# Frozen ComboG(1) confirmation merge — credit Taylor (gtmcknight)

The supplied reports contain 256 consecutive pairs, seeds 9803828–9804083, with identical candidate/qt1 hashes. Full compiler settings equality is **not established**, so this is an evidence merge with conditional descriptive pooling, not an unconditional compatibility pass. Paired mean difference: 0.664085464941164; SE: 0.03844178572389. Candidate afterSwap peak: 220,833; qt1: 209,290. No recorded gas violations or callback failures. Both report validation success and runtime sizes 22,058 / 20,605 bytes, below 24,576. These statements derive from the embedded evidence, not new runs or P/Q/F certification.

Sources: [item-a1s3](../../items/a1s3/result.json) (`seeds`, `gas_stats_raw`, `hashes`, `runtime`, `validation`, `commands`, `method`, `ranges`) and [item-a1s4](../../items/a1s4/result.json) (`completed`, `raw_gas_stats_per_chunk_arm`, `hashes`, `runtime`, `validation`, `commands`, `method`, range fields). Read from `.imd/reads/artifacts/item-a1s3` and `.imd/reads/artifacts/item-a1s4`. Input SHA-256 values in `provenance` were verified against the assignment. Relative links identify the original result files under `artifacts/goal/batches/e6-combo-a1/items/`; their availability outside this delivery is not assumed.

Full raw gas_stats: [a1s3 original](../../items/a1s3/result.json#gas_stats_raw), [a1s4 original](../../items/a1s4/result.json#raw_gas_stats_per_chunk_arm). JSON fragments identify fields, not guaranteed browser navigation. Complete counters are also embedded at `raw_gas_stats.item-a1s3` and `raw_gas_stats.item-a1s4`; each array uses `raw_gas_columns`, including every chunk's Submission/afterSwap counters. The report is self-contained for row and gas recomputation.

Each seed row carries its source item key. Decimal strings preserve the exact input JSON numeric tokens, without rounding; computed statistics are numbers. Copied fields trace to each source; pooled figures derive from embedded rows and counters. `command_outcomes.index` refers to the source `commands` array; exits, durations and timeout limits are retained wherever present. A timeout limit is not a timeout event. Both items' limitations say P/Q/F were not rerun.

```json
{"batch":"e6-combo-a1","merge":"02","credit":"Taylor (gtmcknight): solved policy, Gaussian filter, qm tables and replica (github.com/gtmcknight/amm-sim at 4812a6382311624e1506aca131ca35c378f930d9, research/solved) and the amm_sim_rs wheel release sim-6b6921f8. qt1 and ComboG are Solidity ports/extensions of that work.","variant":"ComboG(GATE=1), TaylorComboGQmTrim2","status":"evidence_merge_complete_with_compiler_verification_gap","identity":{"matching_hashes":{"candidate":{"sha256":"f904a486b1dcfbd6fcf40aa48920d1bb6b79ad2ac1c99a2cbbb16d4272c2c616","source_fields":["/item-a1s3/hashes/frozen_gate1_source","/item-a1s4/hashes/frozen_candidate"]},"qt1":{"sha256":"c68887cff61180e12ba2b1ceb333edf76a830f91f63b5d775a8806fb9ec08aca","source_fields":["/item-a1s3/hashes/qt1","/item-a1s4/hashes/qt1"]},"check_py":{"sha256":"cbcfea4c793ac7b78e0ee27dd723c9e6af4d9d704a70a8038c985acffffcfed1","source_fields":["/item-a1s3/hashes/tools_check_py","/item-a1s4/hashes/check_py"]},"engine_py":{"sha256":"306c529d0c84c88610c1e8a9a6aa34634534b73ab83312e9155ef14476e46300","source_fields":["/item-a1s3/hashes/tools_engine_py","/item-a1s4/hashes/engine_py"]},"wheel":{"sha256":"aedb68280aca34c110968f00148387c95885207913fb2cf19a1ab4c5cfd6887a","source_fields":["/item-a1s3/hashes/amm_sim_rs_wheel","/item-a1s4/hashes/engine_wheel"]}},"engine_commit":"6b6921f8d463314aa7c96234e1be25a25245f704","engine_commit_sources":["item-a1s3/hashes/engine_checkout","item-a1s4/method/engine_commit"],"compiler_version":"solc 0.8.24","compiler_sources":["item-a1s3/runtime/compiler","item-a1s4/method/compiler"],"full_compiler_settings_equality":null,"unconditional_compatibility_pass":false,"gap":"Both report pinned SolidityCompiler with identical check.py and engine commit. Neither enumerates optimizer, runs, viaIR, evmVersion or metadata settings. a1s3 has no bytecode hash for comparison. Matching sizes/helper hashes support consistency but do not prove full settings equality. Pooled statistics are conditional descriptive arithmetic."},"provenance":{"item-a1s3":{"input_sha256":"62d149fb34c504c0473d277f44a823ec74296662d4e9eb81eeb149aaae27ac58","status":"complete","blocked":null,"runtime":{"candidate_bytes":22058,"candidate_expected_bytes":22058,"candidate_matches_expected":true,"candidate_creation_bytes":22087,"qt1_bytes":20605,"qt1_creation_bytes":20633,"limit_bytes":24576,"candidate_within_limit":true,"qt1_within_limit":true,"compiler":"solc 0.8.24 via amm_competition.evm.compiler.SolidityCompiler (tools/check.py compiled())"},"validation":{"candidate":{"command":"amm-match validate frozen/Candidate.sol","exit":0,"output":"Strategy 'TaylorComboGQmTrim2' validated successfully!"},"qt1":{"command":"amm-match validate frozen/qt1.sol","exit":0,"output":"Strategy 'TaylorGaussianQMSpline' validated successfully!"},"setup_starter":{"command":"amm-match validate contracts/src/StarterStrategy.sol (last line of scratch/setup.sh)","exit":0,"output":"Strategy 'StarterStrategy' validated successfully!"}},"ranges":{"assigned_inclusive":[9803828,9803955],"attempted_half_open":[[9803828,9803844],[9803844,9803860],[9803860,9803876],[9803876,9803892],[9803892,9803908],[9803908,9803924],[9803924,9803940],[9803940,9803956]],"completed_half_open":[[9803828,9803844],[9803844,9803860],[9803860,9803876],[9803876,9803892],[9803892,9803908],[9803908,9803924],[9803924,9803940],[9803940,9803956]],"completed_seed_count":128,"missing_seeds":[],"missing_ranges":[],"failures":[],"stop_file":null},"reported_paired":{"n":128,"mean_diff":"0.6264815792494729","se":"0.04754921875529431","worst5":[{"seed":9803921,"diff":"-0.9854398388081904"},{"seed":9803860,"diff":"-0.651158901822896"},{"seed":9803933,"diff":"-0.5495162955198793"},{"seed":9803899,"diff":"-0.4901948433156349"},{"seed":9803929,"diff":"-0.21762898749773285"}],"sample_sd":"0.5379580003518588","se_definition":"sample SD (n-1) / sqrt(n)","t":"13.175433701099832","wins":114,"losses":14,"ties":0,"mean_candidate_edge":"525.0185155519143","mean_qt1_edge":"524.3920339726649","cross_check":"identical to K/tools/engine.py paired() over the 128 rows"},"command_outcomes":[{"index":0,"exit":0},{"index":1,"exit":0},{"index":2,"exit":0},{"index":3,"exit":0},{"index":4,"exit":0},{"index":5,"exit":0},{"index":6,"exit":0},{"index":7,"exit":0,"wall_seconds":41},{"index":8,"exit":0,"wall_seconds":39},{"index":9,"exit":0,"wall_seconds":39},{"index":10,"exit":0,"wall_seconds":38},{"index":11,"exit":0,"wall_seconds":42},{"index":12,"exit":0,"wall_seconds":40},{"index":13,"exit":0,"wall_seconds":39},{"index":14,"exit":0,"wall_seconds":40}],"failed_commands":[],"timeout_events_reported":[]},"item-a1s4":{"input_sha256":"24a2a274b4a23e41ff20f8b0c59e08cc00a17639b657589eac42e3ed0d1e7497","status":"complete","blocked":null,"runtime":{"candidate_bytes":22058,"qt1_bytes":20605,"candidate_expected_bytes":22058,"limit_bytes":24576,"passed":true,"bytecode_sha256":{"candidate":"48c29ec5de7626f2c66f7a4cf3dd7e7a6b294473188029f197208c71ee49f0cb","qt1":"79c8d6c305ec6dfc29770b27cfb15b6cbd57b1fb01a23309cf8c131ca5c70189"}},"validation":{"setup_exit":0,"starter":"passed","candidate":{"exit":0,"output":"Validating strategy...\nCompiling strategy...\nStrategy 'TaylorComboGQmTrim2' validated successfully!\n"},"qt1":{"exit":0,"output":"Validating strategy...\nCompiling strategy...\nStrategy 'TaylorGaussianQMSpline' validated successfully!\n"}},"ranges":{"assigned_range":[9803956,9804084],"attempted_ranges":[[9803956,9803972],[9803972,9803988],[9803988,9804004],[9804004,9804020],[9804020,9804036],[9804036,9804052],[9804052,9804068],[9804068,9804084]],"completed_ranges":[[9803956,9804084]],"missing_ranges":[],"missing_ranges_by_arm":{"candidate":[],"qt1":[]}},"reported_paired":{"n":128,"mean_diff":"0.7016893506328548","se":"0.060424819387048266","worst5":[{"seed":9804033,"diff":"-3.382924368189947"},{"seed":9804027,"diff":"-1.1936333716049603"},{"seed":9804002,"diff":"-0.7697832597276602"},{"seed":9804038,"diff":"-0.5826361932944337"},{"seed":9804026,"diff":"-0.26441677909792816"}]},"command_outcomes":[{"index":0,"timeout_seconds":470,"exit":0},{"index":1,"exit":0},{"index":2,"exit":0},{"index":3,"exit":0},{"index":4,"exit":0},{"index":5,"exit":0},{"index":6,"exit":0},{"index":7,"timeout_seconds":465,"range":[9803956,9803972],"end_exclusive":true,"exit":0,"seconds":"39.03300428390503"},{"index":8,"timeout_seconds":465,"range":[9803972,9803988],"end_exclusive":true,"exit":0,"seconds":"36.256064653396606"},{"index":9,"timeout_seconds":465,"range":[9803988,9804004],"end_exclusive":true,"exit":0,"seconds":"37.66226410865784"},{"index":10,"timeout_seconds":465,"range":[9804004,9804020],"end_exclusive":true,"exit":0,"seconds":"36.346352338790894"},{"index":11,"timeout_seconds":465,"range":[9804020,9804036],"end_exclusive":true,"exit":0,"seconds":"36.97865653038025"},{"index":12,"timeout_seconds":465,"range":[9804036,9804052],"end_exclusive":true,"exit":0,"seconds":"39.51457715034485"},{"index":13,"timeout_seconds":465,"range":[9804052,9804068],"end_exclusive":true,"exit":0,"seconds":"36.79644274711609"},{"index":14,"timeout_seconds":465,"range":[9804068,9804084],"end_exclusive":true,"exit":0,"seconds":"36.433335304260254"},{"index":15,"exit":0},{"index":16,"exit":0}],"failed_commands":[],"timeout_events_reported":[]}},"method":{"source_fields":["item-a1s3/method","item-a1s4/method"],"engine":"Each arm alone vs 30 bps VanillaStrategy, run_batch(...,8), same configs for pairing; gas reset/read per arm. Sixteen sequential chunks, eight per shard, sixteen seeds per chunk.","configs":"Both report pinned engine.py configs matching MatchRunner._build_configs, all three BASELINE_VARIANCE flags enabled. a1s3 reports field-by-field config-only comparison; a1s4 states 10000 steps.","execution_difference":"a1s3 uses original engine.py; a1s4 reports guarded_engine.py evaluating original engine.py with an inserted per-arm stop check and replay reservation. Both report policy sources frozen. a1s4 child timeout 465s inside 470s command timeout; a1s3 chunk commands use timeout 470.","scope":"No new simulations, tuning, source changes or board claims in this merge."},"coverage":{"assigned_inclusive":[9803828,9804083],"expected_n":256,"recorded_n":256,"unique_n":256,"duplicate_seeds":[],"missing_seeds":[],"out_of_range_seeds":[],"missing_or_failed_attempts":[],"diffs_equal_binary64_candidate_minus_qt1":true},"paired_descriptive_conditional":{"n":256,"mean_diff":0.6640854649411638,"sample_sd":0.6150685715822393,"se":0.038441785723889954,"worst5":[{"source_item":"item-a1s4","seed":9804033,"candidate":"725.0060688704483","qt1":"728.3889932386382","diff":"-3.382924368189947"},{"source_item":"item-a1s4","seed":9804027,"candidate":"638.5237539133296","qt1":"639.7173872849346","diff":"-1.1936333716049603"},{"source_item":"item-a1s3","seed":9803921,"candidate":"434.58121589604895","qt1":"435.56665573485714","diff":"-0.9854398388081904"},{"source_item":"item-a1s4","seed":9804002,"candidate":"592.5382809652008","qt1":"593.3080642249284","diff":"-0.7697832597276602"},{"source_item":"item-a1s3","seed":9803860,"candidate":"718.8369906648027","qt1":"719.4881495666256","diff":"-0.651158901822896"}]},"statistics_method":"Python statistics.mean/stdev over binary64 conversions of every preserved diff, sample SD denominator n-1; SE=sample_sd/sqrt(n). worst5 ascending diff. Never average shard SEs.","gas_method":"For each arm/role/callback sum calls, ok, sum_ok_gas and all failure counts; max max_ok_gas; mean=sum_ok_gas/ok. Baseline=VanillaStrategy; Submission=tested arm. Each raw chunk counted once.","gas_aggregates":[{"arm":"candidate","role":"Baseline","callback":"afterInitialize","calls":256,"ok":256,"sum_ok_gas":5579776,"max_ok_gas":21796,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":21796.0},{"arm":"candidate","role":"Baseline","callback":"afterSwap","calls":2754020,"ok":2754020,"sum_ok_gas":62138248384,"max_ok_gas":22592,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":22562.744055598723},{"arm":"candidate","role":"Baseline","callback":"getName","calls":256,"ok":256,"sum_ok_gas":5510656,"max_ok_gas":21526,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":21526.0},{"arm":"candidate","role":"Submission","callback":"afterInitialize","calls":256,"ok":256,"sum_ok_gas":23597568,"max_ok_gas":92178,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":92178.0},{"arm":"candidate","role":"Submission","callback":"afterSwap","calls":2797279,"ok":2797279,"sum_ok_gas":422635505196,"max_ok_gas":220833,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":151088.07709062987},{"arm":"candidate","role":"Submission","callback":"getName","calls":256,"ok":256,"sum_ok_gas":5545216,"max_ok_gas":21661,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":21661.0},{"arm":"qt1","role":"Baseline","callback":"afterInitialize","calls":256,"ok":256,"sum_ok_gas":5579776,"max_ok_gas":21796,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":21796.0},{"arm":"qt1","role":"Baseline","callback":"afterSwap","calls":2770091,"ok":2770091,"sum_ok_gas":62500819108,"max_ok_gas":22592,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":22562.73137164086},{"arm":"qt1","role":"Baseline","callback":"getName","calls":256,"ok":256,"sum_ok_gas":5510656,"max_ok_gas":21526,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":21526.0},{"arm":"qt1","role":"Submission","callback":"afterInitialize","calls":256,"ok":256,"sum_ok_gas":23259648,"max_ok_gas":90858,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":90858.0},{"arm":"qt1","role":"Submission","callback":"afterSwap","calls":2794877,"ok":2794877,"sum_ok_gas":385620905803,"max_ok_gas":209290,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":137974.19557390182},{"arm":"qt1","role":"Submission","callback":"getName","calls":256,"ok":256,"sum_ok_gas":5524224,"max_ok_gas":21579,"oog":0,"revert":0,"other_halt":0,"tx_error":0,"bad_return":0,"mean_ok_gas":21579.0}],"gas_violations":[],"limits":{"afterSwap_peak":245000,"runtime_bytes":24576,"scope":"Observed runs only, not exhaustive bounds."},"chunk_Submission_afterSwap":"For each chunk and arm, the full Submission/afterSwap counters are embedded in raw_gas_stats: select row with role Submission and callback afterSwap using raw_gas_columns. No duplicate subset is added to totals.","raw_gas_columns":["role","callback","calls","ok","sum_ok_gas","max_ok_gas","oog","revert","other_halt","tx_error","bad_return"],"raw_gas_stats":{"item-a1s3":[{"range_half_open":[9803828,9803844],"candidate":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",174626,174626,3940038820,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1474848,92178,0,0,0,0,0],["Submission","afterSwap",177126,177126,26738170834,219871,0,0,0,0,0],["Submission","getName",16,16,346576,21661,0,0,0,0,0]],"qt1":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",175552,175552,3960927716,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1453728,90858,0,0,0,0,0],["Submission","afterSwap",176765,176765,24368300967,208233,0,0,0,0,0],["Submission","getName",16,16,345264,21579,0,0,0,0,0]]},{"range_half_open":[9803844,9803860],"candidate":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",167120,167120,3770686684,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1474848,92178,0,0,0,0,0],["Submission","afterSwap",170123,170123,25786109468,219808,0,0,0,0,0],["Submission","getName",16,16,346576,21661,0,0,0,0,0]],"qt1":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",168098,168098,3792754360,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1453728,90858,0,0,0,0,0],["Submission","afterSwap",169932,169932,23498540808,208645,0,0,0,0,0],["Submission","getName",16,16,345264,21579,0,0,0,0,0]]},{"range_half_open":[9803860,9803876],"candidate":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",173765,173765,3920630020,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1474848,92178,0,0,0,0,0],["Submission","afterSwap",176326,176326,26612676253,219917,0,0,0,0,0],["Submission","getName",16,16,346576,21661,0,0,0,0,0]],"qt1":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",174837,174837,3944818680,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1453728,90858,0,0,0,0,0],["Submission","afterSwap",176487,176487,24335616385,208809,0,0,0,0,0],["Submission","getName",16,16,345264,21579,0,0,0,0,0]]},{"range_half_open":[9803876,9803892],"candidate":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",166658,166658,3760242868,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1474848,92178,0,0,0,0,0],["Submission","afterSwap",169863,169863,25755852887,219792,0,0,0,0,0],["Submission","getName",16,16,346576,21661,0,0,0,0,0]],"qt1":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",167626,167626,3782083952,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1453728,90858,0,0,0,0,0],["Submission","afterSwap",169728,169728,23472881920,204594,0,0,0,0,0],["Submission","getName",16,16,345264,21579,0,0,0,0,0]]},{"range_half_open":[9803892,9803908],"candidate":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",175521,175521,3960236916,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1474848,92178,0,0,0,0,0],["Submission","afterSwap",178299,178299,26867836201,220187,0,0,0,0,0],["Submission","getName",16,16,346576,21661,0,0,0,0,0]],"qt1":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",176506,176506,3982457012,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1453728,90858,0,0,0,0,0],["Submission","afterSwap",177918,177918,24509794711,206736,0,0,0,0,0],["Submission","getName",16,16,345264,21579,0,0,0,0,0]]},{"range_half_open":[9803908,9803924],"candidate":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",165551,165551,3735266428,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1474848,92178,0,0,0,0,0],["Submission","afterSwap",168617,168617,25600278091,220130,0,0,0,0,0],["Submission","getName",16,16,346576,21661,0,0,0,0,0]],"qt1":[["Baseline","afterInitialize",16,16,348736,21796,0,0,0,0,0],["Baseline","afterSwap",166546,166546,3757722248,22592,0,0,0,0,0],["Baseline","getName",16,16,344416,21526,0,0,0,0,0],["Submission","afterInitialize",16,16,1453728,90858,0,0,0,0,0],["Submission","afterSwap",168390,168390,23308330450,206209,0,0,0,0,0],["Submission","getName",16,16,345264,21579,0,0,0,0,0]]},{"range_half_open":[9803924,9803940],"candidate":[["Baseline","afterInitialize",16,16,348736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items report complete 128-pair confirmations; no blocked errors, nonzero exits or timeout events recorded. Missing results were not imputed as zero.","P/Q/F were not rerun in either item, so these shards provide no Python fee parity certification.","a1s4 sources.json and original chunk files are not separately supplied; raw counters contained in both reports are fully embedded.","Full compiler settings equality remains unevidenced, not a pass. No board claim or exhaustive gas guarantee."]}
```