# Root merge 1: observable classification, posterior quoting, and residual fees

Credit throughout: Taylor (gtmcknight), whose pinned replica, solved policy, Gaussian/lattice filters, dynamic program and qm tables underpin this work; the upstream IdentityMD qt1/QMRef, TwoComp and COMBO authors supplied the compressed reference and extensions. This is a synthesis of the 25 supplied results, not a new experiment or a leaderboard submission.

**Outcome.** None of these results establishes #1, a deployed improvement, or an engine-qualified contract. The strongest completed live replica result in this group is posterior-a: **+1.018694 (SE 0.014377) over qt1**, including **+0.421303 (SE 0.012069) over COMBO**, on 2,048 report seeds. It is a costly full-posterior research implementation with two flagged upstream citations, not a contract-ready winner. Routing's guarded compact classifier adds +0.078039 (SE 0.009144) over COMBO; its teacher adds +0.119282 (SE 0.009579). Finer tables add about +0.09–0.10, and the best completed early residual head adds +0.076499 (SE 0.008473). These gains were measured separately and must not be added together. [b09-posterior-a: summary, report, limitations; b03-routing: policy; b08-finer-a: report; b08-finer-b: report_10000_12047; b04-eight-output: report]

The requester's target is 528.42 versus qt1 at 524.94, eighth, described as about +3.5 short; these are **brief-supplied board figures, not rechecked live standings**. The brief also supplies about +3.8 over HA and +6.98 with the true flag. The measured frozen COMBO oracle reaches +3.167510 over the actual qt1 Python reference, leaving 0.332490 against the brief's approximate +3.5 target *in replica units*. This is a diagnostic comparison, not a conversion to board points. [Task brief; b07-combo-flag: headline, limitations]

## Evidence and reading conventions

Every bracketed `b…` identifier refers to the exact supplied JSON, with its original path and verified SHA-256 in the source register below. Field names narrow the attribution. All 25 files were present, nonempty, parsed as JSON, and matched the supplied hashes. This verifies input integrity only. No embedded commands were executed, no simulation was rerun, and upstream webpages, dependency bundles, internal file hashes and quoted passages were not independently revalidated in this merge. Source-reported P, Q, invariance and regeneration checks remain source reports.

The requester reports failed source rechecks for data-b (1), filter-only (15), all-observables (1), combo-strata (1), finer-a (1), posterior-a (2), information-a (2), information-b (1), res-c (1), and res-d (1). Neither the exact failed passage nor its URL is identified in the supplied warning. Consequently, none of those results' upstream citations is treated here as independently verified support. Their directly recorded measurements are retained as **qualified worker reports**, with corroboration distinguished from unverified provenance. The absence of a warning on another item is not a certification of its measurements. The warning does not itself prove the numerical result false, and an author's claim that they refetched sources does not supersede it. [Task source-recheck notice]

Unless explicitly marked partial, paired policy results use choose 64000..65023 (n=1024), then frozen report 10000..12047 (n=2048), Taylor replica defaults, fresh policy per seed, 10,000 steps. `mean ± SE` means mean paired edge difference and sample standard deviation of seed differences divided by sqrt(n), not a confidence interval. Classification error is a fraction of callbacks; its sampling unit and split differ across items. `worst5` means the five lowest seed differences, not five percent. Appendix tables retain the main reported paired means, SEs and tails, with partial coverage explicit. No pooling of workers or averaging of their estimates is performed: many use the same seeds and inherited baseline. [b02-data-c: policy, seed_coverage; b03-history: policy; b07-combo-flag: policy]

**Baseline identity matters.** qt1 means QMRef over the QMS1 blob, not Taylor's `real.py` Gaussian+qm gate. Multiple items reproduce actual qt1 at seeds 10000/10001/10002 as 443.101741 / 571.454483 / 525.908441, while the Gaussian+qm gate is 443.522608 / 571.623551 / 525.865859. The unmodified P gate's other columns are perfect information 448.261189 / 576.779199 / 531.886497; Gaussian+plain 443.455598 / 571.463409 / 525.168028; lattice+qm 443.663520 / 571.977293 / 526.411631. All numerical experiments except smoothing-b report reproduction before changes; smoothing-b never obtained the inputs. [b08-finer-a: P; b08-finer-b: P_output; b05-pi-five: task_findings; b10-smoothing-b: blocked]

The repeatedly reproduced reference is COMBO−qt1 choose +0.6096046465295315 (SE 0.01940052280944413), report +0.5973909633856562 (SE 0.013387993974623986); TwoComp−qt1 report +0.42480288330208926 (SE 0.012201543529995694); COMBO−TwoComp report +0.1725880800835669 (SE 0.01076265438861963). Thus most “over qt1” gains in the classifier/head work were inherited before that item began. [b02-data-b: policy_paired; b02-data-c: policy; b06-combo-strata: policy_pairs]

Small baseline discrepancies are preserved rather than overwritten: filter-only/eight-output report about +0.597368, all-observables/information-b +0.597256, res-d +0.597426. Workers suggest interpreter/libm/platform differences; that causal attribution has not been established here. Their within-worker paired comparisons remain the reported comparisons. Identical rounded scores do not prove byte-identical sources, despite eight-joint's stronger wording. [b03-filter-only: policy; b04-eight-output: limitations; b03-all-observables: policy; b11-information-b: controls; b13-res-d: findings; b04-eight-joint: findings]

## Observable data and classifiers

**b02-data-b — offline data, qualified by one failed citation.** Unchanged COMBO generated 1,795,485 first-own rows on 71000..71255: 1,344,857 training rows over 192 seeds and 450,628 held-out rows over 64 seeds. Features are 41 float32 observable/filter/history columns, labels separate uint8, original pi separately float64. First callbacks at timestamp zero are included. A fixed 160-tree, depth-4 histogram logistic GBT (64 bins, learning rate .07, L2 20) had no test tuning/early stopping. Original error/logloss/Brier were .1616388684/.3568441349/.1123940413; full model .1596394365/.3455189903/.1106604704. Error delta −.0019994319 had paired seed-bootstrap 95% interval [−.0024195727, −.0016053314]. History removal raised error .0009142796 [ .0005916273, .0012163045 ]; rival-only removal raised it .0000266295 [−.0001219529, .0001750882], not a resolved effect. Pi-only error .1618274941 did not establish improvement; logloss improved but Brier delta's interval crossed zero. No classifier was put into live quoting. [b02-data-b: seed_coverage, schema, frozen_spec, classification, findings]

The worker reports all 256 unchanged-COMBO outputs matching, 5,120 hidden-input invariance callbacks, exact original-pi replay on all seeds, and exact offline regeneration of seed 71000; binary model roundtrip maximum probability difference 4.488799554280831e-09, scalar test difference zero. Bootstrap uses 2,000 resamples of simulation seeds, conditional on fitted weights. These checks constrain the experiment but do not resolve the external citation warning or measure policy feedback. [b02-data-b: checks, classification.roundtrip, limitations]

**b02-data-c — independent offline dataset, consistent modest signal.** Seeds 72000..72191 train (1,347,914 rows), 72192..72255 test (450,109); 1,798,023 total first-own rows and 2,803,113 collection callbacks. The 52 float64 features cover belief, size/side, timing, fees/rival, and explicit history; separate labels; fixed 192 depth-4 trees, 64 bins, learning rate .08, L2 10. Original error .1617230493058348 falls to .15871933242836736, delta −.0030037168774674494, 95% paired seed-bootstrap interval [−.0035486978835374255, −.00244805317359243]. Logloss .35629205863864305→.3437050752985114; Brier .11255527539462121→.11003814822536129. Net 1,352 errors corrected: false arb predictions down 1,575, missed arbs up 223. [b02-data-c: seed_coverage, frozen_spec, classification, task_findings]

Pi-only error .1617585962511303 again gives no significant error improvement; belief/size/timing-only .1604433592751978; no explicit history .15953469048608226; no fees/rival .15901481641113596. Relative to full, history removal adds .0008153580577149044 (95% interval [.00037031885244991975,.0012753949198148398]); fee/rival removal adds .00029548398276860177 ([.00006643398454299346,.0005314624175946521]). This is not a contradiction of data-b's negligible rival effect: different feature sets, fee-plus-rival versus rival-only ablations, seeds and fitted models. Neither supports a universal feature ceiling. [b02-data-c: classification; b02-data-b: frozen_spec, classification]

Data-c reports 30,081 fixed-callback invariance checks, exact base edges on its first three collection seeds, exact original pi on 6,756 first callbacks of seed 72000, raw/binned inference agreement on 20,581 rows, and a deterministic trainer fixture/resume check. Its `rival_band_low/high` names are reversed relative to actual upper/lower fair-price formulas; “previous step” means previous observed timestamp, and EW spans 10/100 use callback decay 2/(span+1), not elapsed-time windows. No-history retains COMBO filter state. Initial t=0 pi is zero. Model weights regenerate rather than being embedded. Seed bootstrap excludes fitting uncertainty; offline accuracy is not a policy gain. [b02-data-c: checks, classification.schema_notes, limitations]

**Shared live classifier intervention.** The four b03 experiments replace only the first-own-trade probability before posterior collapse, inferred phase/rival updates, and branch quoting, retaining COMBO's remaining logic. This placement matters: changing a displayed hard label alone would not be the measured policy. All report observable-only inference and some hidden-input invariance, but no Solidity fee-equivalence test. Models differ materially in capacity, training, sampling and calibration, so “all observables” need not outperform “routing.” [b03-filter-only: findings, frozen_spec; b03-history: frozen_spec; b03-routing: policy; b03-all-observables: policy_rule, features]

**b03-filter-only — 15 failed source citations; weak incremental gain.** Ten features from filter likelihoods, prior moments, innovation, own move, side and observed amounts; 40 depth≤3 Newton trees trained on 60,000 rows from 112,007 sampled training callbacks. A 16×8×4 correction table over logit(pi), absolute normalized innovation and prior sd has 512 signed Q12 cells (1,024 weight bytes), no additional persistent history. Calibration selected identity; compact nominated for portable inference, teacher only choose-scored. Full choose incremental gains: teacher +.021061266973759818 (SE .011413471095466525), compact +.012284015136659221 (SE .009773070344332729). Compact report +.008646585922404054 (SE .006812894649529338) over COMBO; +.6060149324275661 (SE .013571022099650994) over qt1, chiefly inherited. [b03-filter-only: frozen_spec, policy, limitations]

Sampled choose classification error .16054263669431496→.15999056129150027 teacher / .1601374845841848 compact; logloss .35541526897580017→.3509922154858289/.3537433125057325. Live report compact error .1606263372435925 versus base .16118622390003925; ECE .00365931445140467 versus .00737940336435889, on different endogenous trajectories. Quantization probability bound .000030517578125 is small, but distillation maximum probability error .37946005070821986 is large (MAE .01022175853130433). Invariance reported on 9,389 callbacks per representation; offline bundle smoke on four seeds. The 14k–28k incremental gas estimate is explicitly speculative and excludes inherited filter/tables; teacher report is missing by design. The 15 source failures particularly limit external corroboration; retaining these numbers does not turn citations into a verified replication. [b03-filter-only: probability, checks, frozen_spec.compact, limitations; task warning]

**b03-history — small positive correction, probability loss does not select economic return.** Twenty-four inputs include filter state and last/second-last own callbacks, EW history and inferred pin age; 64 depth-3 teacher trees; adaptive compact partition with 111 nodes/56 leaves, depth≤7, Q20 thresholds/Q12 leaves, packed 1,252 bytes and 11 history scalars. Distillation and calibration use 64000..64127; full versus half-strength compact selection uses the full choose return. Full-strength compact has lower choose Brier but lower return. Compact-half choose +.03182334700248585 (SE .010272398266490089), report +.03748018749726159 (SE .007526575137643317) over COMBO, +.6348711508829178 (SE .013727885580878667) over qt1. Full compact report +.01565358910994738 (SE .00914684430835077); teacher +.04528076658034333 (SE .008814927377648872). [b03-history: frozen_spec, policy, task_findings]

Report errors: teacher .15812215487147313, full compact .158780236891131, half .15916003230741238. Half report Brier .11062073522104728, logloss .3475867525587428, ECE .0029229735448886335. Distillation probability RMSE .019084579802878095 but max .7847612278173357; sampled quantization max probability error .000030414104634557404 with no route/leaf changes. Choose distribution-shift maximum standardized mean change .043640954759162034. Reports exact packed roundtrip, 46,343 nominee invariance callbacks, exact offline seed-10000 replay and retraining of all teacher trees. These are sampled/worker checks, not global distillation bounds or measured gas. [b03-history: probability_calibration_and_error, closed_loop_distribution_shift, frozen_spec.quantization_and_distillation, checks]

**b03-routing — strongest compact classifier in this group.** Teacher trained on 73000..73383 (2,680,512 first trades), heldout 73384..73511 (897,897), shift check 73512..73639. A 400-tree GBT over 23 live features reduces heldout error .16110→.15651, logloss .35515→.33922, Brier .11202→.10846, ECE .00698→.00117. Permutation logloss importance is dominated by logit(pi) .486, then log arb likelihood .02626, rival advantage .0088, crossed-quote offset .00779, displacement .00299 and size .00295. This supports incremental observable information, not a proof that the model has reached a Bayes ceiling. [b03-routing: findings, seed_coverage]

The selected compact network uses 12 features, 16 tanh units, 225 int16 weights (450 bytes; estimated 546 with normalization), and clips its logit to the raw filter logit ±3. It reports three small additional carried integers. Unguarded net choose −.285202 (SE .068667), worst seed 64145 −30.760542; quantized unguarded −.287433 (SE .068838), worst −30.648591. Confident wrong probabilities can cross .005/.995 and collapse the filter. Guarded net choose +.056345 (SE .012335), report +.078039 (SE .009144), versus qt1 +.675430 (SE .014250). Guarded teacher choose +.090140 (SE .013343), report +.119282 (SE .009579), versus qt1 +.716673 (SE .013902). The teacher is not the compact nominee. [b03-routing: findings, policy, frozen_spec_net_q_g3]

Retained alternatives: raw teacher choose +.091912 (SE .014963), worst −6.858425; Platt teacher +.072034 (SE .028277), worst −25.445822; guard-2 teacher +.084663 (.013298), guard-2 net +.053195 (.012359), unguarded table +.029888 (.011485), guarded table +.021253 (.011584), all versus COMBO. Calibration was not deployed. Quantized-vs-float net sampled max probability difference .001539, mean .0001901, 8 threshold flips in 20,000 rows. Closed-loop net error .15685/logloss .34099/ECE .00279; feature mean shifts below .04 open-loop SD, but no retraining under feedback. The worker's ~15k–30k net plus ~5k feature gas costs and cited qt1 engine peak 208,775 are estimates/inherited claims, not this item's engine measurements. Its statement that a contract needs +.5 *over base* misreads the goal's +.5 *over qt1* eligibility; the actual +.675430 exceeds that threshold, while F/engine remain absent. [b03-routing: findings, frozen_spec_net_q_g3, limitations]

**b03-all-observables — one failed citation, completed modest compact gain.** Fixed 48-tree depth-2 teacher and additive distilled table over 18 features, including observable noise/retail-law proxies, timing/rate, direction, fee band, inferred rival and mixture state. Training trajectories 73000..73511, fit 448 seeds, validation 64; deterministic one-in-16 first-callback samples for diagnostics. Choose-pilot scalar calibration selected alpha=temperature=1 for both. Compact has 235 entries, 217 float64 cutpoints, 472 Q12 weight bytes plus 1,736 cutpoint bytes and seven history scalars. No gas estimate. [b03-all-observables: seed_coverage, features, calibration, model_counts]

Teacher choose +.04268041979110149 (SE .01072070857311321), compact +.02592771064529331 (SE .0116201483191013) over COMBO; rule prefers compact within .05 of teacher, and it was frozen. Compact report +.028164469516271523 (SE .00829932267062314) over COMBO, +.625420727193216 (SE .013546117627163672) over qt1. Heldout errors raw .16246748155803428, teacher .16057873917536794, compact .15965218630839956, but compact logloss .3524518338375053 is worse than teacher .3502826556153649. Report compact sampled error .15986549900602165, Brier .11126394542083316, logloss .35010065869788987, ECE .002044318096169823. Distillation logit RMSE .26834903753439326; quantization-only theoretical logit/probability bounds .0023193359375/.000579833984375 at unit calibration, distinct from observed sample errors and from distillation. The result's note mixes global and observed-row wording, so no broader fixed-point bound is inferred. Total measured wall exceeded its one-hour item budget. [b03-all-observables: findings, policy, probability_error_and_shift, quantization, limitations]

## Residual fee heads: positive small runs and negative larger searches

These heads alter fees using live/filter features, not the classification probability directly. Their fee feedback must update stored fees so future no-arb intervals use the fees actually charged. Early b04 searches used diagonal sep-CMA rather than full covariance, small generation budgets and different architectures; later b12/b13 searches are not exact repeats. Negative large perturbations support sensitivity to search scale, not a proof of a local/global optimum or that more training will help. The “lower bound on architecture potential” phrasing in eight-joint is only a demonstrated configuration, not a statistical lower bound. [b04-eight-output/b04-eight-joint/b04-sixteen-output/b04-sixteen-symmetric: training, findings, limitations; b12-res-a/b12-res-b/b12-res-c/b13-res-d: training or run records]

**b04-eight-output.** Fixed eight-unit hidden layer, 18 output parameters; sigma .3 failed (best block candidates −.73 to −1.68, medians about −3.18 to −3.92). Restart sigma .04, six generations, 12 candidates, rotating 256-seed choose blocks; zero candidate retained. Choose M4 +.065918 (SE .013024) versus M6 +.080720 (SE .012550); M6 selected. Report +.076499 (SE .008473) over COMBO, +.673867 (SE .013783) over qt1, 1,220/2,048 incremental wins. Three replays of 3,000 callbacks with randomized hidden fields reportedly preserve fees. Curve still rising is an observation, not measured future improvement; normalization came from eight choose seeds. No engine, gas or contract. [b04-eight-output: training, selection, choose, report, findings, limitations]

**b04-sixteen-output.** Ten inputs, fixed 16 tanh units, 34 output parameters, 8-bps cap. Only one mirrored pair at sigma .05 on 64000..64255: −.725521 (SE .038399) and −.516533 (SE .036154) against zero. Selected zero head (=COMBO); losing candidates not extended to all choose seeds, and fresh qt1 choose comparison missing. Report baseline +.597391 (SE .013388) uses published qt1 seed edges rounded to six decimals, with three spot rechecks, rather than a fresh qt1 run. Nonzero-head invariance: 1,926 callbacks, zero mismatches. No positive head result and no general rejection of the architecture follows from two perturbations. Included eight-candidate training loop was not completed. [b04-sixteen-output: architecture, training, selection, policy_scores, findings, limitations]

**b04-eight-joint.** Eight inputs→eight tanh→two bounded outputs, all 90 parameters trained, cap 5 bps, shrinkage 1e-3‖theta‖². Sigma .15 failed (eight candidates −.318860 to −1.110770); restarted .05, four generations×eight candidates over rotating 256-seed blocks (8,192 runs). Full choose CMA mean +.020765 (SE .010804) beats block-best +.008283 (.011322) and zero. Report +.032444 (.007277) over COMBO, +.629835 (.013682) over qt1, 1,099 incremental wins. Average absolute bid/ask corrections .4332/.4834 bps. About 100 multiply-adds and ten tanh per callback are static counts, not gas. [b04-eight-joint: architecture, training, selection_on_choose_64000_65023, report_10000_12047]

**b04-sixteen-symmetric.** Fixed random hidden layer, 16 trained output parameters, four generations×six candidates. Sigma 1.0 discarded after losses −.591969 to −4.860502; restart .2 fell to .16608. Selected mean choose +.016350 (SE .010841); report +.017715 (SE .007374) versus COMBO, +.615106 (.013826) versus qt1, 1,098 incremental wins. Inputs exclude hidden per-run sigma/rate; no true labels used. This is a small result, not closure of the flag gap. Its wording that another +.5 “beyond COMBO” is required for contract eligibility is incorrect under the goal, although no contract is measured. [b04-sixteen-symmetric: frozen_spec, training, results, findings, limitations]

**b12-res-a.** Joint 90-parameter eight-unit head, four generations in 2,100.0253858566284 seconds, only one complete validation checkpoint. Selected gen4 validation −.19670358351615236; full choose −.1954013666754842 (SE .015565760827464317) over COMBO / +.4142032798540473 (.020907616596659472) over qt1. Report only 10000..10383, n=384: −.1714748293651267 (.02284149368926531) over COMBO / +.430911833134154 (.03579627325384242) over qt1; 1,664 report seeds missing. No Q completion or gain claimed. Effective replica fees/stored fees match at zero, but raw returns do not: COMBO can return .15072871208495497 while the clipped head returns .1. Both are clamped by replica. It reports 42,006 frozen-head hidden-input invariance callbacks. Zero is economically preferable to this negative selected checkpoint; do not promote it based on inherited qt1 improvement. [b12-res-a: frozen_spec, training_curve, choose, report, zero_head_identity_check, hidden_observable_test, limitations]

**b12-res-b.** Eight inputs→eight tanh→two 3*tanh-bps corrections, 90 parameters, sigma .3, population 12. Training alternates 256-seed blocks within 64000..64511 at **2,000 steps**, validates 64512..64767 every fourth generation, 51 generations/2,064.2312245368958 seconds. Every nonzero validation checkpoint loses; gen0 zero selected. Full default-step choose/report differences from COMBO are exactly zero, while qt1 gains are the inherited +.6096046465295315/+ .5973909633856562. Reports exact zero-head equality over 41,645 callbacks and hidden-input checks on four further seeds. The architecture adds corrections before fee conversion and special zero behavior matters when interpreting identity. No learned gain despite more generations; short-horizon training is distinct from full-run scoring. [b12-res-b: frozen_spec, training, choose, report, zero_head_identity, observables_audit]

**b12-res-c — one failed citation, deliberately scaled-down negative experiment.** Fourteen inputs include two component means, SDs and weights; 16 hidden units, 274 parameters, 3-bps bounded outputs. Actual training: 11 generations, population 12, 16-seed minibatches at 1,000 steps, 32-seed validation every four generations, about 1,061 seconds rather than the requested 35-minute/256-seed protocol. Validation gen4 −.06432394775456785 selected versus gen8 −.09495435568519683; gen0 zero was omitted, so selected policy is worse than the available zero baseline. Only choose 64000..64031 and report 10000..10031 at 10,000 steps: report −.3851878035902718 (SE .09058559499532828) versus COMBO, +.1945709761236234 (.12928502586182258) versus qt1; choose −.5037199048617946 (.10671990481075704), +.1426751531118402 (.15745885332703996). Q incomplete. Four zero-output runs have equal edges; 4,302 hidden-randomization trials match fees. Positive best-population short-run fitness in some generations does not reverse the negative validation/report evidence. Unknown unrun seeds remain unknown. [b12-res-c: frozen_spec, training_curve, choose, report, zero_head_identity, leak_test, findings, limitations]

**b13-res-d — one failed citation; distinguish specified and sensitivity runs.** Fourteen inputs→eight hidden→two outputs; all 138 parameters, sigma .3, population eight, rotating 64-seed minibatches at 10,000 steps, validation every four generations on 64512..64767. Specified run: 41 generations/1,179.7 seconds, every nonzero validation negative (−.40 to −.61), final sigma .2259962790103512. Gen0 selected; full choose/report identical to effective COMBO, report versus qt1 +.597426 (SE .013387). Sensitivity: only 18 output parameters, sigma .1, 28 generations/812.9 seconds, gen12 validation +.0240890513331371 selected. Full choose incremental +.004681 (SE .009310), report +.008144 (.006705), versus qt1 +.605571 (.013779): no convincing incremental gain. [b13-res-d: as_specified_run, sensitivity_run, findings]

Zero-head identity is on applied/clamped fees: 43,219 callbacks on seeds 10000..10003, one raw return .12476733159999975→.1. This pre-freeze use of report-overlap seeds is a diagnostic exposure beyond simply P, not evidence of return-based selection, but should be disclosed. Hidden-field replay reportedly covers two seeds only. Single-process cost .0112 seconds/1,000 steps versus COMBO .0066, about 70% more; roughly 130 multiply-adds and ten tanh, no gas. Training stopped short of the 35-minute cap; the output-only sensitivity is explicitly a protocol departure, not the specified result. Its custom sep-CMA implementation was not compared to a reference library. Explanations about noisy high-dimensional search and likely future sigma shrinkage are hypotheses, not established improvements. [b13-res-d: zero_head_identity, findings, limitations]

## Flag localization and ceiling

**b06-qt1-strata.** On report, actual qt1 misclassifies 2,487,830/14,374,445 first-own callbacks (.1730731169), including 1,277,248 false arbs and 1,210,582 false retails. False-arb rate conditional on retail .1959663021818153; false-retail conditional on arb .1540817179819704. This is about 17.3%, not COMBO's 16.1%; the brief's rounded 16% should not be assigned indiscriminately to every baseline. The two oracle buckets were selected on choose aggregate Brier loss, not report returns: amountY `size:small` and prior inferred `phase:1`. Small trades account for .46676689082604583 of callbacks and .6470478288307481 of errors; error .239919726, mean predicted arb .524596201 versus actual .562862740. Phase1 accounts for .46150178319928176 of callbacks and .48748588127002246 of errors; error .182817714, predicted .493513284 versus actual .509126550. [b06-qt1-strata: classification, frozen_spec, findings]

Force true pi before posterior/phase/rival/quotes on all qualifying first callbacks: report +3.167510323083941 (SE .02238577386745225) over qt1. Force it only on small bucket: +2.169006056266096 (.019530877645349675); only phase1: +2.2676383265873543 (.019481244250155846). Fractions .6847668468383445 and .7159055836571178 of the full oracle gain overlap and are **not additive**. False arb can pin belief to a retail-derived price and suppress count/sync updates; false retail can retain a truncated belief and update retail count/rival sync on arb. Counts alone do not quantify each error's causal economic cost. Candidate features (size, inferred phase/pin age, history/timing) remain proposals unless separately tested. [b06-qt1-strata: policies, findings, proposed_observable_features, limitations]

**b06-combo-strata — one failed citation, oracle core corroborated by b07.** Report COMBO errors 2,318,251/14,382,447 (.16118613195654397): false arb 1,339,200, false retail 979,051; mean pi .5527807701337125 versus true arb prevalence .5475384682453549. Pi near .4–.6 is most ambiguous. Prior count/gap, own Y size and inferred pin-age stratification selected two joint buckets on choose: largest error counts among bins n≥50,000 and error≥.25. Both require prior count1, gap1, own Y<10; pin age2–5 versus age6+. Report counts/errors: 975,010/269,447, error .2763530630455072; 575,375/176,493, error .3067442971974799. [b06-combo-strata: classification, frozen_spec, task_findings]

Oracle bucket1 report +.4909698033068071 (SE .010976393427030811) versus COMBO, +1.0883607666924633 (.015549781545403022) versus qt1; bucket2 +.3623098590816244 (.00959676016469145), +.9597008224672805 (.01504320035029972). Bucket2 has a severe negative incremental tail at seed11701 −5.036255376407439 despite positive average. Full COMBO flag +2.5701193596982845 (.020762656700385372) over COMBO; TwoComp full flag +2.7427074397818516 (.02083164912819269) over TwoComp. Both flagged paths reach the same reported +3.167510323083941 over qt1 as the qt1 oracle. Marginal buckets overlap, and each intervention changes subsequent observations; gains cannot be composed. Base fixed-callback invariance here checks only three callbacks, much weaker than some other items. [b06-combo-strata: policy_pairs, task_findings; b07-combo-flag: policy]

**b07-combo-flag — direct frozen-base ceiling, not a deployable policy.** `pi=float(bool(arb))` is inserted immediately after first-trade likelihood for dt≥1, before hard call, posterior, rival, phase and quoting. No hidden p/s2/j/config; t=0 and later same-step callbacks unchanged. Hard pi bypasses the ambiguous two-component/MIX path. Choose Flag−COMBO +2.503378 (SE .028560), Flag−qt1 +3.112983 (.030987); report +2.570119 (.020763), +3.167510 (.022386). Report mean edges qt1 533.262831, COMBO 533.860222, Flag 536.430341. Flag−COMBO loses on nine report seeds, Flag−qt1 on two (11062 −1.300795, 10146 −.016155); oracle improvement is not per-seed monotonic. [b07-combo-flag: frozen_spec, headline, findings, policy]

Using stored report HA rows (not fresh HA runs), HA mean 529.557434; Flag−HA +6.872907 (SE .043751), COMBO−HA +4.302787 (.037598), qt1−HA +3.705396 (.038086). Taylor's quoted +6.98 refers to his true-flag `real.py`, not exactly this compressed-reference intervention; suggested filter/compression explanation is unmeasured. No choose HA rows exist. About 90.5% of approximate +3.5 is reached by this fixed-base oracle, 17.07% by COMBO; .332490 still remains in that informal replica-vs-board comparison. It is neither a global bound on observable policies nor a guaranteed upper bound under changes to quoting/filtering. [b07-combo-flag: headline, findings, limitations]

## Action-value tables, full posterior, and information buying

**b05-pi-five — blocked/incomplete, useful algebra only.** Goal was to optimize one common physical action against pi-weighted branch values, then interpolate optimized quotes across five pi knots. At retail-mean anchor mt and H=5e-4, define w=ln(spot/exp(mt))/H, delta=(lp−mt)/H, branch-specific Ra and Rr. `Uarb(a,b)=VN0(w−delta,Ra,a−delta,b+delta)`; `Uret(a,b)=Σ q_sd(e) VN1(w−e,r(e),a−e,b+e)`, with r(e)=Rr−e when synced, otherwise clipped to ±6. Optimize pi*Uarb+(1−pi)*Uret before refinement. Averaging branch argmax quotes generally differs from argmax expected values; synthetic counterexample validates that algebraic point only. Preserving COMBO belief requires separation, retail SD, branch rival estimates and sync mode as well as w/pi, not merely an extra pi axis on a Gaussian table. [b05-pi-five: task_findings]

Unmodified DP regeneration timed out at 470 seconds, exit124, before saved VN arrays or convergence. Last logged sweep10 diff .0217, “gain/run” 551.817 at solver449s is an intermediate solver quantity, **not a replica score**. Prototype used kappa=0, unlike COMBO's 1e-5; no knots chosen, integrated policy, complete tensor/slab generator, freeze, Q scores or live invariance. Finite action-grid clamping may break endpoint equivalence at nonzero separation. P and input hashes reportedly passed; this is not a negative empirical result for probability-axis quoting. [b05-pi-five: blocked, convergence, checks, limitations]

**b08-finer-a and b08-finer-b — similar positive results, different fine grids/convergence.** Both hold COMBO filter/initialization and kappa=1e-5 fixed, replace QMS1 with independently regenerated uncompressed qm tables, and include matched 5-bps C5 and identical flag controls. Fine own lattice is 2.5 bps, 641 own nodes and 85 actions, preserving own/rival extent ±800 bps, band/price-move support ±30 bps, actions −60..150 bps, midpoint lambda .8/sigma9.45/size20, 62-node retail quadrature, and sd levels [0,4,8,12,16,20,26,34]. Both report matched C5 tables identical to original tables and choose-only live selection. [b08-finer-a: params, geometry_boundary_checks, controls, selection; b08-finer-b: geometry, solver, controls, selection]

Finer-a (one failed citation) uses 73 rival nodes, original normalized VD0 tolerance 2e-7: 5-bps solve 110 sweeps, residual 1.883128843971349e-7; fine warm-start 46 sweeps, residual 1.899801700400161e-7. Full saved passive VN arrays are **not** converged to that tolerance: last-sweep fine VN0/VN2 changes .00011571325039660962/.00012077152430101101 (coarse .001427133843749484/.001488460487270471). Fine report C−COMBO +.097021237206314 (SE .007661383758794843), C−qt1 +.6944122005919702 (.013533847187353384); choose +.08792224762412026 (.011464527433440546) over COMBO. Grid increment C−C5 +.05393421549459437 (.007497747186681763), compression-removal C5−COMBO +.04308702171171963 (.00755014112041885). Grid attribution still includes unresolved solver error. [b08-finer-a: solvers, report, choose, limitations]

Finer-b uses 61 rival nodes (less dense outside the ±30 band), fine solve38 sweeps, residual 9.210865195008466e-7 under relaxed 1e-6 stopping, not Taylor's 2e-7. Report C−COMBO +.093105 (SE .007779), C−qt1 +.690496 (.013667); choose +.085929 (.011606). C−C5 +.050018 (.007569), same C5−COMBO +.043087 (.007550). Thus the two fine estimates are compatible but not identical replications; retain both settings rather than call one erroneous or average them. [b08-finer-b: solver, controls, choose_64000_65023, report_10000_12047; b08-finer-a: geometry_boundary_checks]

With true flag, finer-a Cflag−Flag +.11924507850136579 (.006824305346381084), Cflag−qt1 +3.2867554015853067 (.022613323550471); Cflag−C5flag only +.006753867134959096 (.0053634662086404165). Finer-b counterparts +.117648 (.006745), +3.285159 (.022562), grid-only +.005157 (.005324). Shared coarse compression removal under flag is +.11249121136640669 (about SE .006068). Therefore most flagged gain is compression removal; no convincing extra fine-grid flagged improvement. Classifier error stays about16.1% on live C. [b08-finer-a: report; b08-finer-b: controls, report_10000_12047, first_call_errors]

Boundary/numerical checks matter: finer-a zero invalid action cells, off-center exact reflection but center-row asymmetry .71bps coarse/.54bps fine, 3,000 boundary lookups each scale; symmetry-optimized three-sweep VN checks agree within about1e-16. Finer-b shared-node A1 mean absolute difference .316bps, maximum46.449bps; action upper-bound hits largely reflect extreme w feasibility. Neither removes boundary clipping. Fine tables are large (finer-b ~20MB qm JSON; finer-a VN arrays hundreds of MB to over1GB each) and not delivered as a contract/runtime; regeneration recipes and hashes are supplied. Finer-a repaired a wrong-global numba cache crash and memory-killed attempts via isolated scale modules/checkpoints; aborted outputs excluded. No compressed fine contract or measured post-compression gain. [b08-finer-a: geometry_boundary_checks, controls, solvers, limitations; b08-finer-b: geometry, boundary_checks, limitations]

**b09-posterior-a — best reported live result, two failed citations and significant portability limits.** Candidate uses a 121-cell, 2.5-bps lattice posterior and maximizes a common feasible physical quote against weighted solved VN, rather than averaging per-hypothesis optima. Price hypotheses are linearly rebinned to the 5-bps action/value lattice. Under hypothesis offset e the lookup shifts `(w,R,a,b)` to `(w−e,R(e),a−e,b+e)`. Ambiguous first trade uses separate phase0 arb and phase1 retail hypotheses with hypothesis-specific rival clip/sync; other callbacks use inferred phase and rival. Add kappa times expected variance-drop information bonus with phase weighting; this is a QMDP approximation, not a rigorous upper bound. Ctrl uses the identical lattice filter with COMBO mean/SD and weighted-branch table quoting. [b09-posterior-a: objective]

Chosen kappa5e-6, hard threshold .999, rho .26, silent cap30; a dev prescreen on 62000..62127 placed choose grid [2.5e-6,5e-6,7.5e-6,1e-5]. Full choose C−COMBO respectively +.400204 (.017446), +.411819 (.016819), +.401888 (.016650), +.329008 (.017155); Cflag inherits selected live settings. Report C−COMBO +.421303 (.012069), C−qt1 +1.018694 (.014377), C−Ctrl +.345436 (.011450), Ctrl−COMBO +.075867 (.008241), Ctrl−qt1 +.673258 (.013822). This control attributes most gain to quoting under the lattice representation, but includes the entire quoting change (objective, interpolation, information weight), not a pure isolated theorem about posterior shape. [b09-posterior-a: params, report]

Report Cflag−Flag +.105171 (.008712), Cflag−COMBO +2.675290 (.021282), Cflag−qt1 +3.272681 (.022819); Cflag−CtrlFlag +.100811 (.008488); CtrlFlag−Flag +.004360 (.002582). Cflag−C remains +2.253987 (.020678). Live C error .158520 (2,276,651/14,361,984), Ctrl .159680, COMBO .161190, qt1 .173070. The worker says C “closes none” of the call gap; read this as failure to solve the flag problem, not literally no error/gap reduction: these recorded errors and remaining oracle difference do change, and the quoting control carries most measured value. [b09-posterior-a: summary, report]

Lattice-port gate reproduces the three original lattice scores. Point-mass quote checks at every DP node give max fee differences .000760/.000791/.000821bps for phases0/1/2; these are Python table checks, **not Gate F**. Off-node comparison is much weaker: median quote gaps .17–.21bps, maxima5.1/11.7/8.5bps across phases. A perfect-information three-seed check differs from DPPolicy (448.230088/576.888218/531.877992 versus 448.261189/576.779199/531.886497), exposing interpolation differences. Candidate range bug was fixed using these report-overlap seeds before choose; no live C/Ctrl/Cflag report-seed run before freeze is reported, but this extra diagnostic exposure limits a strict untouched-report claim. [b09-posterior-a: controls, numerical_errors, limitations]

Report C numerical diagnostics: 22,391,976 quotes, max42 hypotheses, mean15.311, posterior weight-sum deviation up to .005125266137450013, 77,146 own-coordinate clamps, zero belief-death events. Cflag mean6.02 hypotheses, 31,659 clamps, weight deviation about2.05e-12, zero belief deaths. Float32 VN and clipped action bounds persist; rebinning can add up to2.5bps SD. Needs numpy/numba and ~262MB VN plus 43×43 action search per callback, far beyond an established 245k-gas implementation; no contract. Two-seed live hidden-input checks and 12 exact frozen row replays are reported. Two failed citations remain unresolved even though baseline/control comparisons support internal coherence. [b09-posterior-a: report.posterior_numerics, numerical_errors, controls, limitations]

**b09-posterior-b — incomplete, strongly negative implementation, not corroboration of posterior-a.** Same broad expected-value-before-argmax idea, but 4D multilinear clipped lookup, a physical fee grid0..150bps step5, half-grid parabolic probes accepted on objective improvement, hard .995 instead of .999 and different implementation/details. It times out in Q.choose, exit124, after 30 seeds64000..64029; **no report runs**. C−COMBO −121.95328087786956 (SE7.768201867785101); C−qt1 −121.35946020748096 (7.7626179641035025); C−moment-control −121.81805190871724 (7.753284629401118). Cflag−Flag −133.5957756759172 (8.226313151517239), Cflag−COMBO −131.26559621185754 (8.21054238702329), Cflag−qt1 −130.67177554146895 (8.204754516963783). [b09-posterior-b: blocked, objective, params, choose, report]

Prototype v1 seed64000 C331.13005171866 / Cflag323.28969428713833; latest v2 C330.6821971955818 / Cflag324.0469991406983, versus COMBO437.7100000860294, Flag439.38939781550437, qt1436.4087645205474. Only three real phase0 VN point-mass states and synthetic affine/interpolation tests passed; off-grid and phases1/2 are not comprehensively checked, hidden-invariance candidate test only16 callbacks. C errors33,700/204,262 versus moment-control33,788/207,558; classification alone cannot explain or validate disastrous returns. Suspected zero-fee aliases/off-grid shifts and unspecified belief-death oracle fallback remain unresolved, not a proven root cause. Keep the negative result alongside posterior-a: implementations differ; this is no evidence that full-posterior quoting inherently loses or that posterior-a is independently replicated. No offline execution dependencies/large arrays supplied. [b09-posterior-b: diagnostics, numerical_tests, controls, first_call_errors, limitations]

**b10-smoothing-b — no experiment.** Blocked before P: two pinned clone attempts returned `Recv failure: Connection reset by peer`; required artifact curl returned error56 with the same reset. No baseline, smoothing candidate, scores or gate claims. It says nothing about smoothing's merit. [b10-smoothing-b: blocked]

**b11-information-a/b — concordant negative live result, distinct from full-posterior argmax.** Information-a has two failed citations, information-b one. Both retain TwoComp/COMBO filtering and weighted branch offsets, regenerate full 5-bps tables using ambiguity-aware `igtab2`, and sweep kappas0,1e-5,3e-5,1e-4. IG2 = tau²−Z·V−ambiguity_ask−ambiguity_bid, tau²=belief_sd²+9.45² (bps²), with ambiguity integrating competing arb/retail likelihoods (rho .26, lognormal median11.12bps/log-SD1.176); original IG1 omits ambiguity losses. Objective adds kappa*(1−h_phase)*IG to expected VN. Phase multipliers .449329/.652773/.766890. Between-component variance is included in collapsed moments, but ambiguous first callbacks still use separate branch lookups and averaged offsets: **neither implements a full-mixture action-value argmax there**. [b11-information-a: params, information_formula; b11-information-b: params, information_formula]

Information-a choose live gains over COMBO: −.268082, −.028718, −1.091368, −16.921044; flag gains over Flag: −.001473, +.096967, −.470844, −13.689942. Both live and separate flag selection choose1e-5, so the independently selected flag setting happens to equal the live one. Report live gains: −.283321, −.016225, −1.040046, −16.869191. At selected1e-5 report SE .009022; versus qt1 +.581166 (.014402). Flag-selected report +.102716 (.007554) over Flag, +2.672835 (.021316) over COMBO, +3.270226 (.022922) over qt1. [b11-information-a: selection_on_choose, headline_report_10000_12047, edge_error_tradeoff]

Information-b selected choose −.028803 (SE .013314), report −.016066 (.009024) over COMBO, +.581190 over qt1; oracle increment +.102716 (.007554). Its own baseline COMBO−qt1 .597256 and Flag−COMBO2.570198 differ slightly from information-a. Live error falls from .16199 at kappa0 to .15903 at1e-5, .15085 at3e-5, .10342 at1e-4, while callbacks rise and profits collapse. A's report first-call counts14.097011M→16.294671M across extremes; corresponding means533.576901→516.991031. This is evidence that paying aggressively for informative trades can reduce classification error while hurting profit, not that minimizing error optimizes the policy. High-kappa flagged losses also persist. The worker claim “buying pins only pays once classification is right” is too broad: A's live1e-5 beats its own kappa0 by the difference of reported means, although neither beats COMBO; only the incremental comparison to the existing COMBO policy is negative. [b11-information-a: edge_error_tradeoff, headline_report_10000_12047; b11-information-b: headline, report_10000_12047]

A reports kappa0 point-mass table fees within .005bps of solved tables, zero cells over .01bps, no NaNs and nonnegative IG2 at tested levels. Nonzero-kappa point-mass tables can differ from pure value policy because next-step diffusion still creates uncertainty; zero current SD does not imply zero future IG. B reports point-mass/zero-weight moment identities, between variance .21e-6 plus within .7e-6 = .91e-6, and pi0/pi1 branch endpoint identity. A's IG1 full-table control is choose-only; B does not separate full-vs-spline and IG1-vs-IG2 effects. Neither tests an interpolated finer kappa sweep or joint-mixture information tables. A's flag “errors” are raw likelihood disagreements before override (~11.6–11.8%), B's flag errors are after override (zero); these denominators/definitions reconcile the apparent disagreement. B's statement “No policy reached +.5 over qt1” contradicts its own +.581190 and the goal threshold; no F/engine pass follows from either. [b11-information-a: point_mass_zero_weight_checks, limitations; b11-information-b: point_mass_zero_weight_checks, limitations, headline]

## What this root supports, and what remains unestablished

The useful directions retained are guarded observable corrections, careful treatment of the full posterior when choosing one physical quote, and modest gains from removing compression/finer tables. Localization points toward small own-leg trades with stale inferred pins and prior one-retail-count states, but those bucket benefits were measured with hidden truth, not an observable predictor. The best early residual head is positive; later zero-selected and partial negative heads prevent a general claim that larger networks or longer CMA searches improve it. Source reports of stronger teachers, tiny quantization error, and lower classification loss do not establish compact fee parity or profitable closed-loop behavior. [b03-routing; b09-posterior-a/b; b08-finer-a/b; b06-qt1-strata/combo-strata; b04-eight-output; b12-res-a/b/c; b13-res-d]

Gate status is limited: P is reported reproduced in 24 numeric/prototype items, smoothing-b blocked before P. Full Q is absent for pi-five, posterior-b, res-a (partial report), res-c (partial both); sixteen-output's rejected candidates and choose qt1 comparison are incomplete, and its report qt1 rows are inherited. Other full-window rows are worker evidence subject to selection/protocol/exposure caveats above. Report seeds were generally frozen out of return selection, but posterior-a used report-overlap oracle debugging and res-d used report-overlap identity diagnostics; preserve those disclosures instead of a blanket “untouched report” certification. No result supplies a completed contract F test on 50×2,000 callbacks, deployed ≤24,576 bytes, engine afterSwap peak≤245,000, zero OOG, or fresh engine paired evaluation against qt1 with VanillaStrategy and seeds9900000 upward. Compact model bytes, numerical table tests and gas estimates are not those gates. [Item gate/check/limitations fields; task brief]

Several observable policies exceed the goal's **eligibility threshold of +.5 over qt1** because COMBO already does, but eligibility alone is not a contract qualification. This merge does not perform contract work or broaden the assignment. No leaderboard improvement is certified. No combined policy (classifier+head+finer/posterior tables) was measured here; interaction and compression costs remain unknown. Neither the failed pi-five/smoothing runs nor the unfinished residual/posterior runs can be silently treated as zeros on missing seeds. [All supplied policy/limitations fields; task brief]

Source preservation is intentionally a write-up, not a runnable policy package. The inputs contain compressed source bundles, weights, commands, row commitments and regeneration instructions; this merge retains conclusions, formulas, principal metrics, checks, failures and provenance, but does not copy their opaque base64 payloads, full weight vectors, every per-seed row or every redundant calibration/training cell. Such material is **not delivered by this Markdown** and cannot be assumed available to an offline verifier from the hashes alone. The section below preserves principal quantitative comparisons and localization detail; omissions of repeated raw data are explicit, not invented reconstructions.

## Paired-result tails retained from Taylor-replica worker reports

All rows below are report 10000..12047 unless marked partial/choose. Numbers are rounded to six decimals for compactness; prose above retains key source precision. Tails are `seed:diff`, ascending. Sources are the named item and field; oracle rows remain nondeployable.

| Source / comparison | n | Mean | SE | worst5 |
|---|---:|---:|---:|---|
| b02-data-b `policy_paired.report` / COMBO−qt1 | 2048 | 0.597391 | 0.013388 | 10146:-3.552497, 11062:-2.334849, 11808:-1.822738, 10519:-1.782691, 11376:-1.750296 |
| b03-filter-only `policy.compact.report` / compact−qt1 | 2048 | 0.606015 | 0.013571 | 11062:-2.075097, 11376:-1.689772, 11808:-1.628604, 10519:-1.543136, 11746:-1.526869 |
| b03-history `policy.report` / half−qt1 | 2048 | 0.634871 | 0.013728 | 11062:-2.117144, 11555:-1.765212, 10519:-1.644737, 11376:-1.576370, 11929:-1.454848 |
| b03-routing `policy.report_10000..12047` / net_q_g3-qt1 | 2048 | 0.675430 | 0.014250 | 10146:-2.570815, 10519:-1.805964, 11062:-1.659168, 11376:-1.560564, 11808:-1.439390 |
| b03-routing `policy.report_10000..12047` / gbt_g3-qt1 | 2048 | 0.716673 | 0.013902 | 10146:-2.497190, 10519:-2.038792, 11062:-1.663473, 10401:-1.626419, 10930:-1.365018 |
| b03-all-observables `policy.report` / compact−qt1 | 2048 | 0.625421 | 0.013546 | 10519:-2.637827, 11376:-1.820150, 10416:-1.586546, 10401:-1.504699, 11062:-1.390442 |
| b04-eight-output `report` / HEAD8−qt1 | 2048 | 0.673867 | 0.013783 | 10146:-3.499643, 11808:-1.659541, 10401:-1.599965, 10930:-1.475635, 11062:-1.411680 |
| b04-eight-joint `report_10000_12047` / HEAD−qt1 | 2048 | 0.629835 | 0.013682 | 10146:-3.612504, 11808:-1.999071, 10162:-1.439128, 10331:-1.361200, 10236:-1.347464 |
| b04-sixteen-symmetric `results.report` / HEAD−qt1 | 2048 | 0.615106 | 0.013826 | 10146:-3.440009, 11808:-2.001334, 11376:-1.655570, 10162:-1.603538, 10519:-1.495166 |
| b06-qt1-strata `policies.bucket1.report` / bucket1−qt1 (oracle) | 2048 | 2.169006 | 0.019531 | 10822:-1.566577, 10256:-0.789241, 11062:-0.701552, 11519:-0.658391, 10146:-0.637045 |
| b06-qt1-strata `policies.bucket2.report` / bucket2−qt1 (oracle) | 2048 | 2.267638 | 0.019481 | 11062:-1.483996, 10146:-0.960600, 11376:-0.890582, 10256:-0.862128, 11855:-0.713205 |
| b06-combo-strata `policy_pairs.combo_gate1.report` / combo_gate1−COMBO (oracle) | 2048 | 0.490970 | 0.010976 | 10149:-1.666279, 10476:-1.396555, 11519:-1.336870, 10449:-1.279048, 11233:-1.147833 |
| b06-combo-strata `policy_pairs.combo_gate2.report` / combo_gate2−COMBO (oracle) | 2048 | 0.362310 | 0.009597 | 11701:-5.036255, 10578:-1.952874, 10256:-1.425384, 11937:-1.302698, 11370:-1.297828 |
| b07-combo-flag `policy.report` / flag-combo (oracle) | 2048 | 2.570119 | 0.020763 | 11701:-1.138705, 11519:-0.810231, 11911:-0.365037, 10578:-0.297158, 10367:-0.244856 |
| b07-combo-flag `policy.report` / flag-qt1 (oracle) | 2048 | 3.167510 | 0.022386 | 11062:-1.300795, 10146:-0.016155, 11519:0.095586, 11376:0.277364, 10141:0.297378 |
| b08-finer-a `report.paired` / C2.5−qt1 | 2048 | 0.694412 | 0.013534 | 10146:-3.927124, 10519:-1.762253, 11062:-1.756407, 10236:-1.364891, 11808:-1.229338 |
| b08-finer-b `report_10000_12047` / C−qt1 | 2048 | 0.690496 | 0.013667 | 10146:-3.969523, 10519:-1.989222, 11062:-1.976732, 11808:-1.475022, 10236:-1.446322 |
| b09-posterior-a `report.paired` / C-COMBO | 2048 | 0.421303 | 0.012069 | 11701:-3.297309, 10822:-1.775378, 10942:-1.526736, 11048:-1.387052, 11911:-1.361245 |
| b09-posterior-a `report.paired` / C-qt1 | 2048 | 1.018694 | 0.014377 | 10146:-2.347376, 10822:-2.168156, 11808:-1.379221, 10519:-1.332292, 11376:-1.185107 |
| b09-posterior-a `report.paired` / Cflag-qt1 (oracle) | 2048 | 3.272681 | 0.022819 | 11062:-0.643108, 11701:-0.140637, 11808:0.170575, 11519:0.227687, 10731:0.248658 |
| b09-posterior-b `choose.paired` / C−COMBO, choose64000..64029 only | 30 | -121.953281 | 7.768202 | 64019:-231.126075, 64024:-197.727590, 64003:-177.863205, 64006:-177.725811, 64017:-168.990596 |
| b11-information-a `report pairs` / C_k1e-5-qt1 | 2048 | 0.581166 | 0.014402 | 10146:-3.460459, 11062:-2.315958, 11808:-1.820214, 10519:-1.779457, 11164:-1.747538 |
| b11-information-b `report pairs` / C_1e-5-qt1 | 2048 | 0.581190 | 0.014401 | 10146:-3.460459, 11062:-2.315958, 11808:-1.820214, 10519:-1.779457, 11164:-1.747538 |
| b12-res-a `report` / C−qt1, 10000..10383 only | 384 | 0.430912 | 0.035796 | 10146:-3.489039, 10162:-2.089537, 10148:-1.453741, 10256:-1.315891, 10340:-1.313667 |
| b12-res-c `report` / C−qt1, 10000..10031 only | 32 | 0.194571 | 0.129285 | 10030:-1.242066, 10023:-1.154091, 10007:-1.107533, 10004:-1.033967, 10021:-0.881324 |
| b13-res-d `sensitivity_run.windows.report` / sensitivity−qt1 | 2048 | 0.605571 | 0.013779 | 10146:-3.646338, 10401:-1.881115, 11808:-1.691534, 10519:-1.649196, 11376:-1.571239 |

## Localization detail from Taylor-replica baseline callbacks

These are descriptive report-window strata, not additional causal policy gains. FA/FR denote false arb/false retail. Fields come directly from the stated classification tables; rates rounded to six decimals. Strata within different families overlap.

| Source / stratum | Callbacks | Error | FA | FR | Mean pi | True arb rate |
|---|---:|---:|---:|---:|---:|---:|
| b06-qt1-strata / age:fresh | 6281967 | 0.115857 | 591106 | 136702 | 0.712851 | 0.718528 |
| b06-qt1-strata / age:recent | 5068566 | 0.209541 | 462829 | 599242 | 0.406037 | 0.422674 |
| b06-qt1-strata / age:stale | 3023912 | 0.230811 | 223313 | 474638 | 0.373547 | 0.397045 |
| b06-qt1-strata / gap:1 | 10899285 | 0.165293 | 1118372 | 683199 | 0.632688 | 0.647632 |
| b06-qt1-strata / gap:2-5 | 3338969 | 0.199179 | 157332 | 507720 | 0.224474 | 0.232600 |
| b06-qt1-strata / gap:6+ | 136191 | 0.155715 | 1544 | 19663 | 0.149336 | 0.157037 |
| b06-qt1-strata / phase:0 | 4325478 | 0.155916 | 470381 | 204032 | 0.611971 | 0.613554 |
| b06-qt1-strata / phase:1 | 6633832 | 0.182818 | 536924 | 675858 | 0.493513 | 0.509127 |
| b06-qt1-strata / phase:2 | 3415135 | 0.175874 | 269943 | 330692 | 0.510888 | 0.534496 |
| b06-qt1-strata / size:large | 907396 | 0.023046 | 13840 | 7072 | 0.155754 | 0.140883 |
| b06-qt1-strata / size:medium | 6688417 | 0.128158 | 516427 | 340744 | 0.598660 | 0.590854 |
| b06-qt1-strata / size:small | 6709515 | 0.239920 | 746981 | 862764 | 0.524596 | 0.562863 |
| b06-qt1-strata / size:tail | 69117 | 0.000029 | 0 | 2 | 0.007238 | 0.007263 |
| b06-qt1-strata / synced:0 | 5602050 | 0.163633 | 574741 | 341939 | 0.589986 | 0.599266 |
| b06-qt1-strata / synced:1 | 8772395 | 0.179102 | 702507 | 868643 | 0.497079 | 0.512931 |
| b06-combo-strata / 10to30 | 3197120 | 0.065197 | 125096 | 83346 | 0.531351 | 0.521893 |
| b06-combo-strata / ge30 | 466101 | 0.002572 | 705 | 494 | 0.018599 | 0.018191 |
| b06-combo-strata / lt10 | 10719226 | 0.196713 | 1213399 | 895211 | 0.582400 | 0.578205 |
| b06-combo-strata / pin0to1 | 9636786 | 0.135302 | 850491 | 453386 | 0.613217 | 0.607058 |
| b06-combo-strata / pin2to5 | 2969429 | 0.207609 | 309087 | 307392 | 0.435437 | 0.430479 |
| b06-combo-strata / pin6+ | 1776232 | 0.224011 | 179622 | 218273 | 0.421059 | 0.420315 |
| b06-combo-strata / prev1/gap1/lt10/pin2to5 | 975010 | 0.276353 | 168988 | 100459 | 0.539480 | 0.525513 |
| b06-combo-strata / prev1/gap1/lt10/pin6+ | 575375 | 0.306744 | 95548 | 80945 | 0.524758 | 0.515867 |

qt1 size thresholds are amountY 5/20/80; phase is the previous inferred own-callback phase; age thresholds1/5 reference the last inferred arb; gap is time since previous own callback; synced is pre-update rival sync. COMBO size thresholds10/30, pin thresholds1/5, and prior count/gap joint definitions differ. Small-bin results across the two policies are therefore not directly interchangeable. [b06-qt1-strata: frozen_spec, classification.field_definitions; b06-combo-strata: classification.strata_definition]

## Source register: Taylor-derived input results and integrity

All reads were `.imd/reads/artifacts/<ID>`. The canonical source path for each row is `artifacts/goal/batches/<batch>/items/<item>/result.json`; the table gives `<batch>/<item>` to avoid repeating the path prefix. These originals are not delivered as Git files here. Each SHA-256 below was recomputed and matched the task pin.

| ID | Canonical batch/item | SHA-256 |
|---|---|---|
| b02-data-b | e02-observable-data/data-b | `9ad92c75774d2fc3017ce7ae61e3ee7ad4adda56d39c5dae2eaec6fd310d6cba` |
| b02-data-c | e02-observable-data/data-c | `a3a0433adaad7dad947712f170a6695ebf004970ff3ebddbcda3c0605f4bf2e0` |
| b03-filter-only | e02-classifier/filter-only | `1a10e0a8678302c7d3ebd1b43ebc8be455875056e49fe31b3e8d4a82dfe287a4` |
| b03-history | e02-classifier/history | `d7e393cec8170bfabe58c96dff7587f009549f15872a170e313a4a8c4e66b632` |
| b03-routing | e02-classifier/routing | `97a141c50913e84226bb1325b07811650efdcc88703eaffa42535c585c470cfd` |
| b03-all-observables | e02-classifier/all-observables | `7f051da91f89af93e274f87f8184cad471344b5f6f54fa27face2cbad9d4e46f` |
| b04-eight-output | e02-residual-head/eight-output | `a2d5a0dea7982a84bd2238f143f045b44600c35ac5638d2307fdeadc15bfc757` |
| b04-sixteen-output | e02-residual-head/sixteen-output | `f970c3e1976559de37242c49258571be5edfe1432f6c12ce3164cd474b2ed980` |
| b04-eight-joint | e02-residual-head/eight-joint | `a07e5c50d1de616664acb8620a5866fff591aa3bce003e9cbfcbb09fea93f1d4` |
| b04-sixteen-symmetric | e02-residual-head/sixteen-symmetric | `c6078881da24f510d04536d21d25046f6f90ec9af22a7c6dc49fb3e1ba69e1c2` |
| b05-pi-five | e02-probability-tables/pi-five | `181095692733c539cecd8e00a564bcc3e217c0bb34da0a6f64f02d3f08eade64` |
| b06-qt1-strata | e02-flag-localization/qt1-strata | `8681150633a8a73dac8418fea21d6810d6cb721272f92d9c04dd1590383750ec` |
| b06-combo-strata | e02-flag-localization/combo-strata | `c4af9861f11091d37c670e613d0fe510a6dc5df52bbf23a476e6fa08c856c8fb` |
| b07-combo-flag | e02-flag-ceilings/combo-flag | `1842fc87a159d56311a5af097b11bccfc683a63cb72d381003aa6d601cd2d90b` |
| b08-finer-a | e03-finer-solve/finer-a | `c9424570f99f01367e719ed46378211153686292a6282dc92eb6ac6f7800fd77` |
| b08-finer-b | e03-finer-solve/finer-b | `cba776811b926000a6c2c8c24b65916872c17bcb364545d0860f99ab61128d3f` |
| b09-posterior-a | e03-full-posterior/posterior-a | `acba14abb456ea0a5a157388ef9c1e77bb65e2c171dd27927742193ea154b152` |
| b09-posterior-b | e03-full-posterior/posterior-b | `a49b4294c8725b3f51c175c6b15bb4285de989172aba088163fd1289c21b82de` |
| b10-smoothing-b | e03-smoothing/smoothing-b | `a02b0fdfe84f008df8a82a29a35c01ea23fdf0431092b50a6cc9afa933c013ee` |
| b11-information-a | e03-information/information-a | `428275c47e5a8592f1294aa2f1ee99acf09dcadf4c74ce144f65e1f16e713ee7` |
| b11-information-b | e03-information/information-b | `ef0264d5fdffe1231dd399054570d558b87e2e4be26a600582ae831a2a1ca610` |
| b12-res-a | e04-residual-a/res-a | `6b954c10483490954b598a59c45263ba5fda0830d6f569d71832a20bff4760d5` |
| b12-res-b | e04-residual-a/res-b | `359d7a6af71d64b0f95180496bf641c888c19231fe729f02ba1535ed068f7b1a` |
| b12-res-c | e04-residual-a/res-c | `2d7792cfec1fee5527284c0f522f649ca101bf01f220b194bb23d5f5b7dba743` |
| b13-res-d | e04-residual-b/res-d | `35837edd834e40a6c6907d11db8de4d329c69b849095208a3e6cc96119db8210` |

Upstream locators retained as provenance, **not independently fetched or certified in this merge**: [Taylor's pinned solved directory/README](https://github.com/gtmcknight/amm-sim/tree/4812a6382311624e1506aca131ca35c378f930d9/research/solved), [pinned gates.py](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/gates.py), [pinned dp.py](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/dp.py), [pinned qmdp.py](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/qmdp.py), and [qt1 reference directory](https://github.com/identity-md-launches/goal-3170-beat-network-s-amm-entry/tree/31ff8ed128b463cde10ea0a71d354f8c54d4464a/reference/qt1). These locations appear in the input provenance; numerical experimental claims above cite the workers that measured them, not these pages. [b03-filter-only: hashes.downloads; b08-finer-a: provenance; b13-res-d: regeneration]

The shared artifact locators recorded by the inputs are [8a6e303b…](https://api.imdnotdead.fun/artifacts/8a6e303b662e1a5ea9bb47f31acedd3988ef65b3ddb66d074517aa59ad41ca40), [d3c849db…](https://api.imdnotdead.fun/artifacts/d3c849db2ac31e567b57e52b80b86e8c24c842e5b4125b9d75c78e3cb07115b9), [d360bea6…](https://api.imdnotdead.fun/artifacts/d360bea6c8c982717b7b43a8069a87013169c89ee3e4da25622db4d880b936d4), and [17d249ab…](https://api.imdnotdead.fun/artifacts/17d249ab0c33fc44931d9b105cf3f9e3846a560bd518b67310c2a56defacdecc). Their availability and quoted support remain unverified here; the exact affected URLs in the requester's failed-source list could not be identified from that notice. [b03-filter-only: hashes.downloads; task source-recheck warning]