# Merge 2: per-spread findings

## Scope and baseline

This merge combines all eight supplied item results. The baseline is the network's 108.47 entry. The task gives the board comparison as: first 109.93 (128.26 retail, −18.34 arbitrage), second 109.59 (130.77, −21.18), and this network 108.47 (130.37, −21.90). Thus the network already has the highest stated retail edge among these three, while its stated arbitrage loss exceeds the leader's by 3.56 per run. Those figures and the clues about final wealth and the best spread-4 run come from the task brief, not independent measurements in the item files.

The item authors generally replayed the earlier scorer against the supplied reference mean 108.63974289615767. a3-free, a3-rich, a4-free, a4-jumps, and a4-ledger report exact reproduction; a4-stock also reports exact reproduction, though its 600-run attempt took 1262 seconds. a4-after and a4-middle instead report 108.64128535876738, a difference of 0.001542462609705808, and explicitly say the cause is unknown. Treat that small Python/runtime-dependent mismatch as unresolved rather than claiming exact reproduction for all items. The simulator source is [the pinned challenge revision](https://github.com/danrobinson/prediction-market-challenge/tree/b244530ee2a6247b5f930830eeca9dd950da0e7e); the challenge description and scoring sequence are also stated in the task brief.

All eight results are present and nonempty: [a3-free](.imd/reads/artifacts/item-a3-free), [a3-rich](.imd/reads/artifacts/item-a3-rich), [a4-after](.imd/reads/artifacts/item-a4-after), [a4-free](.imd/reads/artifacts/item-a4-free), [a4-jumps](.imd/reads/artifacts/item-a4-jumps), [a4-ledger](.imd/reads/artifacts/item-a4-ledger), [a4-middle](.imd/reads/artifacts/item-a4-middle), and [a4-stock](.imd/reads/artifacts/item-a4-stock). The reported paired differences below compare candidate against start; positive arbitrage difference means less edge lost to the arbitrageur.

## Spread 3: retain both measured changes, with interaction untested

**Remove the above-probability ceil-tick ammunition bid (a3-free).** When the estimated probability has just crossed below a tick, omit the ammunition branch that buys YES at `ceil(p)`. On the 2,020 spread-3 confirmation runs in seeds 90000–97999, the paired mean edge increased **0.2840 per run** (SE 0.0421): arbitrage edge improved 0.3199, retail edge fell 0.0359; 299 runs improved and 83 worsened. The author reports all other spreads bit-identical. The report's mechanism is that this bid can sit above current probability and be taken in full by the arbitrageur. Its other ablations warn against removing the whole ammunition system: dropping branch B improved arbitrage edge by 1.04 but cost 1.16 retail edge, for a net loss; dropping the tick-1 stock bid lost 4.15 per run because the stock supported profitable asks, and removing the bridge lost 1.22. Source: [item-a3-free](.imd/reads/artifacts/item-a3-free).

**Use ordinary bid-risk weight after the full-horizon cover target is met (a3-rich).** In spread 3, below the low-price boundary, when current YES inventory covers inferred retail-buy flow over the remaining horizon, size additional low bids using the existing ordinary adverse-selection weight instead of the subsidized cover weight. The item reports a +0.4776 mean paired gain over all 1,938 spread-3 choosing runs (SE 0.0654), including +0.7430 arbitrage edge and −0.2653 retail edge; 741 runs improved and 181 worsened. Its independent rich-subgroup confirmation was positive but noisy (+0.3946, SE 0.3164; n=295). It also reports rejected alternatives: shortening the tick-1 reservoir horizon lost 17.85 per rich development run, and applying the ordinary weight before the full remaining demand was covered had a −0.1082 development mean. Preserve the long-horizon stock reserve; the proposed guard applies only after the inferred cover requirement is met. Source: [item-a3-rich](.imd/reads/artifacts/item-a3-rich).

These are distinct, spread-3-only conditions and each has a positive reported result. The files did not test the two changes together, so their gains cannot be added as a measured package result. The a3-rich report says one of its one-source citations failed rechecking; no source-dependent assertion from that citation is used here. Its run counts, paired scores, and described ablations are recorded as the item's own simulator experiments, not independently verified measurements.

## Spread 4: three retained findings

**Add resting probes between the estimated probability and main quotes (a4-free).** Keep all original probes and add 0.01-share resting probes at intervening ticks strictly between the estimate and each main quote. The rationale is to preserve a tighter probability bracket when retail clears probes on one side during a move. On all 1,937 spread-4 confirming runs in 90000–97999, mean edge improved **0.5003 per run** (SE 0.1461): retail +0.3333, arbitrage +0.1670; 1,122 improved and 815 worsened. The item attributes the result to the full change, while noting the arbitrage component alone is small relative to its noise. Removing crossing probes instead was harmful: the variants lost 1.69 to 113.25 per run in the reported tests, consistent with their information value. Source: [item-a4-free](.imd/reads/artifacts/item-a4-free).

**Correct spread-4 main-bid sizing when inventory meets the cover target (a4-ledger).** Reuse the existing spread-4 flow estimate for main-bid size, and skip the low-probability stock-building loss discount once YES inventory is at or above the inferred target; retain that discount when stock is still short. The frozen change gained **0.5809 per run** on 1,937 confirming spread-4 runs (SE 0.0484): arbitrage edge +0.6594 and retail edge −0.0785; 809 runs improved and 162 worsened. It gained 0.5086 over all 2,050 choosing runs, with positive gains across the four reported validation quarters. By contrast, removing the above-value ammunition purchase branch gained 0.2013 in discovery but lost 0.1546 on the previously unused choosing half, so that ablation was rejected. Source: [item-a4-ledger](.imd/reads/artifacts/item-a4-ledger).

**Cap routine above-fair-value stock purchases at current desired ask quantity (a4-stock).** In spread 4 only, cap the existing flow-scaled routine stock target by `qa`, the current desired ask size; preserve the existing crossing buys and flow estimate. On 1,026 choosing runs from the reduced 30000–33999 window, this frozen variant gained 0.2788 per run (SE 0.0405), with 186 improved and 15 worsened. The 976-run confirmation from 90000–93999 gained **0.2593 per run** (SE 0.0550), arbitrage +0.3128, retail −0.0535; 195 improved and 11 worsened. The choice was first made using separate 100-run pilot and validation sets; the larger choosing comparison followed with code frozen. This is a promising independently confirmed change, although its confirmation window was only half the prescribed 90000–97999 range because the scorer run was slow. Source: [item-a4-stock](.imd/reads/artifacts/item-a4-stock).

The a4-ledger and a4-stock changes both affect spread-4 acquisition sizing and inventory sufficiency. Neither item tested the other item's rule in its candidate. a4-free's probe additions also change information available to the strategy, and no item tested them together with either sizing change. Therefore, the three positive estimates are separate results, not an estimate for their combined effect. The a4-ledger and a4-stock reports each identify one source that failed rechecking. This merge relies on their described local paired simulations for these experimental findings, not on claims that depend on the failed citations; the inaccessible or unsupported source claims cannot be established from the supplied material.

## Spread-4 findings not retained

- **Jump-specific ask multipliers (a4-jumps): rejected.** Increasing asks below 10 cents by 15% appeared to gain 0.4187 on the first 1,000 choosing runs, but lost 0.3990 on the 1,050 unused choosing runs. The narrower below-5-cent variant likewise changed from +0.1927 to −0.1212. These reversals do not support retaining either adjustment. The item returned the start strategy unchanged. Source: [item-a4-jumps](.imd/reads/artifacts/item-a4-jumps).
- **Belief resets, quote pauses and temporary exposure reductions (a4-after): no gain established.** Increasing the uniform belief component after outward shifts was essentially flat over all 2,050 choosing runs (+0.0038, SE 0.0245). Other measured alternatives were negative, including resets after missing probes (−15.37) and keeping quotes farther from the estimate after a shift (−0.334). The item kept the start unchanged. Its reported diagnostic found outward quote shifts, but the tested reactions did not establish an improvement. Source: [item-a4-after](.imd/reads/artifacts/item-a4-after).
- **More conservative interior sizing and probe pruning (a4-middle): reject tested versions.** On 516 discovery runs, full modeled marginal-loss sizing lost 3.15 per run; suppressing quotes within one tick of estimated fair value lost 0.60; suppressing just bids lost 1.26; pruning interior probes lost 0.92. A separate variant imposing a five-callback stock pause after an adverse-fill proxy lost 0.305 over all 2,050 choosing runs. The submitted strategy was unchanged. Source: [item-a4-middle](.imd/reads/artifacts/item-a4-middle).

The no-change outcomes matter: they do not refute the retained, narrower proposals, but they provide no support for broad pauses, blanket quote shrinkage, interior-probe pruning, or the tested jump multipliers.

## Cross-item interpretation and limits

Several measurements explain why blanket inventory reduction is risky. a3-free reports that low-price asks earned substantial retail edge and that removing cheap stock sources harmed the score. a3-rich reports long low-price episodes and rejects a short stock horizon. a4-stock's FIFO accounting attributes most ending YES to main quote fills rather than its named stock rules, and explicitly cautions that attribution is not a causal estimate. a4-ledger's surplus guard targets main bids after inferred cover is already satisfied, preserving bids while inventory is short. These findings support targeting excess acquisition after cover rather than deleting the inventory and quotes that generate retail fills. Sources: [item-a3-free](.imd/reads/artifacts/item-a3-free), [item-a3-rich](.imd/reads/artifacts/item-a3-rich), [item-a4-stock](.imd/reads/artifacts/item-a4-stock), [item-a4-ledger](.imd/reads/artifacts/item-a4-ledger).

The supplied task calls out a failed or unsupported citation in each of a3-rich, a4-ledger, and a4-stock. Their source-derived background claims are consequently not treated as established here. The measured strategy comparisons cited above are reported as experiment results in those files; they are not source-page facts. The remaining item files contain no recheckable URL list in the supplied JSON. Apart from the task brief's pinned simulator link and the simulator commit URL in a4-middle, no further external source content can be confirmed from the supplied results. Accordingly, no external claim about Paradigm or the simulator beyond the brief and those recorded experiments is added.

## Merge recommendation

Carry forward the five retained conditional changes as candidates for a combined strategy: both spread-3 rules (a3-free and a3-rich), plus the spread-4 probe addition, surplus-aware main-bid sizing, and current-ask stock cap. Every rule is confined to its stated spread. The positive per-change means are evidence for each rule on its reported seeds, not a forecast of the combined file: the cross-rule interactions remain unmeasured, and the a4-stock confirmation covers only 976 spread-4 seeds. Keep the rejected/no-change results above attached to this recommendation so none of the eight items' findings are silently lost. No combined score, leaderboard placement, or net gain for the full five-change package can be inferred from these item results.