Credit: Taylor (gtmcknight), [amm-sim, commit 4812a6382311624e1506aca131ca35c378f930d9, research/solved][Taylor], for the solved policy, Gaussian filter, replica, exact-arithmetic arb/retail tell and U1 tables. QLX5 and AGE are network extensions of Taylor's work. This is root merge 1 of 2, covering exactly the 25 supplied results; it is not a merge of the other root.

**No qualifying improvement is established by this root.** QLX5+AGE has a reported implementation/parity pass, but its fresh engine results do not show the required +0.04 over QLX5. The structural search returns 64 small screens, with no qualifying winner; all 20 idea tests decline promotion. The useful positive deliverable is an engine-faithful, integer-exact QLX5 reference, with a later audit strengthening its evidence from rounded final scores to unrounded scores and full traces. These are research and validation results, not a leaderboard submission. [b01-qa] [b02-qa] [b04-qa] [b09-merge-01] [b09-merge-02] [b10-merge-01] [b10-merge-02] [b13-r3]

The supplied goal states **528.3333 (4th)** versus **#1 (528.4152)**, about **+0.08** needed, with exact engine-to-board gain transfer; this merge did not read the live board. Historical AGE is **+0.032, SE 0.008, 512 engine seeds over LEAN**, not over QLX5 ([origin][AGE], [engine][AGE-engine]). Required: **>=+0.04 over QLX5 on 1,024+ fresh engine seeds**, also paired against QT1; <=50,000 source characters, <=24,576 deployed bytes, engine afterSwap peak <=245,000, 0 OOG. Gates: P; Q (choice 64000..65023, report 10000..12047); T (Python-reference labels); F (<=0.01 bps); G; E. AGE confirmation requested 2,048 fresh seeds. These are goal requirements, not achievements.

**Evidence convention.** Citations resolve to the 25 supplied artifacts and full SHA-256 addresses below. All input hashes and JSON parsing were checked locally. Figures are attributed worker measurements unless marked “merge calculation”; no engine/compiler/strategy was rerun here. Repeated code, commands, manifests and per-seed diagnostics are consolidated into citations; missing observations stay missing, and overlapping seed sets are counted once.

**Frozen identities and common measurement setup.** The following source/runtime identities recur in the AGE work; they distinguish the policy under test from its artifact container. [b01-qa] [b02-qa] [b04-qa] [b11-s1] [b12-s7]

| Arm | Solidity source SHA-256 | Runtime SHA-256 | Source characters / deployed bytes |
|---|---|---|---|
| QLX5 | `e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40` | `903a0cf860910022916e7c16aa1ffcfb94b0db9e25074665947d786615a44ae8` | 47230 / 22440 |
| CAND = QLX5+AGE | `c0fb05961b60655744bfc5597a098e2f91bc5b90db9e8688e488d077864fb5da` | `d5d5ddaddcfac4a7212f7be41e26453776536571bd006c4c24b177523f63a0d9` | 47757 / 22558 |
| QT1 | `c68887cff61180e12ba2b1ceb333edf76a830f91f63b5d775a8806fb9ec08aca` | `79c8d6c305ec6dfc29770b27cfb15b6cbd57b1fb01a23309cf8c131ca5c70189` | 42990 / 20605 |

QLX5 comes from `code_zb64.QLX5` in the [base artifact][base], with the [base certification][cert]. The unchanged production QPL1 blob hashes to `830868f9b3e5ad162c4f2070e6faed0782c7b4cc308ab69044b2cf7306f68099`. The certified Python source mapping hashes to `35a93a38433a6860d2843504651f703b4b195b5aa7d58d7ff432d3900d7777cb`. AGE's Python payload is an overlay, not a self-contained reference: it needs the certified patches/production lookup, unchanged QLX5 tables and Taylor's `pol_mid.json` and `qm_k1e-5.json`. [b01-qa] [b02-qa]

The engine is benedictbrady/amm-challenge at `6b6921f8d463314aa7c96234e1be25a25245f704`; the kit is pinned at `45e7563d1a29ffca9d608fdf60c90bf2624d2d01`. The native release engine hashes to `ff88b6353c2aad7342f0a26194f7347e78b9c3b38d683a7449006d423978cd14`. The compiler is solc 0.8.24, optimizer 200, viaIR, Paris, binary SHA-256 `fb03a29a517452b9f12bcf459ef37d0a543765bb3bbc911e70a87d6a37c30d5f`. The [block-driver artifact][driver] supplies unchanged driver bytes with SHA-256 `d3f8646b541a76921a47e9d03247c8c9dfab594076a7c5dca79c36b6c048a282`. [b01-qa] [b04-qa] [b11-s1] [b11-s2] [b12-s6]

Engine arms run separately against fixed 30-bps VanillaStrategy, identical seed/config, 10,000 steps. Later AGE wrappers compare all 12 config fields and call unchanged score.py summarize on unrounded differences, using the requested two-SE rule rather than the CLI's seed restrictions/three-SE rule. They report build -> check -> engine, generally eight workers. The goal requires after dependencies and requires {platform: linux-x64, minCpus: 4}; s5/s8 allocation caveats follow. [b04-qa] [b11-s1] [b11-s2] [b11-s3] [b11-s4] [b12-s5] [b12-s6] [b12-s7] [b12-s8]

**AGE implementation and certification.** On nonbinding retail without a split hit, alpha=0.35 becomes WAD `floor(7e17*age/(age+1))`, age=timestamp−rt (a0=0, ainf=.7, tau=1). A binding bound or split hit sets rival=c and refreshes rt; arb leaves rt unchanged. Zero weight leaves rival unchanged but sets synced. rt starts at 0 in slot-2 bits 224..254, adds no word, wraps at >=2^31, and supports engine timestamps 0..10000. Slot-6 offset, filter, tell, phases, tables, split algorithm and fee guard remain unchanged. Source adds 527 characters in five hunks. [b01-qa] [b02-qa]

The build checked all 10,001 integer ages 0..10000: zero pull-weight mismatches, maximum float-reference error 2.220446049250313e-16, and disjoint storage masks. Its four-seed T/F smokes (74200..74203) found no label, offset, rt, synced or fee failures: autonomous/fixed streams had 45,201/45,187 callbacks, 29,180/45,076 split tests, 25,970/783 split hits and the same number of rt split resets. Both compared 8,000 fee callbacks; worst fee errors were 2.62e-11/7.077e-11 bps. Executable runtime matched the engine compile after excluding source-name CBOR metadata. [b01-qa]

The build's gas-only engine seeds **10202048..10202055** produced CAND peak 204280, QLX5 peak 206296, 85,056/85,059 afterSwap calls and no callback failures/OOG. Their CAND−QLX5 mean was −0.014718714192632376, SE 0.03894421482389398; worst seed 10202052 was −0.1895118848515267. These eight already-consumed seeds are neither fresh efficacy confirmation nor QT1-paired evidence. `ready: true` means the build/smokes passed. [b01-qa]

The larger check reports P/T/F/G pass for the same frozen source. On seeds **74200..74249**, autonomous T compared **549905 callbacks / 356959 split tests**; fixed-input T compared **549733 / 548149**. All listed arb/split/offset/AGE branch/age/weight/rt/synced/twin-fee/twin-state mismatches were zero. Autonomous branch counts were arb 191729, binding 320342, pull 37834; fixed-input counts were arb 146, binding 440688, pull 108899; neither stream recorded a “neither” branch. Maximum relative rival errors were 8.731332265820772e-15 / 6.795853303475876e-15. F checked the first 2,000 callbacks per seed, both fee sides before quote feedback: 100000 callbacks per stream, worst errors **6.0834e-10 / 8.254e-11 bps**, zero sides above 0.01 bps. The instrumented twin matched unchanged candidate outputs and storage words 0,1,2,6. Python state received prior observable quotes, not hidden fair price or storage injection. [b02-qa]

b02 explicitly did **not** run Q/E or independently replay gas: its “all pass” covers listed checks only. Later AGE items reran P on Taylor originals and compile/gas, but inherited T/F unchanged. One b02 external source was later flagged, so retain T/F as artifact-local reported evidence; copied assertions add no independent confirmation. [b02-qa] [b11-s1] [b11-s2] [b11-s3] [b11-s4] [b12-s5] [b12-s6] [b12-s7] [b12-s8]

**AGE fresh engine outcomes.** Cells give CAND−baseline mean (paired SE). Peaks are per arm: s1/s5 top-level peak_gas means all-arm maximum, unlike several other items' CAND-only field. Null is unmeasured; sources are per row.

| Source | Completed seeds (n) | Whole retired lease | ΔQLX5 (SE) | ΔQT1 (SE) | Peaks CAND / QLX5 / QT1 |
|---|---|---|---|---|---|
| [b04-qa] | 10200000..10200255 (256) | 10200000..10200255 | -0.007228683302933803 (0.010490847671915037) | 3.3001984695358138 (0.06835404312743072) | 209329 / 208532 / 209315 |
| [b11-s1] | 10208000..10208255 (256) | 10208000..10208255 | 0.014754469120679792 (0.009765126744169886) | 3.375054388720423 (0.06792476264665795) | 207006 / 207890 / 208800 |
| [b11-s2] | 10208256..10208383 (128) | 10208256..10208511 | -0.018355603594308434 (0.014726233378506495) | 3.169496474838945 (0.08583728540740386) | 208123 / 204120 / 208826 |
| [b11-s3] | 10208512..10208639 (128) | 10208512..10208767 | -0.006058036845584702 (0.014212114516348287) | 3.1329544652864576 (0.088694567415392) | 207158 / 207784 / 209284 |
| [b11-s4] | 10208768..10208895 (128) | 10208768..10209023 | -0.00799112390550416 (0.013177711735361829) | 3.4479454011450623 (0.09039708053540112) | 208377 / 206317 / 208812 |
| [b12-s5] | 10209024..10209151 (128) | 10209024..10209279 | 0.01027160793390447 (0.010939690883178763) | 3.360276870694595 (0.09320941376620462) | 206153 / 207892 / 209004 |
| [b12-s6] | 10209280..10209407 (128) | 10209280..10209535 | -0.007357393288509595 (0.01150317548516753) | 3.3842242895724053 (0.09560454670810703) | 207617 / 207462 / 209138 |
| [b12-s7] | 10209536..10209663 (128) | 10209536..10209791 | -0.03130674059796856 (0.01372703728786144) | 3.2563790957279553 (0.08907374550549063) | 207618 / 207919 / 209173 |
| [b12-s8] | none (0) | 10209792..10210047 | null | null | null / null / null |

b04's mean edges were CAND 534.8308249624034, QLX5 534.8380536457064, QT1 531.5306264928677. CAND beat QLX5 on 121/256 seeds (range −0.977780756056859 at 10200226 to +0.7672970012115456 at 10200095) and QT1 on 256/256 (range +0.11181065737571316 to +6.699688692960763). QLX5−QT1 was +3.3074271528387476, SE 0.06819800993187863, positive on all 256. CAND/QLX5/QT1 afterSwap calls were 2779309/2779312/2780836, mean gas 136583.89826967783/136645.68570782986/138024.11809937732, and every reported callback error category was zero. b04 `pass_peak: true` and `go: true` are block flags; n=256 and a negative incremental mean do not satisfy the goal. [b04-qa]

Follow-ups planned two rounds of 128, stopping after round 1 when cumulative CAND−QLX5 mean + 2*SE < 0.04. Only s1 reached round 2: its first-round result was +0.024177773588951013, SE 0.013152841140899601; the completed 256-seed mean fell to +0.014754469120679792. Every s1..s8 `advance` flag is false. s2..s7 stopped for futility, with reported upper-two-SE values respectively 0.011096863162704557, 0.02236619218711187, 0.018364299565219497, 0.03215098970026199, 0.015648957681825466 and −0.003852666022245682. Their unused second halves are retired, not observations. [b11-s1] [b11-s2] [b11-s3] [b11-s4] [b12-s5] [b12-s6] [b12-s7]

s4 additionally reports 58/128 positive CAND−QLX5 seeds, minimum −0.36234369872749994, maximum +1.1146073462150525 (seed 10208816); all 128 CAND−QT1 differences were positive, from +1.0022244983562132 to +6.33449342328953. Its QLX5−QT1 was +3.4559365250505665, SE 0.09065562616239921. Its four successive 32-seed CAND−QLX5 blocks were +0.004127942732024437 (SE 0.02009556494162752), +0.002713433397873999 (0.041091536317347), −0.02164517364538021 (0.017862984473054566), −0.017160698106534866 (0.020422066770766995). The source's reading that AGE adds no measurable edge is specific to this block, not proof of universal equivalence. [b11-s4]

s8 is **unrun**: source/runtime, compilation and P passed, but its worker could not verify eight allocated cores under its operator restrictions. It started no simulation: n=0, empty rows, null gain/SE/gas/OOG/failures, G incomplete, E uncertified, whole lease retired. s5 instead ran eight workers with allocation verification null. That provenance difference remains unresolved; it supplies neither s8 observations nor grounds to invent replacements for s5's numerical rows. [b12-s5] [b12-s8]

**Merge calculations from embedded AGE rows.** The b04 CSV and s1..s7 JSON row payloads were decoded as data; recorded row hashes were checked where supplied, seed uniqueness checked, and paired differences recomputed. Summarizing complete rows only, `SE = sqrt((sum(d²)-sum(d)²/n)/(n*(n-1)))`, gives:

| Rows included | Unique paired seeds | CAND−QLX5 mean / SE | CAND−QT1 mean / SE | Positive vs QLX5 / QT1 |
|---|---:|---|---|---|
| s1..s7 | 1024 | −0.003911044 / 0.004711946 | +3.312673172 / 0.032579872 | 499 / 1023 |
| b04 plus s1..s7 | 1280 | −0.004574572 / 0.004312390 | +3.310178231 / 0.029419720 | 620 / 1279 |

These are merge calculations from rows_zb64 in [b04-qa], [b11-s1], [b11-s2], [b11-s3], [b11-s4], [b12-s5], [b12-s6], [b12-s7]. CAND−QLX5 sum/sum-of-squares: s1..s7 approximately −4.004909063246259 / 23.273871269261864; including b04, −5.855451988797313 / 30.471826982670375. Follow-up completion is 1,024 of 2,048 leased seeds. Outcome-dependent stopping makes these descriptive, not fixed-size certification; they do not support returning a +0.04 contract.

Measured AGE follow-ups report zero OOG/other callback errors. Gas is a block maximum, not a universal or per-seed bound; candidate Q is unrun. Historical AGE-over-LEAN and negligible AGE-over-QLX5 use different baselines; additivity is unestablished. [b01-qa] [b02-qa] [b04-qa] [b11-s1] [b11-s2] [b11-s3] [b11-s4] [b12-s5] [b12-s6] [b12-s7]

**Engine-faithful core: retain the corrections, distinguish the versions.** The four b-core workers all tested constant 30/30 and 25/45-bps policies over seeds 9700000..9700063, 128 runs of 10,000 steps. Their “ready” flags have different evidentiary strength. They are overlapping validations, not four independent seed sets. [b06-r1] [b06-r2] [b06-r3] [b06-r4]

| Core | Exactness of 128 constant-policy edges | Main-file SHA-256 | Warm runs/core-s |
|---|---|---|---|
| [b06-r1] | 128/128 exact; maximum error 0 | `0e34b1320895d2b4c630c56c2aa174503660258b4aa41ee362b4e5f93e52638c` | 209.4 |
| [b06-r2] | 128/128 exact; maximum error 0 | `0c7fe0e2fff79f278cf5eddcf2c8883d0ce81099962ca5e93b8a76279013784b` | 227.4 |
| [b06-r3] | 16/128 exact; max absolute 1.8443984117766377e-8; relative 5.943033337599645e-11 | `dbda349fb8107612adc58e1b3d7f15e0ca5b084485dad7547328576a491e7ae2` | 227.65208402510262 |
| [b06-r4] | 16/128 exact; max absolute 1.8443984117766377e-8; relative 5.943033337599645e-11 | `3c445696cea8149d97e708984d1e460e323173584f3ccd0325a272c1c9c6d65f` | 160.86503559982987 |

Shared engine corrections: recompute k from rounded reserves at every quote/arb sizing; preserve operand order, closed-form arb/99% cap/profit>0 and execution requote; incremental amount−fee reserve changes with separate fee buckets; price, submission arb, normalizer arb, then retail, submission first; both splits computed before callbacks, original buy/sell arithmetic, sell size/fair-price and strict >0.0001 threshold; WAD-truncated callbacks and retail-output roundtrip for edge/volume, binary64 arb profit; engine PnL/edge/volume/average-fee accounting. This covers the [known differences][differences], beyond constant-k alone. [b06-r1] [b06-r2] [b06-r3] [b06-r4]

**Fee-failure disagreement:** r3/r4 clamp signed callback outputs to [0,1e17]; r1/r2 say an above-cap fee causes refusal of the pair, retaining both old fees (initialization errors). r2 tested 24854 refusals in 53237 callbacks/eight seeds: edges, 80 totals and 560080 step values matched; exactly 10% was accepted. Initialization rejection was unit-tested only. Thus r3/r4's clamp is an approximation outside their in-range policies. r4's (−1,−1) failure sentinel and native callbacks do not emulate general EVM failure. [b06-r1] [b06-r2] [b06-r3] [b06-r4]

The consequential newly found arithmetic difference is **retail LogNormal and Poisson using the Rust libm/fdlibm exp, while price GBM uses host exp**. With host exp everywhere r1 got only 16 bit-identical edges, maximum error 1.8443984117766377e-8; with its `_libm_exp`, all 128 matched. r2 independently reports the same correction and exact constant-policy parity. r3/r4 retain the small constant-policy error. r1 found one-ULP size differences on 38 of 540 probes; such a difference can be invisible to a constant-fee policy's score yet alter the rival fill and exact-arithmetic inference. [b06-r1] [b06-r2] [b06-r3] [b06-r4]

r1's source-built logging engine matched four seeds × two policies: 178258 TradeInfo lines, 55381 arbs, 160000 end-step reserve/fee-bucket rows, 63782 orders, 80000 prices, 122877 fills. All eight logging edges matched the wheel; separate release-API checks matched 560000 step fields/96 totals. Moving-fee probe: 8/8 exact edges, 76743 callbacks, peak 45429. r2 matched 560080 release-summary values without exposing raw orders/fills/reserves, plus a low-WAD-digit probe on 16 seeds/166246 callbacks, peak 23409, with 140020 extra matching step values. [b06-r1] [b06-r2]

r3's first release-summary divergence was normalizer PnL at seed 9700000, step 517: engine 173.95420707825178, core 173.95420707824815. Its 80000 prices all matched, but only 145908/160000 spots and 141967/160000 PnLs did; maxima were 1.1368683772161603e-13 / 1.0186340659856796e-10. r4 reports the same first summary divergence. Their lack of instrumented logs was explicit, so `first_divergence: null` for an unperformed full trace is not evidence of exactness. [b06-r3] [b06-r4]

RNG: Pcg64/Lcg128Xsl64, 128-bit state/XSL-RR; seed_from_u64 expands eight little-endian PCG32 words, forces odd increment, adds/steps. Price uses s, retail s+1. NumPy config draws size 19..21, rate 0.6..1, sigma 0.000882..0.001008 in order. Draws: ziggurat normal, Knuth Poisson, lognormal size then uniform side. Port versions: rand 0.8.5, rand_core 0.6.4, rand_pcg 0.3.1, rand_distr 0.4.3; r1/r2 libm 0.2.8/num-traits 0.2.19. No upstream Cargo.lock or recovered wheel patch versions. Later audit build's rand 0.8.8/libm 0.2.16 is not the wheel lock. [b06-r1] [b06-r2] [b06-r3] [b06-r4] [b13-r3]

Callbacks expose only own post-trade WADs/state. r1/r2 use float64 holding exact truncated integer values plus piece-recovery helpers (amounts exceed int64); r3/r4 use uint64 high/low limbs: APIs differ. None models EVM gas/storage/revert/OOG. r1 omits unreachable pool counts/extreme exp; others omit high-rate Poisson (lambda>=12)/general configs. These cores do not port/tune LEAN/QLX5. Golden fixtures are host-specific; price math uses host libm. [b06-r1] [b06-r2] [b06-r3] [b06-r4]

**LEAN/QLX5 policy ports: agreement and limits.** All four b-qlx ports report the same final policy scores on **512 saved seeds 10010512..10011023**, for both arms. Against six-decimal stored engine rows, LEAN mean/mean-absolute/max-absolute errors are 2.3856583819537036e-8 / 2.467403068528995e-7 / 4.991815103494446e-7; QLX5's are −1.7222758774693148e-9 / 2.5279466320249355e-7 / 4.994752202946984e-7. All 512 per arm are within both 1e-6 and 1e-4. Worst seeds are LEAN 10010819 and QLX5 10010679. This is agreement to printed precision, not 1,024 unrounded bit-equality proofs, and not four independent efficacy confirmations. [b07-r1] [b07-r2] [b07-r3] [b07-r4]

QLX5−LEAN is **+0.035185415827387545** in the ports and **+0.03518544140624724** from rounded stored rows (reported engine summary +0.035185). The reported mean edges round to LEAN 535.841242 / QLX5 535.876428. QLX5 has **3256738 hits / 3655997 split tries = 0.8907934005416306**, on qualifying inferred-retail callbacks at gap <=6. Callback totals are LEAN 5619897 / QLX5 5626901. An older measured hit rate 0.89233 used different seeds 10005164..10005227, so it is not a contradiction. These figures validate the known QLX5 extension over LEAN; they are not a new improvement over QLX5. [b07-r1] [b07-r2] [b07-r3] [b07-r4]

Policy arithmetic is integer-exact: truncating division, fixed-point ln/exp/root/pdf/cdf/trunc/filter, QPL/QT/W2L decoding/interpolation, tell/grid chance, guard and tracked offset. r3 reports a 1e-11 float fee error can reroll exact inference; F tolerance alone cannot establish market-stream fidelity. [b07-r1] [b07-r2] [b07-r3] [b07-r4]

| Port | Source identity and implementation | Reported warm throughput and extra checks |
|---|---|---|
| r1 [b07-r1] | `02bf84d91568f0fdb9ab67b673844cb797bed8ace89cba91f2ba3129fb4003c0` is the decompressed source tar | LEAN 2.3655785874465263 / QLX5 2.235744373400893 runs/core-s; 32 constant edges exact; 110953 integer-operation checks and 22215 reference callbacks, no tell/split mismatch |
| r2 [b07-r2] | `d1f29a9d0ab1c87fcfbe96dcad0d34f5b0ea8ea1a8f5f020c82af37e5e13a105` is `qlx_engine/fixed.c`; C integer policy and C market | Aggregate 5.560954436167772; LEAN 5.645003066989704 / QLX5 5.479371893178748; native vs supplied core exact for all 1024 policy/seed pairs; 32 constant edges and 140020 step-log values exact |
| r3 [b07-r3] | `701dbfd1175fee7d129de92db21b1ddc78645796c422b29d8efba2eda501ab00` is `qlxcore.py`; Python integers through Numba objmode | 0.946 runs/core-s, about 37 s wall using 30 processes; exact reference rather than the old float fastlean's cited 149.1 runs/core-s; 51706 EVM replay callbacks, zero fee-WAD mismatches |
| r4 [b07-r4] | `802962e861d3a922087e897dae86d43b5d36a7e9253b69547086c943da8f7007` hashes sorted filename-NUL-bytes-NUL members; C++20 | Aggregate 6.663051527420624; LEAN 6.933639973561164 / QLX5 6.41278950707317; 12000 bigint cases, 512 config triples, EVM fee replay 9519 LEAN / 12228 QLX5 callbacks exact |

Throughputs differ in implementation/timing/worker scope. r1/r2/r4 are compiled-source alternatives; r3 is the audited reference. Interpreters/compilers remain prerequisites, not bundled installations; this Markdown is not an executable distribution. [b07-r1] [b07-r2] [b07-r3] [b07-r4]

r3 measured the as-delivered r3 core with host exp: only LEAN 291/512 and QLX5 222/512 matched stored rows within 1e-6, with mean errors −0.002837612400714784 / +0.002639547624255112, maximum absolute errors 0.2907337736917839 / 0.3048128115408417; QLX5−LEAN was incorrectly +0.04066260143121714. Changing only the retail-size/Poisson exp call sites restored all printed-row matches and changed constant-policy exactness from 7/32 to 32/32. Its repaired `enginecore_f.py` hashes to `60af56a7570fabd603c6374d38a38f88b3c35a8f1e8192f588769460a96bfcfd`. The measured fdlibm-vs-host exp discrepancy was one ULP on 29295/300000 arguments in [−2,7]; switching the normal sampler's exp/log too broke two saved seeds. r3 initially labelled the libm dependency explanation an inference. [b07-r3]

r4 independently found a retail-buy size-bit difference at saved seed 10010512 step 15: old core 4631889513306034565 versus instrumented engine 4631889513306034564. Its repaired market matched 28418 instrumented events and 32 constant-policy edges. r3/r4 EVM fee replays included pre-repair or over-repaired market streams: they establish callback arithmetic on those inputs, not complete engine stream parity. r3's replay count includes initialization; r4's listed replay counts exclude it. [b07-r3] [b07-r4]

Knobs expose split/window/count/tracking/sync/pull; variance/silent cap; size likelihood/posterior/truncation; tell budget/domain/chance; rival clip/gamma; phases/tables/SD/grid/scales; initialization/cap/guard. Defaults: gap<7, offsets 0,+1,−1,+2,−2, budget 4, variance WAD 893025000000, rho .26, pull .35, rival gamma .997, first-retail count 1, tables 0/1/2/3/4, SD 0/4/8/12/16/20/26/34 bps. Guard interval [2999999999999948,3000000000000057] escapes to 2999999999999947/3000000000000058. These exact preimages are not tunables. Nondefault knobs are unverified; r3's split_synced=0/split_skip_pull=0 are absent from original QLX5. [b07-r1] [b07-r2] [b07-r3] [b07-r4] [b08-map]

Metadata precision differs: r1/r3 render size-log-mean magnitude 6801595083153747000; r4's exact string/map give **6801595083153746944**. Use source bytes, not rounded JSON-number metadata. Default scores agree. Hash scopes differ as tabulated. None tunes, meters native-policy gas, certifies fresh E or returns a winning contract. [b07-r1] [b07-r2] [b07-r3] [b07-r4] [b08-map]

**The later r3 audit strengthens QLX5 parity, without claiming strategy gain.** b13 audits the unchanged b07-r3 policy and repaired core. On all **512 saved seeds**, it reran the release engine unrounded: **512/512 bit-identical edges, maximum difference 0**, mean engine/port **535.8764277580433**. Saved rounded-row mean was 535.8764277597656 and maximum rounding difference 4.994752202946984e-7. Its payload CSV also records equal engine/port float hex values on every row, 5626901 callbacks, 3655997 split tries and 3256738 hits. Reported tell-positive/arb-label totals are 1959880 / 1958240. Release-wheel peak was **208366**, with no reported OOG/revert/other halt/bad return. `gain_vs_base: 0`, `SE: 0` here mean **port-minus-engine parity error**, not a new strategy's edge. `advance: true` means the parity audit passed. [b13-r3]

Audit traces: four seeds 9700000..9700003 × C30/C25-45/QLX5 × 10000 steps; **1348988 comparisons, zero mismatches/f64-relative error/fee-bps error**. Covered prices, ordered count/side/size draws, both pools' arb/no-arb decisions, splits, fills/reserves/WAD callbacks including init/fees, step reserves/fee buckets/edge/end fees and QLX5 slots 0..6. QLX5 state checks: 43717; m0 −22..+26. No fair-price/rival injection. Logging off/on and release wheel matched all 12 edge/PnL bit values and full step-summary hashes. [b13-r3]

| Proof run [b13-r3] | Exact final edge (engine = port) | Comparisons | afterSwap peak tx gas |
|---|---:|---:|---:|
| C2545_9700000 | 352.8823217819899 | 109274 | 22587 |
| C2545_9700001 | 321.506753091577 | 101357 | 22587 |
| C2545_9700002 | 450.31593203752504 | 116857 | 22587 |
| C2545_9700003 | 326.7575307062019 | 101689 | 22587 |
| C30_9700000 | 346.0273756163182 | 112698 | 22587 |
| C30_9700001 | 311.5331610471041 | 104014 | 22587 |
| C30_9700002 | 438.6735782296562 | 120744 | 22587 |
| C30_9700003 | 317.7764427410588 | 104499 | 22587 |
| QLX5_9700000 | 509.18420604524965 | 121858 | 205620 |
| QLX5_9700001 | 495.1443011057613 | 112110 | 195837 |
| QLX5_9700002 | 709.6945613325859 | 131093 | 191427 |
| QLX5_9700003 | 530.3674113842906 | 112795 | 193348 |

Audit negative controls localize what the coarse earlier summaries hid. Replacing only retail/Poisson fdlibm exp with host exp first changes a sell order at proof seed 9700000 step **6**: engine size bits `0x4046de9d0ba64626`, core `0x4046de9d0ba64625`; prices remain exact. C30 then has 21024 trace mismatches, first WAD-callback difference at step 4601 and arb-decision difference at step 4602, but final engine−port edge only 8.185452315956354e-12. QLX5 has 57722 mismatches, first callback difference at step 53, storage difference at 368, arb difference at 369, fee difference at 452, maximum fee error **19.86241656980601 bps** and engine−port edge **0.03738953382651289**. Maximum relative-f64 errors are 8.082328434522164e-14 / 0.0005801240353047747 respectively. Thus step 517 in the original core reports was the first *visible summary* discrepancy, not the first underlying divergence; different “first” steps here are different observations, not conflicting traces. [b13-r3] [b06-r3] [b06-r4]

b13 attributes generic exp to rand_distr's num-traits defaults-off/libm-on dependency. Instrumented engine SHA-256: `eb87407dfae4e9d5563967eb76e07875581eb25107cb10f158d088efae89d4ee`; evidence tar: `c9d5f89540cbcb02096c74f12e797d2f225b43adeb6002b24594dedf9b1d9ef5`. No residual defect/repair. Two external-source warnings qualify dependency/build attribution; embedded comparisons and negative controls remain the observations. [b13-r3]

Limits: four full-trace seeds; 512 final-score/callback/gas comparisons only; labels inferred through exact state consequences, not separate engine outputs. Proof gas is tx gas (QLX5 max 205620), separate from release peak 208366. LEAN not re-audited; no gates/tuning/fresh E/submission; ~160 MB raw traces remained scratch-only. [b13-r3]

**Structural map and all 32 items.** Six families: table levels 7, phases 4, rival clip/band 7, sync 4, split 5, tell floors 5. All 64 single-replacement variants compiled/validated; max 47258 characters/22493 runtime bytes (base 47230/22440). Initial level_interp LO `tt=0` failed Yul stack depth; replacement lower-level-unless-at-top compiled. Map priority was judgment, with no scoring/gas; c-round1 supplies the subsequent screens. [b08-map] [b09-merge-01] [b09-merge-02]

Definitions compact the map's exact replacements. Each item has 128 paired seeds for LO/HI/base, ranges distinct between items. Cells: **mean delta (SE); positive seeds; peak gas**. Results: [b09-merge-01] k00..k15, [b09-merge-02] k16..k31; definitions/compile hashes: [b08-map].

| k / knob | LO / HI change [b08-map] | Seeds, inclusive (n=128) | LO Δ (SE); positives; peak | HI Δ (SE); positives; peak |
|---|---|---|---|---|
| k00 sd_scale | SD ×0.75 / ×1.25 | 10203000..10203127 | -0.028195203582702444 (0.017812542053287854); 60; 205553 | -0.008916350743449097 (0.021069016899387595); 65; 206080 |
| k01 arb_cut | Arb cutoff 0.25 / 0.75 | 10203128..10203255 | -0.00032695264262017076 (0.0007852842320528156); 9; 205704 | -0.002649226263506055 (0.001645528539373292); 19; 204536 |
| k02 pull | Pull alpha 0.2 / 0.5 | 10203256..10203383 | 0.016254 (0.012277); 75; 210537 | -0.005496 (0.012598); 61; 209022 |
| k03 syn_tables | Always synced / always unsynced tables | 10203384..10203511 | 0 (0); 0; 206341 | -0.6867987211349482 (0.05118148434378271); 10; 196795 |
| k04 window | Split gap <=3 / <=9 | 10203512..10203639 | -0.008332510507614188 (0.008554743347180718); 55; 197644 | 0.0092041703876653 (0.005181513506594154); 62; 216164 |
| k05 mix_band | Mixture band 0.0025..0.9975 / 0.0075..0.9925 | 10203640..10203767 | -0.0004855308649922563 (0.00835365896459474); 64; 208341 | 0.0012494457443925633 (0.006441827182822232); 68; 208006 |
| k06 rival_clip | Rival clip 15 / 45 bps | 10203768..10203895 | -2.785455 (0.094015); 0; 207909 | -0.023202 (0.018374); 55; 205919 |
| k07 phase_cnt | Phase 1: no retail / first two | 10203896..10204023 | -0.15895025014287345 (0.02391582204630997); 33; 202943 | -0.02809454575232717 (0.01867110852685109); 58; 207677 |
| k08 pred_var | Lookup variance +SIG2/2 / +SIG2 | 10204024..10204151 | -0.23993335621308765 (0.03929320255140311); 34; 205921 | -0.5829064429135431 (0.05811271005553819); 22; 207492 |
| k09 pull_syn | Pull synced: never / first retail only | 10204152..10204279 | -0.023737 (0.012728); 50; 205927 | -0.045367 (0.0132); 48; 207160 |
| k10 track | No offset tracking / reset offset on miss | 10204280..10204407 | -0.017334 (0.013068); 56; 198292 | -0.025827 (0.01245); 49; 207567 |
| k11 chance_floor | Grid-chance floor 1e-4 / 1e-2 | 10204408..10204535 | -0.003815878 (0.002667605); 14; 206459 | -0.017091627 (0.015040953); 58; 205397 |
| k12 rival_fee_bound | Marginal rival factor .9985 / .9955 | 10204536..10204663 | -5.0679094377544995 (0.12037782488630899); 0; 208209 | -6.2096725294646475 (0.12435043454156511); 0; 205805 |
| k13 phase_table | All retail phase-1 / phase-2 tables | 10204664..10204791 | 0.010694784003180136 (0.018751205545714963); 67; 205181 | -0.17315390358574234 (0.032437926740230646); 42; 203116 |
| k14 fee_offset | Both log fees −0.5 / +0.5 bps | 10204792..10204919 | -0.11269861451750574 (0.024460442369581874); 48; 205874 | -0.2514637507105921 (0.02590994376426499); 20; 206156 |
| k15 step_syn | New-step sync: carry / set to arb | 10204920..10205047 | 0 (0); 0; 206321 | 0 (0); 0; 206338 |
| k16 move_floor | Move floor 5e-10 / 1.5e-9 | 10205048..10205175 | 0 (0); 0; 207402 | 0 (0); 0; 207402 |
| k17 window_first | Split on first / later retail only | 10205176..10205303 | -0.006516704487211644 (0.006721638205934232); 66; 206609 | -0.023075031125832535 (0.013835259420970808); 51; 198181 |
| k18 rr_scale | Rival column ×0.75 / ×1.25 | 10205304..10205431 | -1.256292466152471 (0.059481610143499446); 4; 204810 | -0.9454850376684591 (0.04239213474334218); 1; 207689 |
| k19 step_cnt | New cnt: arb?1:0 / arb?0:1 | 10205432..10205559 | -0.09260693774225048 (0.021268367145707394); 47; 206890 | -0.07875307170891688 (0.02523994673523188); 49; 202483 |
| k20 fee_scale | Both log fees ×.97 / ×1.03 | 10205560..10205687 | -1.1846334028201224 (0.08393686780121186); 12; 205250 | -1.8618988782159183 (0.1391587043339508); 10; 204319 |
| k21 bound_syn | Bound synced: split-hit only / never | 10205688..10205815 | -0.006052925445377166 (0.00816447649763959); 60; 207633 | -0.6614283923581352 (0.04208612065025354); 7; 199280 |
| k22 budget | Tell budget 3 / 6 | 10205816..10205943 | -3.233131638035621 (0.22632579668552966); 0; 208177 | 0 (0); 0; 206645 |
| k23 bound_rule | Set rival: only split-hit / every c!=r | 10205944..10206071 | -0.038250987858627905 (0.011893302250354724); 48; 204988 | -0.12058503930615583 (0.019920578523295346); 37; 206415 |
| k24 level_interp | SD lower (upper at top) / nearest | 10206072..10206199 | -0.024682576399890355 (0.01720511914567769); 56; 205924 | -0.003963119211058075 (0.013985702653146108); 62; 205608 |
| k25 cand_n | Split candidates 1 / 3 | 10206200..10206327 | -0.019312076784203214 (0.012663026444247558); 53; 197137 | 0.012183704885763369 (0.007291343969593435); 71; 201803 |
| k26 rival_clip_p12 | Retail rival clip ±40 / ±80 bps | 10206328..10206455 | -0.33909046863032577 (0.03630850738180227); 17; 206217 | -0.09194936482829208 (0.016365393780893335); 43; 205903 |
| k27 trunc_floor | Mass floor 1e-14 / 1e-10 | 10206456..10206583 | 0 (0); 0; 206504 | 0 (0); 0; 206504 |
| k28 level_cap | Top SD 20 / 26 bps | 10206584..10206711 | 0.005460232259991926 (0.004933277425606423); 55; 207834 | 0.0034848260148394594 (0.0027783738074849363); 24; 207834 |
| k29 rival_clip_p0 | Phase-0 rival clip ±15 / ±22.5 bps | 10206712..10206839 | -2.5989346981924877 (0.09390497355386199); 1; 206240 | -0.6192964805992864 (0.04482809049636901); 15; 206171 |
| k30 cand_outer | Outer offsets ±3 / ±4 (inner ±1) | 10206840..10206967 | -0.008494133012879601 (0.008729070481542823); 60; 207248 | 0.003967047369530352 (0.0062264177288287635); 65; 205849 |
| k31 fee_cap | Fee cap 2.5% / 5% | 10206968..10207095 | -33.62738878988017 (3.260073178776254); 0; 206573 | -10.972542103216606 (1.979802319810389); 3; 209496 |

For preservation of the retained sufficient statistics, the next table copies **sum(d), sum(d²)** for each variant in the same k order. It adds no evaluations; means/SE above are the source-reported figures. [b09-merge-01] [b09-merge-02]

| k | LO sum(d) / sum(d²) | HI sum(d) / sum(d²) |
|---|---|---|
| k00 | -3.608986058585913 / 5.259567950577775 | -1.1412928951614845 / 7.226271026576458 |
| k01 | -0.04184993825538186 / 0.010038292008906935 | -0.339100961728775 / 0.04491576958458038 |
| k02 | 2.080544 / 2.484105 | -0.70348 / 2.583794 |
| k03 | 0 / 0 | -87.91023630527337 / 102.95995065420486 |
| k04 | -1.066561344974616 / 1.1985602836285905 | 1.1781338096211584 / 0.4472861688755734 |
| k05 | -0.062147950719008804 / 1.1344326705291041 | 0.1599290552822481 / 0.6747772891191427 |
| k06 | -356.53825 / 1136.804677 | -2.969895 / 5.557265 |
| k07 | -20.3456320182878 / 12.531831440336553 | -3.596101856297878 / 5.768039781242105 |
| k08 | -30.71146959527522 / 32.46725091844692 | -74.61202469293352 / 98.38975732223989 |
| k09 | -3.038298803 / 2.705470675 | -5.806966178 / 3.095729624 |
| k10 | -2.218689 / 2.814378 | -3.305898 / 2.605155 |
| k11 | -0.488432337 / 0.117543365 | -2.187728195 / 3.714991284 |
| k12 | -648.6924080325759 / 3523.0771585631614 | -794.8380837714749 / 5187.051239124958 |
| k13 | 1.3689323524070574 / 5.7303753601173035 | -22.16369965897502 / 20.942604660475013 |
| k14 | -14.425422658240734 / 11.351905191737746 | -32.18736009095579 / 19.007016515404207 |
| k15 | 0 / 0 | 0 / 0 |
| k16 | 0 / 0 | 0 / 0 |
| k17 | -0.8341381743630905 / 0.7398887422913203 | -2.9536039841065644 / 3.1797870430264896 |
| k18 | -160.8054356675163 / 259.5333923276661 | -121.02208482156277 / 143.6381156663466 |
| k19 | -11.853688031008062 / 8.451028727124733 | -10.08039317874136 / 11.149826563283497 |
| k20 | -151.63307556097567 / 294.1595925330564 | -238.32305641163754 / 758.5332283742074 |
| k21 | -0.7747744570082773 / 1.0882930968924114 | -84.66283422184131 / 84.79170499119422 |
| k22 | -413.8408496685595 / 2170.6889858592053 | 0 / 0 |
| k23 | -4.896126445904372 / 2.486703251364362 | -15.434885031187946 / 8.312075736284118 |
| k24 | -3.1593697791859654 / 4.890019510974846 | -0.5072792590154336 / 3.1816820363600327 |
| k25 | -2.4719458283780114 / 2.654424400401729 | 1.5595142253777112 / 0.8832297176160059 |
| k26 | -43.4035799846817 / 36.14815038327315 | -11.769518698021386 / 5.435981071359558 |
| k27 | 0 / 0 | 0 / 0 |
| k28 | 0.6989097292789666 / 0.3994421578750457 | 0.4460577298994508 / 0.12704036622678166 |
| k29 | -332.6636413686384 / 1007.9188301893273 | -79.26994951670866 / 81.75897068436414 |
| k30 | -1.087249025648589 / 1.2478883292866252 | 0.5077820632998851 / 0.6322315183403504 |
| k31 | -4304.305765104662 / 317512.5852748479 | -1404.4853892117255 / 79128.07268463858 |

All 32 returned both diffs and all 64 report passing peak checks. Only k20/k22 preserve explicit zero OOG/revert counts here; other rows' missing raw counters are not invented. No screen has +0.04 or 1024+ confirmation. Largest positives: pull .2 +0.016254 (SE .012277); three candidates +0.012183704885763369 (.007291343969593435); phase-1 tables +0.010694784003180136 (.018751205545714963); gap<=9 +0.0092041703876653 (.005181513506594154). These are leads only, without evidence of additive gains. [b09-merge-01] [b09-merge-02]

Always-unsynced loses 0.6867987211349482 (SE .05118148434378271); never sync on bounds loses 0.6614283923581352 (.04208612065025354). Always-synced/step-syn changes are zero on tested seeds only. Narrow clips, wrong rival factors, axis scaling, ±3% fee scales and lower caps hurt. Caps 2.5%/5% lose 33.62738878988017/10.972542103216606 (SE 3.260073178776254/1.979802319810389): large-fee tails matter here. [b09-merge-01] [b09-merge-02]

k16's move-floor variants and k27's mass-floor variants have identical per-seed edges; k22 budget 6 is also identical, while budget 3 loses 3.233131638035621 (SE 0.22632579668552966, 0 positive seeds). k16 attributes inertness below about 8.69e9 WAD to the PDF cutoff; its external-source warning makes that explanation weaker than the directly reported zeros. k27 still records gas-total shifts +182 in LO's first block / −379 in HI's third block, despite identical edges. k28 top levels 20/26 bps give small gains under 0.006; 25/85 of 128 edges respectively equal QLX5 exactly, HI−LO is −0.0020 (SE 0.0048), and neither is distinguishable from QLX5 at these SEs. k19 HI exceeds LO by 0.013853866033 but both lose to base. [b09-merge-02]

Map overlap pairs (2,9), (4,17), (14,20), (15,19) cannot stack by plain replacement; combinations uncompiled/untested. Tell-budget changes need matching T. Exclusions: compression/refits, fitted SD knots/geometry, per-run sigma/rate, math constants, exact tell/split bounds/constants/Vanilla guard; one-step initial state; spent twocomp/lattice/rival-pin, exact rival carry, residual heads, kappa (no kappa identified). Port APIs exposing more constants do not make them new supported search lines. [b08-map] [b07-r1] [b07-r2] [b07-r3] [b07-r4]

**Twenty idea tests.** Both merges use the older constant-K fast LEAN replica **without QLX5 split**, not the repaired engine model. vs LEAN = mechanism+LEAN minus LEAN; on AGE = mechanism+AGE minus AGE. Baselines: LEAN a0=ainf=.35/tau=2; AGE a0=0/ainf=.7/tau=1. Choice: 64000..65023, 128-seed rounds, drop at mean+3SE<0; report **10000..12047, n=2048**. No engine, QLX5/QT1 pairing or full policy gates. [b10-merge-01] [b10-merge-02]

Cells: **mean delta (SE); positive report seeds**. Present=true preserves the basic effect's presence; a nearby missing variant was tested. All 20 promote=false. [b10-merge-01] [b10-merge-02]

| Idea (source) | Present | vs LEAN Δ (SE); positives | on AGE Δ (SE); positives |
|---|---|---|---|
| fill-size [b10-merge-01] | false | 0.00227 (0.003436); 1050 | 0.000241 (0.003519); 1048 |
| fee-memory [b10-merge-01] | false | -0.0006303010545473664 (0.0009622144824857604); 899 | -0.00026428233344610863 (0.0009421979703227205); 921 |
| silence-bound [b10-merge-01] | true | -0.0008279686961202848 (0.0019242159702547905); 1029 | -0.0006687704036579534 (0.0019155571807606612); 1000 |
| age-fee [b10-merge-01] | false | 0.0005244462906790204 (0.0023991125163267874); 1062 | -0.001480369005663923 (0.002419455415421662); 1051 |
| share-feedback [b10-merge-01] | false | -0.0015907482784406624 (0.0028472614476621892); 996 | -0.006530390919671475 (0.0028038291574551885); 972 |
| inventory [b10-merge-01] | true | -0.00881 (0.00275); 946 | -0.00859 (0.0024); 919 |
| undercut [b10-merge-01] | false | -0.004690568590842298 (0.002193183321020636); 941 | -0.009578699512042016 (0.0022076424341107); 949 |
| same-step [b10-merge-01] | true | -0.014588337746420238 (0.0028563254563184217); 913 | -0.010747124174305539 (0.0027241726578222424); 899 |
| post-arb-skew [b10-merge-01] | false | -0.022 (0.0023); 805 | -0.0228 (0.0024); 837 |
| size-run [b10-merge-01] | false | -0.04992351261329561 (0.003577958126681876); 732 | -0.053940194276585585 (0.0037164126133699647); 729 |
| tell-coverage [b10-merge-02] | false | 0.006329 (0.002453); 1076 | 0.004592 (0.002451); 1094 |
| lookahead [b10-merge-02] | false | 0.003492132563304662 (0.002146116474430133); 1029 | 0.0005059215832921293 (0.0022894789176444662); 1044 |
| sd-extrap [b10-merge-02] | false | -0.000105 (0.000258); 480 | 0.000152 (0.000432); 493 |
| endgame [b10-merge-02] | false | 0.00035885772081734046 (0.0003227178901749649); 879 | 3.906800292433066e-05 (0.00032759570186093344); 870 |
| drift [b10-merge-02] | false | 0.003879 (0.002265); 1014 | -0.000171 (0.002565); 1022 |
| mixture-branch [b10-merge-02] | false | 0.000526 (0.000736); 1052 | -0.000455 (0.000733); 978 |
| second-order [b10-merge-02] | false | 0.004102156314634814 (0.001829279029610601); 1021 | -0.0005802840008916621 (0.0018498706799454404); 986 |
| sync-grade [b10-merge-02] | false | 0.003221 (0.001723); 1059 | -0.00349 (0.003145); 1023 |
| side-imbalance [b10-merge-02] | false | -0.001620398002443485 (0.0020789493224039174); 1013 | -0.004243779899149924 (0.0032861145878138203); 972 |
| markout [b10-merge-02] | false | -0.035103 (0.003312); 812 | -0.037481 (0.003495); 812 |

Tested mechanisms/settings and selection findings, in table order. [b10-merge-01] [b10-merge-02]

- **fill-size:** relative retail fill z=min(q/M,3)−0.862, running-mean beta=1/32, M0=11; chosen same-side coefficient 0, other-side +0.25 bps. No running-fill fee term was found; existing size inputs affect likelihood/tell and post-trade spots. Only S11 survived; later settings were adaptive.
- **fee-memory:** post-table fee EMA or dead band before rounding; selected 0.03-bps dead band, reusing prior fees. Choice mean −0.00015745968983243985, SE 0.0016973129869118078. EMA weights >=0.01 dropped; weight 0.3 lost −13.035198353672051 on 128 seeds. The small band rarely changes fees.
- **silence-bound:** existing silent-step truncation already uses absence of trades; the new variant divides variance by 1+strength*max(0,k−start+1), k=min(dt−1,12), with strength 0.1/start 3. All 12 settings reached 1024 choice seeds, none stopped; the selected positive choice result did not hold on report.
- **age-fee:** adds symmetric premium*age/(age+tau) after lookup, using time since inferred arb, distinct from AGE's router-binding clock. Selected 0.1 bps/tau 4; five of 12 survived (0.1 bps at tau 1/4/16, 0.3 at 4/16). Choice mean −0.00098988062173061, SE 0.0030843479989459822.
- **share-feedback:** decaying cross-step own-retail count/paid-volume state, symmetric clipped feedback. Chosen gain 0.5 bps, memory 512, count target 0.75, volume target 10 bps, cap 2 bps; state decays by T/(T+dt). Ten settings dropped, two completed; choice mean −0.005493219484855372, SE 0.003779579743069829.
- **inventory:** literal value imbalance is already the lookup coordinate: ln(x*exp(m)/y)=−(ln s−m). Tested quantity ln(x/100), skew tanh(q/0.3) with chosen amplitude −0.5 bps, opposite bid/ask signs. All 12 choice means were negative; only this setting survived.
- **undercut:** on synced quotes within a fee-space band of rival indifference, snap to point−margin. Chosen margin 0.1 bps/band 0.5; three of 12 survived, all at band 0.5, every choice mean negative. Rival competition is already in the tables; this post-table snap was the tested addition.
- **same-step:** phase-1/phase-2 already distinguishes first/later retail; tested an additional count-dependent fee shift. Selected cnt>=3, own-side −2 bps, other 0, flat multiplier C=0. All 12 settings stopped by round 3 (n<=384); selected least-negative, not a survivor.
- **post-arb-skew:** changes arb-hit/other side fees at arb or with persistent exp(−age/L) decay. Chosen at-arb-only, edge 0/other −1 bps. Phase-0 tables already give side-dependent post-arb fees; persistence would be new state. All 12 stopped after 128; S9..S12 were adaptive.
- **size-run:** invert replica splits to estimate full order size clamped [q,4q], prior mean 20/count 32; coefficient 2 bps per relative size, symmetric mode 0. All 12 settings stopped. Unlike existing fixed size likelihood, this adds an online full-size estimate; its reference/router provenance is flagged.
- **tell-coverage:** snap engine gamma to a coarser lattice before the Vanilla guard. Chosen gamma_2^36_higher_fee, mode 1/par 36/rnd 1. Tell coverage did not move; raising fees by up to 0.0763 bps could explain the gain, and no control isolated it.
- **lookahead:** table-only variance v+h*sigma0², leaving belief state unchanged; h=0.001 chosen. This nearly disabled forecast is not evidence for useful lookahead.
- **sd-extrap:** replace table-edge clipping with extrapolation across SD/own/rival offsets. Chosen own-offset extension 1000 bps, no SD or rival extension. SD exceeds 34 bps only about once per 138000 callbacks (attributed, source-flagged).
- **endgame:** symmetric beginning/end offsets in the fixed 10000-step horizon; selected +2 bps for the last 10 steps, no initial offset. Selection mean −0.00044629770173748584; tiny report effect.
- **drift:** mean prediction adds c*(−SIG2/2) per elapsed step. Selected c=−16, drift +7.1442e-6 log-price/step, opposite the true drift; item calls it a noise pick. Exact-drift c=1 scored −0.0013, SE 0.0027 on choice seeds.
- **mixture-branch:** posterior-weighted arb/retail branch fees on undecided first trades, instead of hard branch. Selected s01: wU=wN=1, eps=.005, own=0, gamma=1. About 26 mixed callbacks/run; over/unsupported cases occurred only once in 14.4 million first trades, so that half was not exercised.
- **second-order:** opposite fee changes proportional to posterior log-price variance (lower bid/raise ask), c=1 selected. Item gives already_present as {present:false}; this merge preserves the false reading, with its source warning.
- **sync-grade:** blend synced/unsynced tables by exact-rival-reading age u, lambda=linf+(l1−linf)*gtau/(u−1+gtau); selected l1=1, linf=.5, gtau=1. Small LEAN gain disappears on AGE.
- **side-imbalance:** classified-retail sign EMA I, bid += A*I / ask −= A*I; selected memory 256, A=−0.5 bps. New cross-step sign feedback, not the existing within-step phase count.
- **markout:** value fills at next-step filter mean and feed per-side markout EMA into fees; selected cross_b005_k+0.03 (k=.03, beta=.005, mode=2, target=0, cap=3 bps, fills=1, beta_slow=0, clip=50 bps). All 12 settings stopped after 128 choice seeds.

Several items give identical report-bank baseline means: LEAN **536.603390956178**, AGE **536.6231002985178**; rounded versions in other items agree. AGE−LEAN is reported as +0.019709 (SE 0.004066, 1140 positive seeds) by fill-size and +0.0198 (0.0041, 1141 positive) by post-arb-skew; drift/markout/sync-grade give consistent rounded +0.0197. Those small precision/positive-count differences are retained rather than treated as separate engine confirmations. They are replica-only and use a different baseline from AGE-on-QLX5. [b10-merge-01] [b10-merge-02]

Selection/report changes: silence-bound chose +0.0029668883392731105 (SE .0026920308615193027), reported negative; fill-size chose −.00231 (.004762), reported near zero. Same-step/size-run/post-arb-skew/markout lost all settings; choices are least-negative. Some later settings were adaptive. fill-size reports fee perturbations ~1e-13 changed every seed, per-seed SD ~.09 and SE floor ~.09/sqrt(n). Environments differed (Python 3.10.12/3.12.16, NumPy/Numba 2.2.6/0.61.2 vs 2.5.4/0.68.1); local baseline checks/common means support replica-level comparison. [b10-merge-01] [b10-merge-02]

No idea reaches +.03. Best on AGE, tell-coverage +.004592 (SE .002451), has unchanged coverage/uncontrolled fee raise. LEAN positives lookahead/drift/second-order/sync-grade vanish or reverse on AGE. Markout −.037481 (.003495) and size-run −.053940194276585585 (.0037164126133699647) lose on AGE. None was retested with repaired market arithmetic; no replica delta is certified to transfer. [b10-merge-01] [b10-merge-02] [b07-r3]

**Idea costs.** Estimates unless marked measured, without engine peak/OOG guarantees. Sketch baseline: ~208000 gas, 22440 bytes, 47230 characters; fill-size cites peak 208366. Negative ideas' costs remain included. [b10-merge-01] [b10-merge-02]

| Idea | New words | Added gas (estimate unless marked) | Runtime bytes | Source characters |
|---|---|---|---|---|
| fill-size | 0 packed / 1 otherwise | +200..400 retail, ~30 arb; own slot ~5000 more | +120..220 | +300..450 |
| fee-memory | 0, reuse prior fees | +100..1500 | +100..500 | +250..900 |
| silence-bound | 0 | Measured isolated +48..564; no integrated peak | Measured probe +247 (119→366) | 80 arithmetic / 200 with credit |
| age-fee | 1 timestamp | +2500..24000 | +150..500 | +400..1000 |
| share-feedback | 1 state | +6000..10000; estimated total 214000..218000 | +250..800 | +700..1400 |
| inventory | 0 | +1500..3000, log+tanh/linear | +300..600 | +250..400 |
| undercut | 0 | +500..3000 | +200..900 | +700..1600; Python patch 1118 |
| same-step | 0 packed / 1 otherwise | +150..300 | +40..80 | +150..250 |
| post-arb-skew | 0 chosen; 0 packed/1 persistent | Chosen +30..60 arb/~10 other; persistent +100..200 packed plus exp +300..800; own slot cold read 2100/write 2900 (first 20000) | +20..50 chosen / +250..450 persistent | +60..120 / +400..700 |
| size-run | 2 | Unmeasured: 2 roots, split inversion, mean update | Unmeasured | Unmeasured |
| tell-coverage | 0 | +2000..2600; peak ~210000..211000 | +250..400 | +600..900 |
| lookahead | 0 | Unmeasured, constant addition in sqrt | Unmeasured | ~16 at expression |
| sd-extrap | 0 | +50..150; peak sketch ~208100..208500 | Unmeasured | Unmeasured |
| endgame | 0 | +30..200 | +40..200 | +200..500 |
| drift | 0 | Opcode estimate ~100..200 | Measured 22440→22464 (c=−16), 22462 (c=1) | Measured +34 / +32 |
| mixture-branch | 0 | Extra lookup, ~2 logs/4 multiplies per mixed callback | Unmeasured | Python mechanism 2548; Solidity unmeasured |
| second-order | 0 | +50..1000 | +40..250 | +100..400 |
| sync-grade | 0 packed | Fee-rule Forge probe only; no engine peak supplied | Baseline 22440, integrated change not supplied | Not supplied |
| side-imbalance | 1 | First update +22500..24000; later retail +5500..8000; arb +2300..3500 | +200..700 | +500..1200 |
| markout | 1..2 | +7000..14000 peak callback | +350..600 | +900..1300 |

Silence-bound's probe used solc 0.8.24/optimizer 200/Cancun (not the production Paris engine compile): dt 1/4/12/100 gave increments 48/559/559/564, against base gas 5271. Its byte delta is isolated, not an integrated afterSwap bound. Drift's byte/character numbers are compiled, while its gas remains an estimate. Sync-grade measured fee-rule gas in Forge without retaining an engine peak in the supplied merge. [b10-merge-01] [b10-merge-02]

Merge inference: fill-size/sync-grade zero-word sketches use slot-2 bits 224..254, already occupied by AGE rt. Stacking cannot reuse those bits unchanged; revise packing/storage and recheck costs. No gas increase was measured for this conflict. [b01-qa] [b10-merge-01] [b10-merge-02]

**Source warnings.** The requester supplies failed reread/unsupported-quote counts below. Exact failed URLs/quotes were not identified in these inputs. Original “all quotes rechecked” claims do not override later flags. Local rows/code/traces remain attributed measurements; flagged quotations and inherited assertions are not independent corroboration. Counts are supplied notices, not this merge's measurements.

| Input(s) | Failed-source count | Material effect on interpretation |
|---|---:|---|
| b02-qa / a-check | 1 | External provenance of the reported certification is uncertain; later T/F copies inherit that limitation, Q/E remain unrun. |
| b06-r1 / r2 / r3 / r4 | 2 / 3 / 7 / 7 | Port/source/crate attributions are qualified. Local parity differences and the r3/r4 limitations remain explicit; later corrected-policy/audit evidence is not replaced by their `ready` flags. |
| b07-r1 / r2 / r3 / r4 | 1 / 2 / 1 / 3 | Retain the supplied rounded-row comparisons and exactness limits; do not promote them to general engine certification. r3's dependency explanation was initially an inference. |
| b11-s1 / s2 / s3 / s4 | 2 / 2 / 1 / 3 | Numerical rows/gas summaries are local; externally based configuration/provenance and inherited T/F claims are qualified. |
| b12-s5 / s6 / s7 | 1 / 2 / 1 | Same qualification; s5 also records allocation verification as unknown. |
| b13-r3 | 2 | Trace/CSV evidence is retained; crate-source and engine-build provenance are qualified, not independently source-certified by this merge. |

The supplied lower merges carry additional warnings that must survive: c-round1 k01 (1), k03 (2), k06 (4), k16 (2), k20 (1), k28 (3), k30 (1); d-ideas same-step (1), size-run (2), undercut (1), sd-extrap (4), second-order (1), sync-grade (2), endgame (1). Exact failed URLs were not recoverable from those merged inputs either. The c screens' numerical outcomes are retained as local reports, with weaker externally sourced mechanism explanations. [b09-merge-01] [b09-merge-02] [b10-merge-01] [b10-merge-02]

same-step's Taylor line quotes and size-run cites use **66604b3426d8e97a73e2c39940b9b4dece51cc73**, not pinned **4812a6382311624e1506aca131ca35c378f930d9**. Exact lines and their presence/size-likelihood/router readings remain unconfirmed; other supplied readings support broad phase-count/fixed-likelihood descriptions. Undercut's no-snap reading depends on a flagged reference bundle, while its negative numerical outcome remains. The second idea merge cannot map its source failures to individual claims, so external structure/provenance statements stay attributed. [b10-merge-01] [b10-merge-02]

**Seed ledger.** Completed/retired: b04 10200000..10200255; gas 10202048..10202055; structural 10203000..10207095 (32×128); AGE leases 10208000..10210047. AGE s1 completed 256, s2..s7 128 each (remaining halves retired), s8 all 256 unrun/retired; no partial pairs. Never reuse completed or unused leased seeds. Proof 9700000..9700063 and saved 10010512..10011023 are reused validation seeds, not fresh E. Other-root allocations are unknown here. [b01-qa] [b04-qa] [b09-merge-01] [b09-merge-02] [b11-s1] [b11-s2] [b11-s3] [b11-s4] [b12-s5] [b12-s6] [b12-s7] [b12-s8] [b13-r3]

Still absent: repaired-model retuning, 2048-completed AGE-on-QLX5 confirmation, candidate Q, 1024+ structural confirmations, idea engine tests and a qualifying new contract. The audited reference and faster alternatives provide capability with their stated scopes. No result reports a submission; the goal requires the requester to ask the user before any future submission. [b02-qa] [b04-qa] [b07-r1] [b07-r2] [b07-r3] [b07-r4] [b09-merge-01] [b09-merge-02] [b10-merge-01] [b10-merge-02] [b12-s8] [b13-r3]

**Source register.** All 25 inputs were present/nonempty. Links use their supplied full content hashes; local .imd/reads/artifacts copies were read, not newly fetched web pages. b09/b10 underlying items were not separately supplied: those figures cite their merges. Member manifests/diagnostics remain in payloads; local decoding/checks carry no independent behavioral authority.

Original result paths below share prefix `artifacts/goal/batches/`.

| Supplied id / artifact citation | Original result path |
|---|---|
| [b01-qa] | `a-build/items/qa/result.json` |
| [b02-qa] | `a-check/items/qa/result.json` |
| [b04-qa] | `a-engine/items/qa/result.json` |
| [b06-r1] | `b-core/items/r1/result.json` |
| [b06-r2] | `b-core/items/r2/result.json` |
| [b06-r3] | `b-core/items/r3/result.json` |
| [b06-r4] | `b-core/items/r4/result.json` |
| [b07-r1] | `b-qlx/items/r1/result.json` |
| [b07-r2] | `b-qlx/items/r2/result.json` |
| [b07-r3] | `b-qlx/items/r3/result.json` |
| [b07-r4] | `b-qlx/items/r4/result.json` |
| [b08-map] | `c-map/items/map/result.json` |
| [b09-merge-01] | `c-round1/merges/01/result.md` |
| [b09-merge-02] | `c-round1/merges/02/result.md` |
| [b10-merge-01] | `d-ideas/merges/01/result.md` |
| [b10-merge-02] | `d-ideas/merges/02/result.md` |
| [b11-s1] | `a2-age-a/items/s1/result.json` |
| [b11-s2] | `a2-age-a/items/s2/result.json` |
| [b11-s3] | `a2-age-a/items/s3/result.json` |
| [b11-s4] | `a2-age-a/items/s4/result.json` |
| [b12-s5] | `a2-age-b/items/s5/result.json` |
| [b12-s6] | `a2-age-b/items/s6/result.json` |
| [b12-s7] | `a2-age-b/items/s7/result.json` |
| [b12-s8] | `a2-age-b/items/s8/result.json` |
| [b13-r3] | `b2-audit/items/r3/result.json` |

[b01-qa]: https://api.imd.fun/artifacts/5ea62c673b4209edeb110939538195fafd35943b6796a659f5ffb57683cc8eec
[b02-qa]: https://api.imd.fun/artifacts/dcda482dfdc67a08edbd81196d26cff298d5a34e18483fa7dd4ce356662baed0
[b04-qa]: https://api.imd.fun/artifacts/d86d42204cc75a022d939e17fd8dfb35d2a716fea35b896a71e79f3287f1b9f9
[b06-r1]: https://api.imd.fun/artifacts/571feeda0f5945b677b2b02601382c39767917b22edbf5b3f8903b6f6c2c42b5
[b06-r2]: https://api.imd.fun/artifacts/119048e48f5262b349cca0865e6adc67e005c017bd625a0f9d722862fecb18d9
[b06-r3]: https://api.imd.fun/artifacts/2ad2abf45223c729557e83e77d22de54c5db7da2be0599658144906b91dbf0f7
[b06-r4]: https://api.imd.fun/artifacts/e4c77091941c6ff24d80cb9f94016d05a33fb58a1d38dcea097c46aead1b0b2a
[b07-r1]: https://api.imd.fun/artifacts/993e41264d95bcd849cb5705e9301d7a6c15d1fe142e4ff47c28c7c23cb1e399
[b07-r2]: https://api.imd.fun/artifacts/8958d2b74cb9febafc4ee700cba464967006e7ddb00512f10c5476037990a5da
[b07-r3]: https://api.imd.fun/artifacts/60dc237fa0a4d42f3b6e2d2bed61c1a2df08d27c31ccd95cce508ee9c8689de4
[b07-r4]: https://api.imd.fun/artifacts/a1eef2f3dbbcbc7a1de9d15a2b22d1d25ac6d316a72efde67275b5d5a16ab16b
[b08-map]: https://api.imd.fun/artifacts/f921f2133d55d8ce81b5d809494003e898fc2a72d1fe47cdc34606ff269d676e
[b09-merge-01]: https://api.imd.fun/artifacts/7e4de1eb8bb3c9a765b69dfcfef48fb733f991f22ef2c1eeabb531cf7a6b3059
[b09-merge-02]: https://api.imd.fun/artifacts/314ef0c35e184deecd663bbeac5464776fe56aa200c5bc663cd896e1673dbab8
[b10-merge-01]: https://api.imd.fun/artifacts/11370d30d60924389d256b8f912ddaabd471a5b47b24c6e066394f1a4bc8998b
[b10-merge-02]: https://api.imd.fun/artifacts/10baa5ddac1390f4d516d601c707adce24d5e67416c8f4acb5f0dc1777bc49d8
[b11-s1]: https://api.imd.fun/artifacts/b8f2b229f15d55d7be109b329aa10b3fbecc52e3ef7e0b89d5d4f790d6f877d0
[b11-s2]: https://api.imd.fun/artifacts/9a65b24d78ea78874cd967955b882f8dd5aaae093b3872f887e060205560294b
[b11-s3]: https://api.imd.fun/artifacts/a448e15cdedc7c93ccb621ce7210c21c486129208097e10ed303bf268fe08909
[b11-s4]: https://api.imd.fun/artifacts/32a751ea60a0e329bc9b5f9b20b9580ba26b16603c573390c67f978a07377fd6
[b12-s5]: https://api.imd.fun/artifacts/6658ece654095a55edd7f4e5262185c86005f7f3ab820463be10c847fa47b08e
[b12-s6]: https://api.imd.fun/artifacts/6901af970cb651a9ba754b4a995990ef5e6bb1a4fe0dc6ce22b806d3a98ac633
[b12-s7]: https://api.imd.fun/artifacts/56f8992531f9e64cae6b1e74a163a0ee07653ff64ffcd8501500c61b5ecec8ab
[b12-s8]: https://api.imd.fun/artifacts/3f17310b2240f2a0677865c59a59cf5e25deee9e6d084adaaddaf6b7dbae12db
[b13-r3]: https://api.imd.fun/artifacts/362fb97f041087bf3548c302af4c0f82d2537d6a6c0157a95ac06d0cb70a5ce4

[Taylor]: https://github.com/gtmcknight/amm-sim/tree/4812a6382311624e1506aca131ca35c378f930d9/research/solved
[base]: https://api.imd.fun/artifacts/1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15
[cert]: https://api.imd.fun/artifacts/d73c1749574cce67042552e9278be2ba20c8fedf9720bdee71c27d4019f21f02
[AGE]: https://api.imd.fun/artifacts/0343e8049294da6680c2ee1ad413fa5dc95843b1893e96c3b173df49b850b3e1
[AGE-engine]: https://api.imd.fun/artifacts/87dfbac60f00625d53477537621d5d15b2b95529011ed061eab3bb64452d677c
[driver]: https://api.imd.fun/artifacts/764c9461a9f3bab6e277178f4bb48553d1b97c6cca33bed016f7c9bfd611cc42
[differences]: https://api.imd.fun/artifacts/8b18deed94ffc0ce7268140f652b5a1d2cf1a55e98a7e18575d1c51ce83cb098