`, and it beat
  RS1 by `+0.06554100421904574 +/- 0.018824555313678614`; retail was `+1.0968126284911683`,
  arb `-0.9634048634046943`, gas 200,601, OOG 0. (b21-c)
* **b21-d:** a copy/control of RS1 scored `+0.09393557961150167 +/-
  0.01886682624369501` versus V10 on 512 held-out seeds, exactly equal to RS1 on
  those seeds. Its hash is `f225d339f6f6b3a00d00e3b2d3b3f119084e745f4f79fa67036591406afee50b`;
  retail delta `+0.05434782750466305`, arb `+0.03958775210684013`, afterSwap 202,381,
  OOG 0. (b21-d)

### Existing STACK extensions and shadow/transport ideas

* **b13-b:** the horizon-hazard add-on was negative: held-out (only 128 seeds of a
  planned 512) `-0.0464 +/- 0.016`, retail `-0.0673`, arb `+0.0209`, hash
  `b44c06ce7cd9591d00e8132fc0ce46b0c85f69b55bb824f23513ecd57d2613f7`, gas 233,969,
  OOG 0. Its planned confirmation was correctly not run. (b13-b)
* **b14-a:** the shadow-value overlay's best positive-kappa arm lost held-out
  `-0.023709651182443503 +/- 0.009924094726245032`; it gained arb `+0.1318469238465615`
  but lost retail `-0.155556575029005`. Hash
  `263a8b85ce918e2e97ca650e12141e599ab0537bcdc5c4c91de6d54749ca92f1`, gas 222,723,
  OOG 0. Kappa zero was bit-identical to STACK on its check. (b14-a)
* **b14-b:** a second shadow variant lost `-0.04513793151763412 +/- 0.012969337368919887`
  on 512 held-out seeds; arb `+0.46179260788959176`, retail `-0.5069305394072259`,
  hash `0cedfc21bec98c29a673edc8fb02a38849bfe7a0de5ab33afeadbcc47ebb02d3`, gas 233,732,
  OOG 0. (b14-b)
* **b16-a:** a fee-state/flow overlay had retail `-0.027521553848475988 +/-
  0.005526355379147049`, arb `+0.0015873721222756723 +/- 0.001870614937477682`,
  hash `c4bdfae56273046c33e286add9808bfd38cf7ca3b2d81353a4bd44c1e5a6b67e`, gas
  221,343, OOG 0. (b16-a)
* **b16-b:** a directional/size overlay had retail `+0.025967712435194135 +/-
  0.0034113648431324853`, arb `-0.023181285679078775 +/- 0.0012605957497631225`,
  hash `008aad665c799dc97d70440adcd1e8478f9b3e7c7b4d4c937b0926f05d31fb91`, gas
  221,233, OOG 0. (b16-b)
* **b17-a:** a band-transport/displacement-control arm gained retail `+1.096507729447647`
  but lost arb `-1.2836638930629798`; net was therefore negative. Hash
  `51b8a9260dcda83a26014c6c028919cccc7ce9dcad9a15079882d0f0dbb3817e`, gas 202,854,
  OOG 0. (b17-a)
* **b17-b:** another band-transport arm gained retail `+0.7277613712419916` and lost
  arb `-0.7684287014782585`; hash `d11fe36b99e607fefacdca7ff7875ea24c02063e27c53a705928d0ec13bcd4ad`,
  gas 199,295, OOG 0. (b17-b)

## Designs and static analyses (not measured candidates)

* **b18-a:** proposes a two-step continuation-value overlay: value current retail
  routing plus the next opening-arbitrage edge, using only observable own-pool state and
  an offline table, with identity fallback. It is design-only: no compiled candidate,
  simulation, search, confirmation, or gas measurement. The exact router/CFMM/arb
  equations and static examples are useful hypotheses, not gains. (b18-a)
* **b18-b:** supplies the companion continuation design and falsification plan. It
  explicitly warns that first callbacks have no observable arb/retail label and that
  latent price, normalizer, future orders, and terminal inventory must not enter the
  deployed controller. No measured result is present. (b18-b)
* **b19-a:** proposes distribution-aware size-tail/censoring residuals and gives static
  quadrature calculations. Its own document labels these static calculations, not
  simulation gains or board estimates; its gas estimate is unmeasured. (b19-a)
* **b19-b:** gives a second size-tail design/analysis and prototype. It reports exact
  algebraic/static checks and candidate families, but no simulator run, candidate hash,
  paired result, or gas measurement; its arb-rule details were taken from the rules
  artifact rather than independently re-read. (b19-b)

## Continuation implementations and ablations

* **b23-cont-a:** implemented a 135-cell continuation table with identity fallback,
  trained from synthetic/empirical conditional rollouts. Frozen B hash
  `ff0575c4bfc0c15da14f44baf03e6b193aa1fb4fffd90687b05b1dd806d3d3d9` lost on held-out
  512 seeds: `-0.04449439399748534 +/- 0.012973072985185826`; retail `-0.48914170915166333`,
  arb `+0.4446473151541761`, gas 199,536, OOG 0. C0 ablation was also negative
  (`-0.046409840746823194 +/- 0.012069378954380367`). The result says its synthetic
  NumPy fitting is not Rust-RNG parity, its gates are heuristic, and no STACK or
  >=5,000,000 seed was used. (b23-cont-a)
* **b23-cont-b:** implemented a safer quantized continuation table. A2safe hash
  `3618c7886b7c24f867421f1dfa3055319d3994b796f944b32ea0f8aab5fa22e6` had recheck
  `+0.0045123305298000304 +/- 0.003710714282191342` but held-out
  `-0.002863054135920473 +/- 0.0031686271910556702`; retail `-0.02747415093549499`,
  arb `+0.02461109679957524`, gas 212,731, OOG 0. The un-gated A2 arm was much worse
  (`-0.2942523802211514` recheck). The result explicitly says the safe arm has no
  positive held-out gain and is not a board claim. (b23-cont-b)
* **b23-tail-a:** evaluated tail/DAR families and retained identity hash
  `9016d1ea81a401231e97d772cf74006d4c195b12fdeffded46a61b6219093259`. Identity was
  exact zero delta on recheck and held-out; the strongest small-tail ablation lost
  `-0.606617018174123 +/- 0.031301836445944704` held-out, and best controls were also
  negative. Identity gas max was 195,027, OOG 0. The CH calibration reproduced
  `525.5258821780834` exactly on seeds 0..999. (b23-tail-a)

## Direct RS1/V10/STACK run and disagreements

**b20-a** and **b20-b** both report the same RS1 hash
`df2817ba4ec233a456eb45909faa4a706efe0fabd1734a908fe52545f4d07577`, all 2,000
confirmation-block seeds, and zero OOG. They disagree slightly on observed gas and
component means because their concurrent runs had different observed paths: b20-a
reports afterSwap 202,387, retail `+0.022317766818636557`, arb
`+0.049897725743113776`; b20-b reports afterSwap 202,479, retail
`+0.03841017636069265`, arb `+0.046498311310773546`. Both report initialization
243,099 and zero halts. These are V10-harness decompositions; neither result supplies
the requested final paired-vs-STACK object, so they must not be silently converted into
one.

**b13-a** is blocked at setup on an incompatible Darwin arm64 host (no simulation,
`n=0`). **b21-b** is blocked before setup because its network proxy refused GitHub and
api.imdnotdead.fun (no simulation, `n=0`). These are missing results, not negative evidence.

The supplied source-reliability warning names failed or mismatched source reads for
e04-retail-state, e04-transition-policy, e04-continuation-design, e04-size-tail-design,
e05-confirm-rs, e05-rs-search, e05-rs-ablate, and e05-design-impl. Accordingly, the
design claims and offline/source-derived causal explanations in b15-a, b16-a/b,
b18-a/b, b19-a/b, b20-a/b, b21-a/c/d, b22-a/b, and b23-cont-a/b/tail-a are retained as
reported but are not treated as independently verified source facts. Measured numeric
outputs are attributed to their result files; where a result itself says its model,
decomposition, or RNG is approximate, that limitation governs.

## Consolidated action

The stable findings are: (i) size-aware retail state is more promising than count-only
flow, but observed V10-relative gains are only tenths; (ii) several overlays trade
retail edge for arb protection and lose or nearly cancel; (iii) continuation and tail
implementations failed held-out tests; (iv) every reported measured candidate had OOG 0,
but several initialization maxima are near 243,099 and must be kept distinct from the
250,000 afterSwap limit; and (v) no supplied result provides the required fresh,
>=2,000-seed, STACK-paired confirmation needed to claim a top-10 move. The next merge
should preserve these hashes and seed ledgers, reject negative/unconfirmed candidates,
and require the exact requested paired/gas/retail/arb report before submission.