LOCKR: A Hidden-State Trajectory-Guided Planner for Detecting and Repairing Stable-but-Wrong Lock-In in Diffusion Language Models

1 INTRODUCTION

• A diffusion model can expose an answer that appears converged while still wrong, and correct and erroneous trajectories can show similarly stable answers and surface signals.The shaded region in Figure 1 marks the lock-in window; stability before the midpoint checkpoint does not establish correctness.Source: §1 · pp. 1–2, Figure 1 · p. 1
• LOCKR treats the observed hidden trajectory as a planning state to decide whether to allocate computation, expand targeted repair branches, and select a continuation.Its risk detector gates intervention; a fixed local action bank supplies counterfactual branches, which trajectory-aware verification and selection rank.Source: §1 · p. 2
• 2.21–5.37 percentage-point absolute accuracy gains across five model–dataset settings accompany hidden trajectories’ advantage over surface statistics and single snapshots.Repair rates range from 22% to 41%.Source: §1 · p. 2

Diffusion Language Models and Inference Dynamics

• Prior diffusion work explores generation and inference dynamics, while recent methods use denoising dynamics for token ordering, caching, early commitment, and convergence-aware decoding (Wu et al., 2025; Liu et al., 2025; Wang et al., 2026b;a; Li et al., 2026b; Mohamed et al., 2026; Li et al., 2026a).LOCKR’s focus is whether an apparently stable answer is correct, rather than whether decoding has stabilized or can terminate efficiently.Source: §2 · pp. 2–3

Test-Time Scaling and Self-Correction

• Test-time reasoning methods include diverse sampling, verification, structured search, and iterative refinement; diffusion-specific correction work includes remasking and trajectory refinement (Wei et al., 2022; Cobbe et al., 2021; Lightman et al., 2024; Wang et al., 2023; Madaan et al., 2023; Yao et al., 2023; Besta et al., 2024; Snell et al., 2025; DeepSeek-AI, 2025; Wang et al., 2025; Dang et al., 2025; Huang et al., 2026; Kim et al., 2026; Bai et al., 2026).LOCKR uses prefix trajectories to decide whether to expand a repair space and repair trajectories to select among continuations.Source: §2 · p. 3

Internal Representations for Error Detection and Verification

• Reliability research studies calibration, self-evaluation, semantic uncertainty, and internal representations, while HIVE aggregates hidden evidence across denoising steps for post-generation verification (Guo et al., 2017; Jiang et al., 2021; Kadavath et al., 2022; Manakul et al., 2023; Chen et al., 2024a; Su et al., 2024; Zhang et al., 2025a; Zhao et al., 2026).LOCKR instead studies early lock-in under surface-matched conditions and makes hidden trajectories a planning signal for intervention and branch selection.Source: §2 · p. 3

3.1 ITERATIVE DENOISING AND EARLY LOCK-IN

• An example is early-locked when valid extracted answers are identical throughout the most recent half-window at the midpoint checkpoint; its label is correct or wrong according to the gold answer at that checkpoint.The label does not require the answer to remain unchanged during later denoising.Source: §3.1 · p. 3

3.2 THE SBW PHENOMENON

• SBW lock-in accounts for 14.9%–60.5% of processed generations across five formal model–dataset settings, while correct and erroneous lock-ins can show similarly stable answers and surface cues.This motivates controlling observable decoding behavior before testing hidden trajectories.Source: §3.2 · pp. 3–4

3.3 SURFACE-MATCHED BENCHMARK CONSTRUCTION

• The benchmark one-to-one matches early-correct and early-wrong examples using 18 prefix-level statistics covering confidence, entropy, margin, stability, answer-emergence timing, and log-probability behavior.Hidden representations are not used in matching, and learned Surface-18 classifiers remain meaningful controls because low SMD does not guarantee identical multivariate distributions.Source: §3.3 · p. 4
• For DiffusionGemma + MetaMathQA, matching reduces mean/max |SMD| from 0.671/0.934 to 0.016/0.065; maximum absolute SMD is below 0.085 in every formal setting.Figure 2 shows the representative before–after balance shift and summarizes post-matching maxima across all five settings.Source: Figure 2 · p. 4, §3.3 · p. 4

4.1 OVERVIEW

• Prefix hidden trajectories form the planning state; a risk model retains the baseline path or triggers targeted remasking, after which repair trajectories are scored to select a continuation.The planner learns when to allocate computation and which continuation to retain, but the repair-action bank is fixed rather than learned.Source: §4.1 · pp. 4–5, Figure 3 · p. 5

4.2 HIDDEN-STATE TRAJECTORY ENCODING AND RISK DETECTION

• LOCKR records representations across denoising positions and model layers, then encodes the resulting hidden trajectory to predict early-lock-in correctness and estimate wrong-lock-in risk.The risk decision uses only hidden states observed no later than the early-lock-in checkpoint; later states cannot revise it.Source: §4.2 · pp. 5–6

4.3 TARGETED REMASKING AND REPAIR BRANCH GENERATION

• For high-risk generations, LOCKR reuses baseline drafts, locally remasks an answer-related region, and resumes denoising to create counterfactual repair branches.A fixed bank varies intervention time and strength; the prefix-level risk estimate determines whether to intervene, while later baseline states may serve as repair starting points.Source: §4.3 · p. 6

4.4 TRAJECTORY-AWARE BRANCH VERIFICATION AND SELECTION

• A trajectory verifier scores each repair continuation, and a selector combines that score with risk context, answer agreement, and repair metadata to retain the highest-scoring branch.The verifier's score indicates evidence of correctness; the final selector returns the branch with the highest final score.Source: §4.4 · p. 6

5.1 EXPERIMENTAL SETUP

• Experiments covered DiffusionGemma on three mathematical benchmarks and LLaDA-2 on two, with 32 denoising steps and a 256-token maximum generation length unless otherwise specified.The balanced surface-matched benchmark supported controlled detection, branch-selection, and end-to-end analysis; original model–dataset distributions measured overall accuracy under selective intervention.Source: §5.1 · pp. 6–7

5.2 DETECTING SBW LOCK-IN

• LOCKR reached 77.29–83.92% AUROC and 78.24–84.08% pairwise accuracy; full trajectories improved over single hidden snapshots across all five settings.Trajectory modeling added 1.33–3.61 percentage points in AUROC and 1.41–4.75 percentage points in pairwise accuracy over the validation-selected snapshot; Figure 4 shows the detection hierarchy.Source: §5.2 · p. 7, Figure 4 · p. 7, Table 2 · p. 7

5.3 SELECTING SUCCESSFUL REPAIR BRANCHES

• 55.2–67.8% selected-branch accuracy made LOCKR the best non-oracle selector in all five settings, improving 1.6–4.3 percentage points over a single hidden snapshot verifier.All methods rank the same repair candidates.Source: §5.3 · p. 8, Table 3 · p. 8

5.4 END-TO-END TEST-TIME REPAIR

• On DiffusionGemma, LOCKR reached 67.9%, 66.4%, and 55.4% accuracy on MetaMathQA, Orca-Math, and NuminaMath V2, beating the strongest non-LOCKR baseline by 6.0, 5.3, and 1.8 percentage points, respectively.It was Pareto-efficient at 2.9–3.1× relative denoising cost; the visual summarizes the accuracy–compute trade-off.Source: §5.4 · p. 8, Table 4 · p. 8, Figure 5 · p. 8

5.5 RESULTS ACROSS MODELS AND DATASETS

• On LLaDA-2, LOCKR gave the best non-oracle accuracy on both datasets, reaching 57.2% at 2.9× cost on MetaMathQA and 51.9% at 2.5× cost on Orca-Math.The trajectory-over-surface and trajectory-over-snapshot ordering matched DiffusionGemma; several surface- or remasking-based baselines did not improve over the 50% matched-set baseline.Source: §5.5 · pp. 8–9, Table 5 · p. 8

5.6 NATURAL-DISTRIBUTION EVALUATION

• Accuracy gains of 2.21–5.37 percentage points across all five natural-distribution settings came with repairs on only 22–41% of examples.The corresponding relative denoising cost was 1.8–2.6×.Source: §5.6 · p. 9, Table 6 · p. 9

5.7 ABLATION AND REPAIR-SPACE ANALYSIS

• Replacing the trajectory with a single snapshot or removing branch trajectories, GRU modeling, or targeted remasking reduced accuracy by 3.2–5.2 percentage points; repairing every example raised cost to 5.0×.A random trigger at comparable cost lost 8.8 percentage points, while oracle headroom showed that outcomes also depend on whether the fixed bank exposes a correct continuation and the selector ranks it first.Source: §5.7 · p. 9, Table 7 · p. 9
• The evaluation covered two white-box diffusion language model families and mathematical reasoning, using a fixed repair-action bank; normalized cost measures denoising work, not hardware-specific latency.The authors identify broader domains and architectures, adaptive repair-space construction, and stronger trajectory-aware verification as future directions.Source: §5.7 · p. 9

• Across two dLLMs and three reasoning benchmarks, LOCKR yields consistent gains in detection, branch selection, and end-to-end accuracy with selective intervention.Source: §6 · p. 9
• Hidden-state trajectories provide stronger correctness signals than observable decoding statistics or single hidden snapshots under surface-matched evaluation.Source: §6 · p. 9
• The trajectories serve as actionable state representations for deciding when and how to intervene during reasoning.Source: §6 · p. 9

• Definitions of SBW lock-in, surface matching, trajectory construction, repair actions, and branch selection are detailed in the main text and appendix.Source: REPRODUCIBILITY STATEMENT · p. 10
• The appendix specifies preprocessing, generation, trajectory extraction, training, validation, hyperparameters, and compute accounting.Source: REPRODUCIBILITY STATEMENT · p. 10
• Reported comparisons use fixed data splits and validation-selected operating points, with test sets reserved for final evaluation.Source: REPRODUCIBILITY STATEMENT · p. 10
• Implementation and experiment configurations are provided through the anonymized code repository and supplementary materials to facilitate reproduction.Source: REPRODUCIBILITY STATEMENT · p. 10

AI USE STATEMENT

• AI assistants helped edit and organize manuscript text, check LaTeX and code, and identify implementation or pipeline errors; authors determined and verified the research and conclusions.Source: AI USE STATEMENT · p. 10

A ADDITIONAL EXPERIMENTAL DETAILS

• Appendix A details configurations, preprocessing, model selection, and relative-cost accounting; Table 8 summarizes base-generation settings, including DiffusionGemma’s native schedule.Source: A ADDITIONAL EXPERIMENTAL DETAILS · p. 13, Table 8 · p. 14

A.1 MODELS AND GENERATION SETTINGS

• Both models use 256-token, 32-step generations recorded at every step, with midpoint lock-in assessment; DiffusionGemma retains its native schedule, while LLaDA-2 uses 32-token blocks.Source: §A.1 · p. 14

A.2 DATASET PROCESSING AND ANSWER EVALUATION

• MetaMathQA and Orca-Math use shared numeric-clean pools, while NuminaMath V2 excludes overlap sets; numeric normalization and one shared 10^-6-tolerance rule govern evaluation.LLaDA-2 downstream repair evaluation uses MetaMathQA and Orca-Math; NuminaMath V2 is used only for benchmark-construction diagnostics.Source: §A.2 · pp. 14–15

A.3 TRAINING AND VALIDATION PROTOCOL

• Matched pairs and their derived repair branches stay grouped across splits, and validation—not test outcomes—selects models, snapshots, and intervention operating points.Source: §A.3 · pp. 15–16
• Only eligible early-locked examples receive risk scoring; the fixed repair bank runs only when the frozen operating point triggers intervention.Source: §A.3 · p. 16
• Branch selectors rank the same fixed candidate pools, while oracle selection is analysis-only; Surface-18 planning uses LOCKR’s eight-action bank and validation objective.The external PRM scores complete candidates with its official final reward, and ReMDM uses its default remasking rule without LOCKR’s detector or verifier.Source: §A.3 · p. 16

• One standard generation is assigned relative cost 1.0×, and the normalized measure is a model-execution proxy rather than a hardware-specific wall-clock metric.Source: §A.4 · p. 17
• Per-example cost includes the original trajectory and executed repair or restart work; reused prefixes are not charged again, while independent full restarts are charged fully.Source: §A.4 · p. 17
• LOCKR incurs repair cost only on selected examples, with repair rates of 22–41% across five natural-distribution settings; reported cost excludes offline and auxiliary scoring compute.Relative cost tracks denoising work, not exact floating-point operations or elapsed time, which depends on architecture, hardware, batching, parallelism, and implementation.Source: §A.4 · p. 17

B.1 FULL SURFACE-18 FEATURE DEFINITIONS

• The 18 prefix-level Surface-18 features cover uncertainty, local weakness and dispersion, trajectory evolution, answer and token flips, answer emergence, and accumulated confidence, without using hidden activations.Features are computed from records available no later than the early-lock-in checkpoint; examples with missing or non-finite required features are excluded.Source: §B.1 · p. 18, Table 10 · p. 19

B.2 MATCHING ALGORITHM AND CALIPERS

• Matching uses robust-scaled Surface-18 distances with feature-specific calipers, exact matching on answer string flip count, and one-to-one greedy edge selection without replacement.Hidden representations are not consulted until matched pairs are frozen; first answer index may differ by at most two recorded answer states.Source: §B.2 · pp. 19–20, Table 11 · p. 20

B.3 ADDITIONAL BALANCE STATISTICS

• Across all six constructed pools, mean absolute SMD is at most 0.01765 and maximum absolute SMD is at most 0.08494 across the 18 matched surface features.The benchmark controls confidence, uncertainty, stability, answer emergence, and likelihood differences, while not implying the groups are identical in every observable aspect.Source: §B.3 · pp. 20–21, Table 12 · p. 21

C.1 HIDDEN-STATE EXTRACTION

• The detector uses hidden states aligned to the early-lock-in prefix, selecting snapshots at 25%, 50%, 75%, and 100% and layers 5, 10, 15, and 19.For the evaluated models, hidden extraction is tied to the same generation instance used to construct the surface record.Source: §C.1 · pp. 21–22

C.2 RANDOM-SIGN PROJECTION

• Each selected hidden vector is projected to 128 dimensions using a fixed, deterministic, layer-specific random projection, providing common-width features without storing full activations.The projection is fixed before detector training and is not selected using validation or test performance.Source: §C.2 · pp. 22–23

C.3 ANSWER AND CHANGE TRACKS

• The representation combines an answer track over the first eight generated positions with a change track for positions revised between selected snapshots.The tracks capture a stable spatial region and locations undergoing revision, respectively, including internal changes when the answer itself shows little observable change.Source: §C.3 · pp. 23–24

C.4 GRU ARCHITECTURE AND HYPERPARAMETERS

• The first-stage detector uses a separate bidirectional GRU, while its fixed hidden-feature extraction geometry enables a controlled comparison between full trajectories and a single snapshot.Feature extraction settings are fixed before training; only the input projection, GRU encoder, LayerNorm parameters, and prediction head are optimized.Source: §C.4 · pp. 24–25

D.1 REPAIR ACTION BANK

• The repair planner uses a fixed bank of eight paired checkpoint–remasking actions, shared across settings and not chosen using validation or test performance.Each selected example receives eight candidate branches, and the trigger risk remains fixed even when a repair starts from a later baseline state.Source: §D.1 · pp. 25–26, Table 15 · p. 26

D.2 TARGETED REMASKING PROCEDURE

• Both model families preserve most of the draft while reopening an answer-related region, but DiffusionGemma locates answer or numeric spans whereas LLaDA-2 remasks an answer-prefix region.Gold answers are not used to choose remasked positions; DiffusionGemma falls back from answer-span matching to numeric-tail search and then an output suffix.Source: §D.2 · pp. 26–27

D.3 BRANCH-TRAJECTORY VERIFIER

• A separate branch-trajectory verifier uses lock-in, pairwise-ranking, and listwise supervision to score candidate branches, with higher scores ranking more promising alternatives.The verifier is jointly trained on original trajectories and repair branches, then frozen before its scores are used by the final selector.Source: §D.3 · pp. 28–29

D.4 FINAL HGB SELECTOR

• The final histogram gradient-boosted selector combines branch-trajectory scores with first-stage risk, repair metadata, stability, and answer-consensus features to rank branches within a fixed pool.The first-stage detector determines where additional computation is allocated; the fixed bank determines available alternatives, and the selector chooses among them.Source: §D.4 · pp. 29–31

E ADDITIONAL DETECTION RESULTS

• The additional detection analyses report full detector metrics, compare trajectories with validation-selected single snapshots, and examine risk enrichment across intervention coverage.The appendix describes these analyses as complements to the compact main-text AUROC comparison.Source: E ADDITIONAL DETECTION RESULTS · p. 31

E.1 FULL DETECTION METRICS

• 98.5% of DiffusionGemma + MetaMathQA’s highest-risk test decile are wrong lock-ins; the corresponding precision ranges from 85.9% to 94.1% in the other four settings.AUPRC ranges from 75.43% to 84.09% across five settings.Source: Table 20 · p. 32, §E.1 · p. 32

E.2 SINGLE HIDDEN SNAPSHOT SELECTION

• The full trajectory improves AUROC and pairwise accuracy over a validation-selected single hidden snapshot in every setting, with gains reaching 4.75 points in pairwise accuracy and 3.61 points in AUROC on Orca-Math.The snapshot comparison is favorable to the baseline because its observation position is selected separately for each model–dataset setting using validation performance.Source: Table 21 · p. 32, §E.2 · pp. 32–33

E.3 OPERATING-POINT AND RISK-COVERAGE SENSITIVITY

• At 30% risk coverage, 76.5%–85.9% of selected examples are wrong lock-ins, versus a 50% matched-set base rate; the top 5% contains approximately 90%–99%.Risk enrichment decreases as coverage expands, while validation—not test outcomes—determines the intervention operating point.Source: Table 22 · p. 33, §E.3 · p. 33

F.1 FULL END-TO-END DIFFUSIONGEMMA COMPARISON

• The DiffusionGemma end-to-end comparison reports final accuracy alongside relative diffusion-model denoising cost, with standard decoding normalized to 1.0× cost.Reported cost excludes auxiliary scoring-model computation; the end-to-end oracle retains correct baseline outputs and uses a correct repair when available for a baseline-wrong example.Source: Table 23 · p. 34, §F.1 · p. 34

F.2 FULL BRANCH-SELECTION METRICS

• 93.93% AUROC and 67.8% selected-branch accuracy for DiffusionGemma + MetaMathQA leave a 5.0-point gap to oracle branch selection.Across five settings, branch AUROC ranges from 85.93% to 93.93%; oracle gaps are 5.0–6.9 points for DiffusionGemma and approximately 12.7–12.9 for LLaDA-2.Source: Table 25 · p. 35, §F.2 · p. 35

F.3 PER-ACTION REPAIR DIAGNOSTICS

• The eight fixed repair actions are complementary alternatives: an action can add repair-space coverage even when its standalone accuracy is not maximal.Checkpoint fraction and remasking budget are paired, so each action represents one complete intervention configuration rather than an isolated effect.Source: §F.3 · pp. 35–36

F.4 REPAIR COVERAGE AND END-TO-END ORACLE ANALYSIS

• Oracle branch-selection accuracy was 72.8% for DiffusionGemma on MetaMathQA and Orca-Math, 62.1% on NuminaMath V2, and 68.7% and 63.7% for LLaDA-2 on MetaMathQA and Orca-Math.These results show different amounts of usable headroom across model–dataset combinations for the same eight-action bank.Source: §F.4 · p. 36
• On LLaDA-2, individual-branch accuracy was 40.51% on MetaMathQA and 39.53% on Orca-Math; majority-vote accuracy was 41.71% and 41.17%, respectively.Source: §F.4 · p. 36
• Wrong-case repair coverage was 43.33% on LLaDA-2 MetaMathQA versus 31.69% on Orca-Math; end-to-end repair oracle accuracy was 71.66% versus 65.85%, respectively.Wrong-case coverage is the fraction of originally wrong cases with at least one successful repair among eight actions; the oracle retains correct baselines and uses an available correct repair.Source: Table 26 · p. 37, §F.4 · p. 37
• Failures split between exposing no successful counterfactual and ranking successful branches poorly, while repair-space coverage caps recovery when every candidate is wrong.The analyses motivate richer or adaptive interventions to increase coverage and stronger trajectory-aware verification to reduce conditional selection error.Source: §F.4 · pp. 36–37

F.5 ADDITIONAL BASELINES

• Majority voting helps DiffusionGemma on MetaMathQA and Orca-Math but remains substantially weaker than trajectory-aware selection; on LLaDA-2 it stays below the 50% balanced-set baseline.Source: §F.5 · p. 37
• All three additional LLaDA-2 controls fail to beat the 50% baseline; random triggering can harm performance, while always-repair majority voting has the highest cost among these controls.Confidence-guided repair behaves similarly, consistent with weak surface-level discrimination.Source: §F.5 · p. 38
• The results distinguish branch generation, deciding where repair is warranted, and selecting among candidates; strongest performance uses trajectories for both allocation and evaluation.Source: §F.5 · p. 38

G ADDITIONAL ABLATIONS AND ANALYSIS

• The appendix examines additional component ablations, selective-intervention accuracy–compute trade-offs, and residual errors in the complete planning policy.This differs from Appendix F’s focus on the generated repair pool and branch selection.Source: G ADDITIONAL ABLATIONS AND ANALYSIS · p. 38

G.1 FULL PER-DATASET ABLATIONS

• Replacing targeted remasking lowers accuracy by 5.2 percentage points; removing branch-trajectory signal or temporal GRU reduces it by 4.0 and 4.2 points.The complete DiffusionGemma + MetaMathQA policy reaches 67.9% accuracy at 3.1× relative cost.Source: §G.1 · p. 38
• Across both LLaDA-2 datasets, verifier ordering is full trajectory > w/o branch GRU > w/o GRU > consensus only; removing GRU modeling lowers MetaMathQA branch AUROC from 88.34% to 81.48%.On MetaMathQA, planner accuracy falls from 57.15% to 51.73%; on Orca-Math, branch AUROC falls from 85.93% to 83.03%.Source: §G.1 · p. 39

G.2 REPAIR-RATE AND COMPUTE SENSITIVITY

• At 10% coverage, 85.9–98.5% of selected examples are SBW; at 30% coverage, precision remains 76.5–85.9%, above the balanced benchmark’s 50% base rate.The detector supports a continuum of operating points rather than relying on a narrowly tuned threshold.Source: §G.2 · p. 39
• Frozen policies repair 22–41% of natural-distribution examples at 1.8–2.6× relative cost, with repair rates varying across model–dataset settings rather than being fixed in advance.The relatively easy DiffusionGemma + MetaMathQA setting requires repair on only 22% of examples.Source: §G.2 · p. 40
• Full LOCKR reaches 67.9% accuracy at 3.1× cost, versus 67.8% at 5.0× when repairing every example; a random trigger reaches 59.1% at 3.1× cost.The always-repair endpoint adds 1.9× relative cost without improving accuracy over LOCKR.Source: §G.2 · p. 40

G.3 FAILURE AND REPAIR-SPACE ANALYSIS

• On Orca-Math, the fixed bank reaches correct alternatives for 31.69% of wrong cases versus 43.33% on MetaMathQA; selection gaps are 5.0–6.9 percentage points for DiffusionGemma and 12.7–12.9 for LLaDA-2.On LLaDA-2 + Orca-Math, the validation-selected planner reaches 51.93% test accuracy, only 0.21 percentage points below the exhaustive test-side operating-point upper bound of 52.14%.Source: §G.3 · p. 41

H.1 CORRECT EARLY LOCK-IN

• For the correct early lock-in, the hidden detector assigns wrong risk 2.06 × 10^-4 versus 0.5724 for Surface-18, despite stable answers and high confidence.The example retains the correct answer through all nine recorded observations.Source: §H.1 · p. 42

H.2 SBW LOCK-IN

• For the wrong 0.2 lock-in, hidden risk is 0.999996 versus Surface-18’s 0.5227; only one of eight branches reaches gold answer 6, and LOCKR selects it at 0.97511.The successful branch is Action 4, using checkpoint fraction 0.33 and remasking budget 128.Source: §H.2 · pp. 42–43, Figure 6 · p. 43

H.3 SUCCESSFUL REPAIR AND TRAJECTORY-AWARE BRANCH SELECTION

• The hidden-trajectory detector assigns wrong risk 0.999922, compared with 0.6015 from the Surface-18 logistic detector.The baseline answer moves from 16 to 10 and remains there; the lock-in window covers observations 3–6.Source: §H.3 · p. 44
• Seven of eight repair actions reproduce answer 10; only Action 4, at checkpoint fraction 0.33 and remasking budget 128, produces the correct answer 6.A simple majority vote would retain the incorrect answer.Source: §H.3 · p. 44
• 0.999994 trajectory score and 0.97511 final HGB selector score rank the unique correct repair first, despite seven incorrect alternatives.The correct branch receives the trajectory score; after combining trajectory evidence with other branch features, the selector assigns Action 4 the leading score.Source: §H.3 · p. 44

H.4 UNSUCCESSFUL REPAIR: NO CORRECT BRANCH IN THE REPAIR POOL

• In the contrasting failure, seven branches reproduce answer 40 and the remaining branch yields no valid numeric answer; Action 4 is ranked first but remains incorrect.The branch-pool oracle cannot recover this example because none of the available candidates is correct.Source: §H.4 · p. 45
• The unsuccessful case separates detection from repairability: the fixed intervention space fails when it never generates a successful branch, which no selector can recover.The example attributes the failure to intervention-space coverage, not the first-stage trigger or selector.Source: §H.4 · p. 45