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Drafting Agents, Not Just Tokens: Speculative Recursive Self-Improvement for Agentic Systems

Xin Xu, Ke Cheng, Hao Wang, Yangru Huang, Yanghao Xiao, Zhichao Chen, Zhisheng Zhong, Xun Liu, Yi Li, Qian Li, Haibin Lv, Jun Zhang, Jie Jiang, Zhouchen Lin

arXiv:2610.16491v1cs.LGcs.AI

TL;DR

Agent self-improvement must balance exploring revisions with affording the evaluations needed to verify them. SpecRSI drafts successors before their predecessors are fully evaluated, allocates edits and checks by predicted verified return, and updates its improver from completed searches while keeping the real evaluator fixed. It outperforms Janus across the tested scientific backbone–task pairs and exceeds MetaRSI-v1 in system macro-average score across twenty backbones.

  • Problem

    Agent revision requires balancing exploration against costly evaluation, because narrow search can miss useful edit sequences while evaluating every intermediate version can exhaust a limited budget.

    Source: §1 · p. 1

  • Method

    SpecRSI drafts executable successors before full predecessor evaluation, uses VATS to allocate edits and checks by predicted verified return, and uses GVO to update the improver from completed searches under a fixed verification contract.

    Source: §1 · p. 2

  • Results

    SpecRSI outperforms Janus in all 50 scientific backbone–task pairs and exceeds MetaRSI-v1 by 1.85–2.38 pp in four-task macro-average score across twenty backbones.

    Source: §5 · p. 10

  • Takeaways & Limitations

    Full planning achieves the highest mean verified gain and lowest total-cost index among tested planning conditions at all eight budget caps.

    Source: §4.3 · p. 8

Abstract

from arXiv · show

Improving an agent through successive revisions requires balancing exploration and evaluation under a limited budget. A narrow search can miss useful sequences of edits, while fully evaluating every intermediate version can exhaust the budget before those sequences yield a verified improvement. We introduce Speculative Recursive Self-Improvement (SpecRSI), which drafts executable successor agents before their predecessors are fully evaluated, while requiring complete verification before adoption. Verification-Aware Tree Search (VATS) allocates the budget between further edits and outstanding checks using the predicted verified return of a continuation. Group Verification Optimization (GVO) learns the improver from completed searches while keeping the real evaluator fixed. In the main scientific comparison, terminal gains exceed Janus by 33.3%--40.0%. Additional evaluations show that SpecRSI outperforms Janus in all 50 scientific backbone--task pairs and exceeds MetaRSI-v1 by 1.85%--2.38% in macro-average system score across twenty backbones. Coding-validation success reaches 69.4% versus HGM's 64.3% at a 20.8% lower target-cost index.

1 INTRODUCTION

Agent self-improvement must balance exploring revisions against the paid evaluations needed to verify them. SpecRSI drafts successors before full evaluation but adopts only fully evaluated, admissible versions, and learns its improver from complete searches.

1 INTRODUCTION

  • The bottleneck is spending limited time and computation on exploration while still completing evaluations that establish verified progress.A wider search can leave too little budget to finish its most useful branch, while fully evaluating every branch can spend evidence on unused alternatives.Source: §1 · p. 1
  • A candidate’s apparent quality misses the cost of making it usable; budget decisions must value a continuation of edits and checks by its predicted verified return.The estimate must be made before paying for the checks that would reveal the return.Source: §1 · p. 2
  • SpecRSI extends incompletely evaluated versions but adopts only fully evaluated, admissible ones, with the improver frozen during each search and updated between searches.This two-level framework allows successors to be drafted ahead of their parents’ full evaluation.Source: §1 · p. 2, Figure 1 · p. 2
  • VATS selects further drafts or verification bundles using predicted verified gains net of later costs, while GVO trains the Drafter and Policy from complete-search feedback.GVO also trains the Scorer on realized suffix returns and paid same-state comparisons; the real evaluator remains fixed.Source: §1 · p. 2

2 PRELIMINARIES AND RELATED WORK

The paper frames recursive self-improvement as revising executable agent artifacts across rounds, then distinguishes predicted evaluation from real, verified improvement. SpecRSI retains that prediction-validation separation while valuing further edits and checks by their eventual verified return.

2.1 RECURSIVE SELF-IMPROVEMENT

  • Recursive self-improvement revises agent artifacts to support later improvement rounds; a useful stepping stone need not immediately outperform the incumbent.The artifacts can include executable code, prompts, tools, and workflows.Source: §2.1 · p. 3

2.2 EVALUATORS AND VERIFIED IMPROVEMENT

  • A proxy evaluator can prioritize real evaluations, but Janus admits only real-valid candidates; SpecRSI preserves prediction-validation separation while scoring further work by eventual verified return.The cited prior methods search over agents, workflows, or prompts; HGM separates expansion from evaluation, while Hyperagents and MetaRSI adapt improvement generation or scheduling.Source: §2.2 · p. 3, §2.1 · p. 3

3 METHOD

SpecRSI addresses the trade-off between pursuing promising continuations and affording the checks needed to complete them. Its VATS search drafts and verifies under a frozen improver, accepts only complete admissible versions, and GVO updates the improver between searches.

3.1 MOTIVATION

  • A continuation must promise enough verified improvement to remain affordable, because downstream edits, complementary checks, planning, and failed attempts all consume the limited budget.Candidate quality alone does not determine the value of continuing from that candidate.Source: §3.1 · pp. 3–4

3.2 TWO-LEVEL SPECULATIVE RSI LOOP

  • The two-level loop separates inner searches under a frozen improver from outer GVO updates, while the verification contract remains fixed.Independent searches from the same root supply agents and logs for the outer update; carry or reset separately selects the next root.Source: Figure 3 · p. 4, §3.2 · p. 5

3.3 INNER-LOOP SEARCH WITH VATS

  • VATS repeatedly chooses bounded draft or verification work, then replans from the updated state; ACCEPT terminates the search.Draft plans can extend existing, possibly incomplete parents, while verification plans list jobs for existing versions.Source: §3.3 · p. 5

3.3.1 SOLVER

  • The Solver forms budget-feasible completion bundles that cover selected missing checks, accounting for prerequisites, shared setups, conflicts, and reserved budgets.Bundles may include individually low-value checks; feasibility does not guarantee successful outcomes or exhaustive coverage.Source: §3.3.1 · p. 5

3.3.2 SCORER

  • The Scorer estimates the verified return of further work under a frozen procedure, including later edits, checks, branch switches, and subsequent costs.Bundle comparisons use a common conservative state and preserve check interactions rather than summing isolated check scores.Source: §3.3.2 · p. 5

3.3.3 POLICY

  • The Policy selects among remaining work options after preparation, using preference logits that need not maximize the Scorer’s value estimates.Collection samples from the policy; deployment chooses the highest-logit option.Source: §3.3.3 · p. 6

3.3.4 EXECUTION AND ACCEPTANCE

  • Drafts execute edits on immutable versions, while only acquired verification records can authorize adoption of the best complete admissible version.Invalid edits are charged and end that path; forecasts never create evidence, and only the selected version needs complete admissible evidence.Source: §3.3.4 · p. 6

3.4 OUTER-LOOP LEARNING WITH GVO

  • GVO updates the learned components between rounds from completed searches, charging failed or unfinished work and giving no gain when no complete improvement is found.Intermediate edits can receive delayed credit through verified descendants, but these updates guarantee neither per-edit causal attribution nor monotonic improvement.Source: §3.4 · pp. 6–7

4 EXPERIMENTAL RESULTS

Across the reported comparisons, SpecRSI improves scientific and system outcomes, while verification-aware planning and improver updates contribute distinct tested advantages. Results also expose trade-offs among planning capacity, total work, latency, and lifecycle cost.

4.1 EVALUATION SETUP.

  • The evaluation covers five scientific domains, four system tasks, and separate coding, prompt, and workflow profiles, with cross-backbone tests spanning 50 scientific pairs and twenty system backbones.Validation normally uses five training seeds with three nested searches each; cost indices are reported separately rather than pooled.Source: §4.1 · p. 7

RQ1: Does SpecRSI produce better successors within comparable evaluation settings?

  • SpecRSI leads terminal gain and call-axis AUBC in all five scientific domains, exceeding Janus by 33.3%–40.0% and 30.4%–33.7%, respectively.The table reports terminal gain and call-axis AUBC in native units, and task scores within matched edit permissions.Source: RQ1: Does SpecRSI produce better… · p. 7, Table 1 · p. 8
  • Across all 50 scientific backbone–task pairs, terminal-gain and AUBC uplifts over Janus are 17.8%–27.6% and 15.7%–19.8%; SpecRSI also exceeds MetaRSI-v1 on every system backbone by 1.85–2.38 pp.The latter comparison is four-task macro-average score across twenty backbones.Source: RQ1: Does SpecRSI produce better… · p. 7

4.3 VERIFICATION-AWARE SEARCH

  • At fixed full-state information, bundles raise gain from 4.8 to 6.3 pp, lower cost from 63.1 to 59.2, and reduce completion failure from 9.8% to 6.5%.Across eight budget caps, full SpecRSI has the highest reported mean gain and lowest total-cost index of seven conditions.Source: §4.3 · p. 8, Figure 4 · p. 8
  • At 70% budget, full versus additive planning raises gain from 4.73 ± 0.29 to 5.99 ± 0.40 pp while lowering total cost from 65.1 to 58.9.Planning takes 201 versus 141 ms; removing completion seeds reduces gain by 0.77–1.79 pp across the reported paired-difference sweep.Source: §4.3 · p. 8

4.4 IMPROVER LEARNING

  • Improver updates raise reset/carry gains from 4.1 ± 0.18 to 5.2 ± 0.21 pp and from 4.8 to 6.2 pp; updated SpecRSI reaches 21.7 pp by round 5.That cumulative gain exceeds updated Meta’s 17.8 pp and original-improver SpecRSI’s 13.8 pp.Source: §4.4 · p. 9, Table 2 · p. 9

RQ4: When are more planning and parallel work worth their cost?

  • Doubling plans from 32 to 64 raises gain from 6.3 to 6.5 pp but lowers net return from 4.7 to 4.5; eight workers cut elapsed time from 1,287 to 192 s while worker time rises.Batching lowers verification cost in three regimes and raises it in three; the separate lifecycle ledger gives SpecRSI a 5.7% lower total-cost index than MetaRSI-v1.Source: RQ4: When are more planning and… · p. 9, Table 3 · p. 10

5 CONCLUSION

SpecRSI couples successor drafting with complete verification before adoption, and learns its improver from completed searches. The paper reports gains over Janus and MetaRSI-v1 across scientific and system evaluations, while noting a higher scientific cost index than Janus.

5 CONCLUSION

  • SpecRSI outperforms Janus in all 50 scientific backbone–task pairs and exceeds MetaRSI-v1 by 1.85–2.38 pp in four-task macro-average score across twenty backbones.Full planning also has the highest mean verified gain and lowest total-cost index among tested planning conditions at all eight budget caps.Source: §5 · p. 10

A EXTENDED RELATED WORK

  • SpecRSI connects exploration to evaluation completion by selecting branches and outstanding-check bundles for attainable verified improvement under the remaining budget.Unlike systems that revise solvers, workflows, or prompts, SpecRSI’s related-work distinction is its joint selection of branches and check bundles.Source: A EXTENDED RELATED WORK · p. 16

B.1 SCIENTIFIC PERFORMANCE

  • 33.3% is the relative increase in PyBaMM terminal gain from Janus’s 0.36 to SpecRSI’s 0.48, not a percentage-point task-score increase.Across the five native scientific objectives, SpecRSI has the largest reported terminal gain and AUBC in each.Source: §B.1 · p. 17
  • 158.7 versus 148.1 is the scientific cost index for SpecRSI and Janus, a 7.2% premium.The appendix cost breakdown keeps evaluation, proposal, proxy-training, and planning costs visible.Source: §B.1 · p. 17

B.2 MATCHED-PERMISSION RESULTS

Matched-permission comparisons report SpecRSI gains over MetaRSI-v1 across system tasks, alongside separate coding-audit, prompt, and workflow results. The supplied appendix also describes the scope of backbone comparisons and why verification-aware search is examined.

B.2 MATCHED-PERMISSION RESULTS

  • Under D/H/M permissions, SpecRSI exceeds MetaRSI-v1 by 1.6, 2.2, 2.3, and 2.9 pp on TB2.1, SWE-Pro, GPQA-hard100, and AIME, respectively.With D+H permissions, the corresponding differences are 1.4, 2.1, 2.4, and 2.9 pp; D+H excludes model updates.Source: §B.2 · pp. 17–18

B.4 CODING AND AUDIT

  • The frozen-successor audit reports 69.4 ± 1.3% and 23/25 target hits for a selected, frozen artifact on a separately declared untouched split.This audit is distinct from coding-validation success and asynchronous completion.Source: §B.4 · p. 18, Table S5 · p. 18

B.3 BACKBONE COMPARISONS

  • Figure S2 compares scientific and system performance across ten backbones and twenty backbones, respectively, with five training seeds per backbone.Its panels report relative terminal-gain and AUBC uplift over Janus, and four-task macro-average scores over TB2.1, SWE-Pro, GPQA-hard100, and AIME.Source: §B.3 · p. 18, Figure S2 · p. 19

B.5 PROMPTS AND WORKFLOWS

  • 82.4% versus 78.5% is the GPQA-hard100 prompt-optimization score for SpecRSI and GEPA+Merge.Each profile retains its own initial agent and benchmark.Source: §B.5 · p. 20, Table S6 · p. 20
  • On PlanBench, SpecRSI reaches 67.8% success with 9,290 task-inference tokens, versus EMAS at 62.7% and 10,210 tokens.The token comparison counts task inference, not total search cost.Source: §B.5 · p. 20, Table S7 · p. 20

C WHY VERIFICATION-AWARE SEARCH HELPS

  • The appendix separates richer information, completion-aware work scope, and the amount of work executed before feedback as explanations to examine.Resource regimes for the last question are examined separately in Appendix E.2.Source: C WHY VERIFICATION-AWARE SEARCH HELPS · p. 20

C.1 INFORMATION AND WORK SCOPE

The information–scope study compares one-check and bundled work while holding information level fixed. Bundles improve reported gain and cost at both information levels, with a larger gain difference under full-state information.

C.1 INFORMATION AND WORK SCOPE

  • With full-state information, permitting bundles raises gain from 4.8 to 6.3 pp, lowers total cost from 63.1 to 59.2, and reduces failure from 9.8% to 6.5%.Hit rate rises from 84.0% to 92.0% in the same fixed-information comparison.Source: §C.1 · p. 20, Table S9 · p. 21
  • With summaries only, bundles raise mean verified gain by 0.9 pp, from 3.2 to 4.1, versus a 1.5 pp rise under full-state information.At both information levels, bundles yield higher mean gain and lower total cost than the corresponding one-check controller; the 0.6 pp difference is descriptive, not a significance-tested interaction.Source: §C.1 · pp. 20–21

C.2 PLANNING ABLATIONS

Full planning performs best across the reported budget caps, while ablations and evidence-input interventions show how planning choices and available work evidence relate to results. The predictor comparison reports model diagnostics separately from verification outcomes.

C.2 PLANNING ABLATIONS

  • At the standard budget, removing completion seeds lowers gain from 6.3 to 4.5 pp, while greedy value selection reaches 4.8 pp.Full planning spends more time preparing work yet has a lower total-cost index; the 70% cap is a separate budget cohort.Source: §C.2 · p. 21, Figure S4 · p. 21, Figure S5 · p. 22

C.3 EVIDENCE AND RELATIONS

  • Full evidence reaches 6.3 pp gain, versus 3.2 for the blind controller and 5.8 after valid fields are restored.Draft depth and checks per block are observed consequences of selected work, not optimization targets.Source: §C.3 · p. 22, Table S10 · p. 22

C.4 PREDICTION AND VERIFICATION

  • The “SpecRSI evolved evaluator” row has the lowest reported MAE and regret and highest NDCG, but not the smallest fitting cost.It is a historical candidate-predictor label, not a claim that the Verification Contract Γ is learned or editable.Source: §C.4 · p. 23, Table S11 · p. 23

D LEARNING THE IMPROVER ACROSS ROUNDS

  • The repeated-round experiments proceed from starting-artifact controls to learned-role and supervision changes, then to repeated improvement rounds.These experiments test whether the search procedure improves in addition to the task artifact.Source: D LEARNING THE IMPROVER ACROSS ROUNDS · p. 23

D.1 STARTING-ARTIFACT CONTROLS

The controls distinguish improver learning from retaining a stronger task agent, while repeated rounds show an advantage for updated SpecRSI over the supplied comparisons.

D.1 STARTING-ARTIFACT CONTROLS

  • Frozen versus all-role-updated improvers gain 4.1 versus 5.2 pp in reset controls and 4.8 versus 6.2 pp in carry controls.The 0.3 pp difference between update effects would require paired runs for an interaction test.Source: §D.1 · p. 24, Figure S7 · p. 24

D.2 ROLE UPDATES

  • Scorer-only updating has the largest single-role means at 5.2/5.4/5.3 pp across science/code/agent, while updating all three roles yields 6.1/6.3/6.2.The separately permitted shared-backbone extension is distinguished in the figure.Source: Figure S7 · p. 24, §D.2 · p. 24

D.1 STARTING-ARTIFACT CONTROLS

  • From the same released artifact, updating the improver raises mean gain from 5.7 to 6.9 pp and lowers cost index from 54.2 to 50.8.This controls for artifact retention when testing improver transfer.Source: Table S12 · p. 24, §D.1 · p. 24

D.3 SUPERVISION AND COST

  • Adding pairwise return supervision raises Gain from 5.4 ± 0.23 to 6.3 ± 0.25 pp and lowers RMSE from 1.05 to 0.85, with training cost rising 19.8%.At equal acquisition cost, the ordinary-search row reports 5.1 ± 0.22 pp Gain.Source: §D.3 · p. 25, Table S13 · p. 25
  • The earlier acquisition-control record reports reset gains of 4.8 and 5.3 pp for same-arm and means-plus-pair rows, versus 4.5 pp for extra ordinary-search acquisition.These are reset-gain values, not the supervision study’s Gain endpoint.Source: §D.3 · p. 25, Table S14 · p. 25

D.4 REPEATED ROUNDS

  • Updated SpecRSI accumulates 21.7 pp by round 5, versus 17.8 pp for updated Meta and 13.8 pp for original-improver SpecRSI.It leads the other three conditions in every evaluated round across all five training seeds.Source: §D.4 · p. 25

E.1 PLANNING CAPACITY

The resource studies favor bounded planning and state-dependent verification choices, while showing distinct trade-offs in latency, total work, and cost.

E.1 PLANNING CAPACITY

  • A cap of 32 plans yields net return 4.7 versus 4.5 for 64 plans, with overhead 3.9 versus 5.6 and mean gain only 0.2 percentage points lower.Completion seeds plus seeded growth reach Final 5.9 versus 5.8 for exhaustive construction at 56.2% lower planning cost.Source: §E.1 · pp. 25, 27, Table S15 · p. 26, Figure S10 · p. 27

E.2 VERIFICATION BLOCKS

  • Batching lowers mean verification cost by 17.1%, 6.5%, and 12.2% in three configurations, while serial execution is cheaper in the other three.The six configurations are compared within rows, not as a controlled single-factor sweep.Source: §E.2 · p. 27, Figure S11 · p. 28, Table S16 · p. 28

E.3 TIME AND TOTAL WORK

  • Eight workers reduce elapsed time from 1,287 to 192 seconds, a 6.7× speedup, while total worker time rises 9.0%, from 1,287 to 1,403 worker-seconds.Reported gain rises from 6.3 ± 0.25 to 6.5 ± 0.25 pp.Source: Table S17 · p. 28, §E.3 · p. 28

E.4 COST SENSITIVITY

  • SpecRSI’s total-cost index is 5.7% lower than MetaRSI-v1’s, 106.3 versus 112.7; a heavy regression penalty lowers cost to 0.98 while retaining ∆J of +1.7.The standard penalty changes ∆J from +2.4 to +2.1 and cost from 1.03 to 1.00.Source: §E.4 · p. 29, Table S18 · p. 29

F ALGORITHMS AND TRAINING

  • GVO collects independent complete searches before each improver update, while the verification contract Γ and outer update rule remain protected.The table distinguishes the outer training procedure as the only one that updates improver parameters.Source: §F.1 · p. 29, Table S19 · p. 30

F.1 RSI STATE

  • Reset controls hold the starting task agent fixed while changing the improver checkpoint, testing transfer beyond artifact retention rather than every task surface or Γ modification.Source: §F.1 · p. 30

F.2 NOTATION AND EVALUATION

The notation distinguishes editable agent-version paths from verification work and predictions from admitted evidence; VATS preserves feasible work options under budget and execution constraints.

F.2 NOTATION AND EVALUATION

  • Speculative continuations are paths of executable revisions, not token-probability guarantees; failed parents may be repairable, but adoption still requires a complete admissible agent.The illustrative file–test-map revision enables a successor’s focused intermediate retesting while retaining the full test suite, even without an immediate score increase.Source: §F.2 · p. 31

F.3 TREE SEARCH AND SOLVER

  • The solver’s bundles cover requested candidate–item keys subject to dependency, conflict, and resource constraints, and observed status requires a valid record under Γ.Source: §F.3 · pp. 31–32
  • VATS builds feasible completion seeds, refines bundles with predicted continuation values, and retains draft, verification, and acceptance options within a capped menu.Required seeds and fallback slots remain supported; higher-order plans may be omitted under the menu cap.Source: §F.3 · p. 33

F.4 VERIFICATION AND EXECUTION

  • A valid record may document failure, but missing fields remain missing; predictions choose verification work rather than determining which results are admitted.Speculative branches also require isolated snapshots because shared-file or external-service effects may not be reversible.Source: §F.4 · p. 34

F.5 TWO-STAGE TRAINING

The training procedure separates actor updates from scorer fitting and uses completed searches and paid continuations as distinct learning signals, while keeping Γ fixed.

F.5 TWO-STAGE TRAINING

  • The open-model implementation uses frozen text representations, a rank-16 Drafter adapter, and separate trainable Scorer and Policy branches.The Scorer and Policy process parent–child context, candidate–job relations, and plan features through message passing and set attention.Source: §F.5 · p. 34
  • The scorer predicts future verified improvement minus resource costs for a state–work pair, whereas the policy’s scalar logit defines a choice distribution.The two are separate value and preference branches, not two value models.Source: §F.5 · p. 34
  • Ordinary complete searches supply actor likelihoods and return labels, while paid forced continuations supply critic labels only; the next epoch freezes the updated improver and keeps Γ unchanged.Source: Figure S13 · p. 35
  • GVO credits sampled edits and plan choices with whole-search advantages from independent searches; solver outputs, environment results, and forced continuations are excluded from actor updates.Source: §F.5 · p. 36
  • Same-state forced continuations provide realized suffix-return targets for scorer fitting, and matched pair supervision reweights return differences without identifying a common offset.Source: §F.5 · p. 37
  • The scorer is fitted under the collection procedure, so after actor updates its refreshed copy approximates the new continuation policy rather than providing exact new-policy values.Deployment chooses the largest preference, so its calibration and quality need direct evaluation; finite rounds do not establish indefinite recursive acceleration.Source: §F.5 · p. 38

G THEORETICAL ANALYSIS

The appendix gives conditional analytical results on outcome consistency, accounting, planning, and learning—not new agent benchmarks. Each result depends on its stated assumptions.

G.1.1 OUTCOME CONSISTENCY

  • Under immutable candidates and sound direct and inherited records, complete coverage matches full direct execution under the contract.Stochastic services need justified replay semantics or fresh evaluation; prediction errors can still harm allocation even when admitted records remain correct.Source: §G.1.1 · pp. 38–39

G.1.2 REWARD CONSERVATION; G.1.3 FINITE TERMINATION

  • The preparation/work-clock accounting telescopes progress and disjoint charges; regrouping identical realized work preserves the undiscounted objective, and enforced reservations prevent overspending.No-feasible-work termination prevents zero-cost diagnostic loops; these guarantees require backend-enforced caps.Source: §G.1.2 · p. 39, §G.1.3 · p. 39

G.2.1 COMPLETION COMPLEMENTARITY

  • Two complementary checks can each have zero immediate selectable gain while jointly unlocking positive verified gain, so check utility need not be additive or submodular.This does not rule out singleton policies or additive proposal heuristics; a long-horizon policy can anticipate completion.Source: §G.2.1 · p. 39

G.2.2 FULL-STATE SIMULATION

  • Under serial execution, zero dispatch and replanning costs, no shared setup, identical jobs, and finite allowance, singleton policies can simulate bounded-plan policies.This policy-class comparison does not imply a trained singleton learner finds its optimum and excludes real parallel latency, model calls, setup sharing, and function-approximation difficulty.Source: §G.2.2 · pp. 39–40

G.2.3 REPAIRABLE VERSIONS

  • A failed or inadmissible parent need not imply every editable child fails: a structured-output edit can be followed by a parser repair that satisfies the contract.The example uses actual transformations and direct executions, but does not show that such two-step improvements are common.Source: §G.2.3 · p. 40

G.3.1 DELAYED FEEDBACK

  • In the two-check cost-only model, batching has higher return exactly when (1 − p)d > a + pc2.This threshold assumes a fixed output, no early batch cancellation, maximal-path affordability, and no reinvestment; other settings require new accounting.Source: §G.3.1 · p. 40

G.3.2 MENU OVERHEAD

  • A richer menu is worthwhile only when its new options cover both direct builder cost and the lost execution opportunity from spending that budget.The oracle identity assumes nested feasible policies; Figure S14 shows Equation (24) sensitivity, not a fitted batch-versus-serial result or a universal batching advantage.Source: §G.3.2 · pp. 40–41, Figure S14 · p. 41

G.4.1 INCOMPLETE SUMMARIES

  • For serial checks with arbitrary dependence, the batch-versus-sequential cost identity depends on prefix survival probabilities, not independent failure assumptions.Those probabilities are diagnostic inputs, not available to the deployed controller; the reported table lacks the coupled settings needed for a numerical test.Source: §G.4.1 · pp. 41–42

G.4.2 ORDERING-ROBUST REVERSAL

The section formalizes how incomplete joint evidence can make the optimal verification scope depend on context, even when success summaries match. It then gives matched cost comparisons and bounds or qualifications for scorer and learning claims.

G.4.2 ORDERING-ROBUST REVERSAL

  • The optimal first block is size two in context A and one in B; identical compressed inputs impose a tight worst-context excess-cost bound of 3/40.The result assumes three binary hard checks, unit check cost, dispatch cost 3/2, and the stated finite budget; reordering does not remove the reversal.Source: §G.4.2 · p. 42, Table S24 · p. 43

G.5 MATCHED SCOPE CONTROL

  • At full information, blocks reduce expected cost by 11/32; with blocks permitted, context information reduces it by 1/16.These are dispatch-cost differences, not changes in final output probabilities.Source: §G.5 · p. 44

G.6.1 APPROXIMATION ERROR

  • The one-decision loss is bounded by omitted-menu loss plus twice the uniform scorer error and the selected-plan scorer gap.Observed RMSE is not a uniform error guarantee, and the inequality establishes neither global regret nor policy improvement.Source: §G.6.1 · p. 45

G.6.2 SEEDED REFINEMENT

  • Seeded refinement telescopes continuation-value increments without requiring additivity or submodularity.Positive single-job increments can miss a profitable bundle, motivating affordable complete-candidate seeds; this does not provide a general approximation ratio.Source: §G.6.2 · p. 45

G.7.1 POLICY-GRADIENT BASELINE

  • Under fixed-start and fixed-snapshot conditions, the unclipped group estimator matches the displayed policy gradient, but clipping gives no monotonicity guarantee.Each sampled token and plan contributes once; the result does not establish global policy improvement.Source: §G.7.1 · pp. 45–46

G.7.2 CONTRAST IDENTIFIABILITY

  • Prospective forced-arm sample means identify a conditional return contrast, but contrast loss alone cannot calibrate their common offset.Ordinary return loss anchors mean calibration; neither identity establishes actor improvement or causality of an individual edit.Source: §G.7.2 · p. 46

H NOMENCLATURE

  • The nomenclature section collects full forms for abbreviations and published names for systems without initialism expansions.Examples include GRPO as Group Relative Policy Optimization and DVI as Draft, Verify, & Improve.Source: H NOMENCLATURE · pp. 46–47

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