The strongest supported direction is to curb expensive inventory purchases while preserving the cheap stock that funds profitable retail asks. My preferred files are a1-free, a2-after, a3-ledger and a4-rich, with a1-jumps and a4-ledger retained as serious alternatives. These are choices from reported paired experiments, not a demonstrated first-place entry. No combined file or candidate evaluation on Paradigm’s runs is supplied. [M1; M2]

The requester’s board figures are first 109.93, with 128.26 from retail and 18.34 lost to arbitrage; second 109.59, with 130.77 and 21.18; this network 108.47, with 130.37 and 21.90. The network out-earns the leader on retail and loses 3.56 more per run to arbitrage; second place still earns more retail than the network. M2’s statement that the network has the highest retail edge of these three contradicts its own figures. Mean final wealth of 1,036 versus 1,074, and the best spread-4 run paying about 1,362 versus about 1,440, are clues, not proof that less inventory improves scored edge. The earlier warning remains relevant: a change gained 0.95 over 2,035 unseen runs of its spread but lost about 2.9 on Paradigm’s runs, all to arbitrage. [Task brief; M1, “Decision for an operator”; M2, “Scope and baseline”]

Sources and reading conventions:

• [M1] means merge-01, supplied as .imd/reads/artifacts/merge-01, SHA-256 476806c69d1c42987bc9039e81ea38926dda71544b21bed2e68c86c1061b4c24. It covers all 20 of its items. Item IDs identify the subsection, ledger row and synthesis.
• [M2] means merge-02, supplied as .imd/reads/artifacts/merge-02, SHA-256 779a7c829eeaddf1af1f3a13f9966a0704677a0bd74cb64ac24d9b1a5adacf3b. It covers all eight of its items. Item IDs identify named paragraphs. Underlying JSONs and logs were not supplied here.
• The task identifies the start file, earlier scorer file, and simulator. M2 names revision b244530ee2a6247b5f930830eeca9dd950da0e7e. These links were not independently rechecked.

The table has one row per item. “Δ (SE)” is mean paired candidate-minus-start edge per run of that spread, with its standard error; retail and arb are the corresponding signed edge differences. Positive arb means less lost. M1 says its trim generally removes the 20 largest absolute paired differences; it is not a percentage trim. Up/down excludes unchanged runs. Confirmation is on matching seeds in 90000–97999 unless a subset is stated; choosing uses matching seeds in 30000–37999, with reductions described below. [Task brief; M1, “Complete candidate ledger”; M2]

NR means absent from the merges, not zero. Named loss diagnostics are not certified maxima unless stated; losses are per run unless specified. Failed-variant score declines are labeled separately from baseline arb losses. All numerical precision is preserved as printed in the merges; M1 itself rounded its ledger and experiment index, so original item precision cannot be recovered here. Neither merge supplies candidate/start wall-time pairs. [M1, ledger and item-index conventions; M2]

Spread / part; source	Largest loss measured / available diagnostic	Submitted change	Confirming n; Δ (SE)	Trimmed mean	Up / down	Retail Δ; arb Δ	Other spreads identical?	Seconds: candidate / start
1 / after [M1:a1-after]	NR	Halve sizes for 1 step after a rival quote shift of >=2 ticks	64; 0.126070 (0.096832)	0.000337	28/8	0.002189; 0.123881	Yes reported; 36 pairs	NR; 6 runs scaled to 200
1 / free [M1:a1-free]	NR	Lower routine ammo bid one tick	1027; 0.475181 (0.189718)	0.467330	227/69	-0.360230; 0.835411	Yes reported; 450 pairs	NR
1 / jumps [M1:a1-jumps]	Jump-step loss 9.400; other steps 13.180; rule maximum NR	Split ordinary asks at ticks 3..98 equally; back half one tick higher	2032; 0.833990 (0.658410)	0.722121	1357/584	-0.166255; 1.000244	Yes reported; 900 pairs	NR
1 / ledger [M1:a1-ledger]	Tick-1 stock about 11.07; maximum not established	Halve tick-1 stock quantity	506; 0.665594 (1.818570)	-0.715853	97/132	-3.223409; 3.889003	Yes reported; 200 pairs	NR; 40 runs scaled to 200
1 / middle [M1:a1-middle]	Pre-move band: 21.3 lost below 5c versus 2.4 in mid band	Remove bridge at estimated probability >=5c	2032; 0.037533 (0.037321)	0.046876	422/272	-0.151401; 0.188934	Yes reported; 900 pairs	NR
1 / rich [M1:a1-rich]	Arb maximum NR; 67.523 size/no-quote retail-dollar residual is not arb loss	Return start unchanged	2032; 0.000000 (0.000000)	0.000000	0/0	0.000000; 0.000000	Yes; baseline hash; 900 pairs	NR
1 / stock [M1:a1-stock]	Tick-1 stock 8.793; maximum not established	Return start unchanged	2032; 0.000000 (0.000000)	0.000000	0/0	0.000000; 0.000000	Yes; baseline hash; 900 pairs	NR
2 / after [M1:a2-after]	Old resting main asks on jump steps 8.232, identified as largest single loss	One-step hold after tracked main-order depletion; exact order scope not retained	2011; 0.619103 (0.118830)	0.612694	1378/630	-0.438114; 1.057218	Yes reported; 900 pairs	NR
2 / free [M1:a2-free]	Unusable attribution ledger; maximum unavailable	Return start unchanged	240; 0.000000 (0.000000)	0.000000	0/0	0.000000; 0.000000	Yes by unchanged file; 0 tested	NR; timing used 240 pooled runs
2 / jumps [M1:a2-jumps]	NR	Halve bridge quantity when estimated probability is between 0.02 and 0.1	1006; 0.217720 (0.107436)	0.111533	307/194	-0.142351; 0.360071	Yes reported; 450 pairs	NR
2 / ledger [M1:a2-ledger]	NR	Permit routine ammo only at tick 1; preserve crossing and reserve	2011; 0.250538 (0.053333)	0.142697	228/52	-0.114062; 0.364600	Yes reported; 900 pairs	NR
2 / middle [M1:a2-middle]	NR; source locates most arb take at bids filled under 5c	Exact transformed one-step diffusion distribution, 60 nodes	2011; 0.110224 (0.035773)	0.111186	1177/834	0.156757; -0.046534	Yes reported; 900 pairs	NR
2 / rich [M1:a2-rich]	NR	Reduce low-probability ammo reserve: ammo_pmax 0.005, fy 0.2	8, seeds 90000–90019; 0.307978 (0.307978)	0.000000	1/0	-0.175143; 0.483121	Yes reported; 900 pairs	NR
2 / stock [M1:a2-stock]	Tick-1 stock 2.78 versus routine ammo 1.96; whole-ledger maximum NR	Disable tick-2 routine ammo, equivalent to a2-ledger	2011; 0.250538 (0.053333)	0.142697	228/52	-0.114062; 0.364600	Yes reported; 900 pairs	NR
3 / after [M1:a3-after]	NR	Narrow stock delay after downward signal; exact selected duration not retained	1010, every-other subset; 0.060450 (0.106578)	0.030033	204/157	-0.067267; 0.127717	Yes reported; 450 pairs	NR
3 / free [M2:a3-free]	NR	Omit above-probability ceil-tick ammo bid after probability crosses below a tick	2,020; 0.2840 (0.0421)	NR	299/83	-0.0359; 0.3199	Bit-identical reported; count NR	NR
3 / jumps [M1:a3-jumps]	NR	Split cover bids at tick >=2 equally; back half one tick lower	2020; 0.231238 (0.074481)	0.286872	685/340	-0.087722; 0.318960	Yes reported; 900 pairs	NR
3 / ledger [M1:a3-ledger]	Jump loss 14.706 versus other steps 13.597; front asks contribute 10.304 jump loss	Cap routine ammo target by current desired ask size	2020; 0.486756 (0.027370)	0.433424	571/32	-0.006709; 0.493465	Yes reported; 900 pairs	NR
3 / middle [M1:a3-middle]	NR	Scale 41–80c quotes by 0.75 with <=250 steps remaining; source’s “final quarter” label is wrong	2020; 0.008105 (0.001627)	0.006554	314/156	-0.023480; 0.031585	Yes reported; 900 pairs	NR
3 / rich [M2:a3-rich]	Arb maximum NR; shortening reserve lost 17.85 per rich development run in score	Use ordinary low-bid risk weight only after full remaining retail demand is covered	Rich subgroup only, n=295; +0.3946 (0.3164); full confirmation NR	NR	NR for confirmation	NR for confirmation	Spread-only guard described; equality test NR	NR
3 / stock [M1:a3-stock]	Arb maximum NR; about 1010 unsold YES from ordinary bids below 5c versus about 436 from reserve	Cap routine ammo at current ask shortfall; equivalent to a3-ledger	1010, first qualifying half; 0.470072 (0.037322)	0.358004	271/12	0.006068; 0.464004	Yes reported; 450 pairs	NR
4 / after [M2:a4-after]	Arb maximum NR; missing-probe reset lost 15.37 in score	Return start unchanged	NR	NR	NR	NR	Unchanged file reported; test NR	NR
4 / free [M2:a4-free]	Arb maximum NR; removing crossing probes lost up to 113.25 in score	Add 0.01-share resting probes between estimate and main quotes; retain original probes	1,937; 0.5003 (0.1461)	NR	1,122/815	+0.3333; +0.1670	Spread-only change described; equality test NR	NR
4 / jumps [M2:a4-jumps]	Arb maximum NR; below-10c ask enlargement lost 0.3990 on unused choosing runs	Return start unchanged	NR	NR	NR	NR	Unchanged file reported; test NR	NR
4 / ledger [M2:a4-ledger]	NR	Flow-aware main-bid sizing; remove stock-building loss discount once cover target is met	1,937; 0.5809 (0.0484)	NR	809/162	-0.0785; +0.6594	Spread-only guard described; equality test NR	NR
4 / middle [M2:a4-middle]	Arb maximum NR; full marginal-loss sizing lost 3.15 in score	Return start unchanged	NR	NR	NR	NR	Unchanged file reported; test NR	NR
4 / rich [M1:a4-rich]	Low-price bid arb loss 14.791 per rich run; maximum not established	Restore existing low-price bid risk penalty kL	n not stated; 0.589009 (0.053431)	0.622653	792/188	-0.094781; 0.683790	Yes reported; 900 pairs	NR
4 / stock [M2:a4-stock]	NR; FIFO says most ending YES came from main quotes	Cap flow-scaled routine stock target by current desired ask size	976, seeds 90000–93999; 0.2593 (0.0550)	NR	195/11	-0.0535; +0.3128	Spread-only guard described; equality test NR	NR; 1262 seconds is earlier-file calibration only

Timing comparisons and omitted confirmation statistics cannot be reconstructed. a4-rich’s up/down count omits unchanged runs and cannot establish n. M1 reports zero holdout failures but supplies no per-run arrays to recompute uncertainty. [M1, “Counts and timing are heterogeneous” and “Complete candidate ledger”; M2]

The preferred files, and why they lose less:

• Spread 1: a1-free — the conservative choice in M1, lowering routine inventory purchases one tick. It gives up 0.360230 retail edge to save 0.835411 arbitrage edge, with positive trimmed gain 0.467330. The exact strategy identity recorded by M1 is SHA-256 aed6d158efa525beefc4a55d511818df9ba8c2c40cfb9bcc62a4978f3a9b020a, in artifacts/goal/items/a1-free/result.json. a1-jumps has the higher mean and broader run coverage: 0.833990, 1357/584 up/down, trimmed 0.722121, but SE 0.658410. Splitting ordinary asks reduces the amount exposed at the front price. These alternatives were not compared head-to-head on one complete untouched set; the choice is provisional. a1-ledger’s positive mean does not overcome its negative trim and more down than up runs; a1-middle and a1-after remain weak alternatives. [M1:a1-free, a1-jumps, a1-ledger, a1-middle, a1-after]
• Spread 2: a2-after — the broadest strong confirmation in this spread: 1378/630 up/down and trimmed 0.612694. Disappearance of a tracked main-order ID triggers a one-step response, limiting exposure after depletion; it is an observable proxy, not knowledge of who filled the order. Its arbitrage saving 1.057218 outweighs retail loss 0.438114. M1 records SHA-256 963807d6db6ddd2ccf3e594d938edd2c4a7452c7b1172733513b8f013d3688ab, in artifacts/goal/items/a2-after/result.json. a2-stock/a2-ledger offer the same effective tick-2 ammo restriction and count once. a2-jumps is smaller; a2-middle improves total edge while increasing arbitrage loss. The eight-run a2-rich result, with only one winner and no trimmed gain, does not support entry. [M1:a2-after, a2-stock, a2-ledger, a2-jumps, a2-middle, a2-rich]
• Spread 3: a3-ledger — caps routine ammo at the current ask requirement while preserving crossing purchases and the reserve. Its 0.493465 arbitrage improvement costs only 0.006709 retail edge; 571 runs improve, 32 worsen and 1417 are unchanged. M1 records SHA-256 3bcbb5f3d400eb31c7ed5a1f45929987613cea9e96b2df850e5ed1af8335b448, in artifacts/goal/items/a3-ledger/result.json. a3-stock is an equivalent restriction with reduced coverage and a scorer mismatch. a3-free and a3-jumps are alternatives, not additive gains. a3-rich’s +0.4776 (SE 0.0654), +0.7430 arb, -0.2653 retail and 741/181 up/down are choosing results on 1,938 runs; they must not be relabeled as confirmation. Its rich-subgroup confirmation is too noisy to displace a3-ledger on the supplied evidence. [M1:a3-ledger, a3-stock, a3-jumps; M2:a3-free, a3-rich]
• Spread 4: a4-rich — restores the existing low-price bid risk penalty, saving 0.683790 arbitrage edge at a 0.094781 retail cost, with positive trimmed 0.622653. M1 records SHA-256 41f2bb431d34c009ae17d19e19551fbce150cd1b23166374e759ed4f92f0a570, in artifacts/goal/items/a4-rich/result.json. a4-ledger is a close alternative with explicitly complete confirmation coverage and SE 0.0484: it preserves the acquisition subsidy while stock is short and removes it after inferred cover is met. Superiority over a4-ledger is unproven. a4-free improves both components through extra information; a4-stock confirms the routine-ask cap on a reduced window. None was tested together. [M1:a4-rich; M2:a4-ledger, a4-free, a4-stock]

File names and hashes identify worker submissions; no code is included. Cross-spread gains are separable under mutually exclusive guards. Same-spread edits interact through inventory, cash, priority and rival replenishment; overlapping gains cannot be added. The ammo-pair equivalences are M1’s reported code-inspection findings. [Task brief; M1, “Equivalent changes are not additive”; M2, “Merge recommendation”]

What the measurements agree on is more specific than “buy less.” The scored quantity is fill edge against probability after the move: rival lots return, the strategy quotes, probability moves, arbitrage takes all crossed orders, and retail follows. Inventory at expiry is not itself scored. The brief’s older-file map assigns 14.6 of 27.7 lost per run to 3.8 jump steps and 11.0 to arbitrage-filled bids below 5 cents; those categories can overlap and are not a decomposition to add together. [Task brief]

The retained numerical diagnostics are:

• Spread 1, below 5c: a1-middle’s pre-move map reports about 60.3 retail and 21.3 lost below 5c, versus about 2.3 retail and 2.4 lost in the middle band. a1-stock reports 1720 shares of ordinary bids filled by arbitrage below 5 cents, costing 2.80 per run, and 1640 shares of asks below 5 cents, costing 6.94, including 2.03 at tick 2 and 2.90 at tick 1. Its tick-1 stock loss is 8.793; a1-ledger’s smaller-window estimate is about 11.07, not an independently reconciled figure. a1-jumps measures 3.903 actual jump steps/run, losing 9.400 there versus 13.180 elsewhere. Different samples and band definitions prevent combining these figures into one ledger. [M1:a1-middle, a1-stock, a1-ledger, a1-jumps; “Findings retained across approaches”]
• Spread 2, stale asks and costly top-ups: a2-after’s largest single loss is 8.232 from old main asks on jump steps. On non-jump steps immediately after an arb fill it measures approximately 0.03875 lost per step, versus 0.00461 on plain steps; new same-side stock and main bids dominate that next-step loss. a2-stock’s routine ammo costs 1.96 on about 249.5 arb-bought shares, compared with 2.78 on about 3042.4 tick-1 stock shares. Cheap reserve and expensive repeated top-up purchases should therefore be distinguished. The merges do not retain a complete numerical spread-2 price-band table. [M1:a2-after, a2-stock]
• Spread 3, front asks on jumps and above-estimate ammo: a3-ledger records 3.879 actual jump steps/run, losing 14.706 there and 13.597 elsewhere. Front asks alone cost 10.304 on jumps while contributing 124.485 total retail edge. Routine ammo costs 1.608 in arbitrage against only 0.00985 direct retail; that direct comparison omits later ask sales funded by the stock. a3-stock’s FIFO sample leaves about 1010 YES from ordinary bids below five cents versus about 436 from the one-cent reserve. M2 similarly attributes most ending spread-4 YES to main quotes, but retains no numerical breakdown. [M1:a3-ledger, a3-stock; M2:a4-stock]
• Spread 4, low-price bids in rich runs: a4-rich measures 14.791 low-price bid arb loss per rich run, versus static ask-size gap about 9.008, no-stock gap 0.526 and worse-price gap 0.00258. Those gaps are opportunity diagnostics, not realizable gains. Its chosen change gains 1.160 on the frozen confirming rich subset of 253 runs. M2’s a4-ledger independently supports conditioning main-bid subsidy on available cover; a4-free’s +0.1670 arbitrage improvement is small relative to its noise and does not by itself establish a strong arb mechanism. [M1:a4-rich; M2:a4-ledger, a4-free]

Blanket inventory cuts repeatedly damage retail cover: a1-jumps’ stock-rate halving loses 6.914; a2-ledger’s shorter reserve horizon loses 8.045; a3-free’s reserve removal loses 4.15 and bridge removal loses 1.22. These separate experiments cannot be added. [M1, “Inventory acquisition”; M2:a3-free]

Broad ask and belief changes also fail to generalize. a1-jumps’ ordinary ask split succeeds, but a3-jumps’ main-ask split loses 5.811 on discovery. a4-jumps’ below-10-cent ask enlargement goes from +0.4187 to -0.3990 on unused choosing runs; its below-5-cent version goes from +0.1927 to -0.1212. a4-after’s uniform-belief increase is +0.0038 (SE 0.0245), while missing-probe resets lose 15.37 and moving quotes farther away loses 0.334. a4-middle’s full marginal-loss sizing loses 3.15, near-fair quote suppression 0.60, bid-only suppression 1.26, interior probe pruning 0.92, and its stock pause loses 0.305. The unchanged returns in these seats preserve useful failures. [M1:a1-jumps, a3-jumps; M2:a4-jumps, a4-after, a4-middle]

Important evidence limits remain. Actual jump-count-positive steps in a1-jumps and a3-ledger differ from a2-after’s absolute score-move-above-0.08 proxy, a2-free’s four-diffusion-SD proxy, and a2-middle’s probability-move-above-3-cents proxy. Pre-move probability, limit price, fill price and post-move probability bands are different classifications. An ask originally below 5c can be crossed by a jump into the middle band; that is not evidence against an ordinary middle-price quote. a2-free’s wrapper accumulated across runs, inflating attributed loss to roughly 72 versus true loss roughly 26; its absolute diagnostic ledger is unusable. [M1, “Jump definitions differ” and “One unusable ledger”]

Scorer checks are also imperfect. Most completed M1 checks reproduce 108.63974289615767 on the earlier file’s 600 seeds starting at 1000; a1-after has no completed calibration. a3-stock, a4-after and a4-middle report 108.64128535876738, differing by 0.001542462609705808; a3-middle reports 108.6412853587675. The cause remains unresolved. a3-middle’s choosing baseline 126.39561823742822 also differs from a3-ledger’s 126.39937568895706 on the ostensibly same 1938 seeds. a3-middle’s “final quarter” narrative actually applies at 250 steps remaining in a 2000-step run, the last eighth. Its factor/band searches, a2-rich’s numerical search and 500-step development, and a2-middle’s 20 to 60 node change weaken no-tuning compliance. a4-rich explored numerical probes but discarded them in favor of an existing coefficient. [M1, “Scorer discrepancy” and “Timing-label correction”; M2, “Scope and baseline”]

Failed external-source rechecks affect a2-stock, a4-rich, a1-stock, a1-middle, a2-ledger, a2-jumps, a3-ledger and a3-stock in M1, and a3-rich, a4-ledger and a4-stock in M2. Failed-source manifests are absent; exact unsupported quotations cannot be identified. These remain attributed worker experiments. Paradigm seeds, candidate board scores, a combined backtest and reproducible logs are absent. [M1, “External-source warnings” and “What remains unproven”; M2, “Cross-item interpretation and limits”]

The seats propose these next tests:

• Spread 1: a1-free proposes letting the lowered ammo bid rest behind the rival; a1-jumps proposes inventory/time-aware cover and separate terminal-boundary risk work; a1-ledger proposes sizing reserve from realized ask sales; a1-middle proposes cover goals specific to the bands below 5c. a1-after wants better observable discrimination between retail and arb depletion before side-specific holds. a1-rich proposes a probability/jump-risk-aware crossing-cover cap. a1-stock disagrees about spending more effort on tick-1 stock and instead proposes sizing tick-1 asks from time spent below tick 1. Preserve that disagreement and test it on fresh paired runs. [M1, respective “Follow-up hypothesis” paragraphs]
• Spread 2: a2-after proposes responses to rival quote shifts and partial rather than complete holds to recover retail edge; a2-free proposes brief low-ask protection after upward signals, with much broader testing. a2-jumps and a2-ledger want downstream retail liquidation value measured before reducing cover; a2-stock proposes remaining-flow reserve sizing and crossing-price bridge purchases. a2-middle proposes exact-distribution treatment of jumps and the low-price region. a2-rich proposes an inventory-aware reserve schedule, but its current sample is inadequate. [M1, respective follow-up paragraphs]
• Spread 3: a3-ledger wants downstream ask credit attributed to the stock rule and observable retail-use caps tested against front-ask availability; a3-stock wants inventory-aware main bids below five cents and demand forecasts that allow the ask price to change. a3-jumps proposes checking remaining retail demand before reserve purchases. a3-after wants to explain harmful holdback outliers and preserve urgently needed cover. a3-middle proposes a prechosen smooth late/interior size rule with fresh validation. M2 proposes retaining a3-free and a3-rich for interaction tests; it supplies no separate seat-level next-step text for those two items. [M1, respective follow-up paragraphs; M2, “Merge recommendation”]
• Spread 4: a4-rich proposes structural stock caps from expected retail demand and separating ask-capacity misses from rival ladder movement. M2 proposes testing the probe addition, surplus-aware main-bid sizing and current-ask stock cap together, with their interactions measured. Its individual seat-level follow-up proposals are not retained, so none are invented here. Compare these against a4-rich as alternatives before combining acquisition rules. Keep the rejected jump multipliers, broad resets and probe pruning as negative controls. Freeze any new combination before fresh choosing/confirmation work; the already inspected confirming window is not a new independent holdout. [M1:a4-rich and “What remains unproven”; M2, “Merge recommendation”]