Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models

Huan Zhang; Ting Wang; Yan Yan; Yuanjie Shi

arxiv: 2606.08831 · v2 · pith:CQJTZ5IQnew · submitted 2026-06-07 · 💻 cs.AI

Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models

Ting Wang , Yuanjie Shi , Yan Yan , Huan Zhang This is my paper

Pith reviewed 2026-06-30 11:02 UTC · model grok-4.3

classification 💻 cs.AI

keywords conformal predictionfactuality controlreasoning graphslarge language modelsinference-time calibrationuncertainty quantificationcoverage guarantees

0 comments

The pith

Integrating conformal prediction into reasoning graph generation yields nested outputs with valid factuality coverage guarantees.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that large language models produce multi-step reasoning as directed graphs where each claim's correctness depends on its ancestors, making uncertainty structural. It introduces a method that learns a graph-level uncertainty score from claim signals, then calibrates a stopping threshold at inference time so that the generated graphs satisfy user-specified factuality levels with guaranteed coverage. The key theoretical step is proving that the calibration produces nested generation sets, which directly implies the coverage property. Experiments across datasets confirm the coverage holds in practice, and the resulting graphs improve accuracy on downstream tasks compared with graphs that are pruned only after generation completes.

Core claim

The central claim is that a structure-level factuality uncertainty function can be learned to aggregate claim-level signals over reasoning graphs, after which a non-conformity score based on that function can be calibrated at inference time to produce nested generation sequences that deliver valid coverage guarantees for any user-chosen factuality level.

What carries the argument

The Inference-Time Conformal Reasoning framework, which calibrates a graph-level non-conformity score derived from an aggregated factuality uncertainty function to decide when generation stops.

Load-bearing premise

A structure-level factuality uncertainty function can be learned to aggregate claim-level signals over reasoning graphs without complex modeling assumptions.

What would settle it

A test set where the fraction of generated graphs that meet the target factuality level falls below the promised coverage probability after calibration.

Figures

Figures reproduced from arXiv: 2606.08831 by Huan Zhang, Ting Wang, Yan Yan, Yuanjie Shi.

**Figure 1.** Figure 1: Prior post-hoc pruning (Rubin-Toles et al., 2025) vs. our inference-time generation on an example from LLaMA-3.1- 8B-Instruct with GSM8K dataset (Cobbe et al., 2021). (Left) original output with ground truth. Intermediate steps are annotated as correct (blue) and incorrect (red). (Center) existing post-hoc method. After full generation, conformal filtering prunes steps exceeding the threshold, followed by … view at source ↗

**Figure 2.** Figure 2: Motivation for the No-Miss Objective. (a) Distribution of retained node ratios produced by previous method (Rubin-Toles et al., 2025) on the QA dataset (chen et al., 2023). Although the average retained ratio is moderate (0.17), a substantial fraction of samples collapse to 0 retained nodes, corresponding to complete abstention. (b) An example of an original reasoning graph containing both true (solid) and… view at source ↗

**Figure 4.** Figure 4: Empirical validation of the nestedness condition in Proposition 3.3 on MATH dataset. (a) Distribution of κ(X) on the calibration set, showing that the slope bound is finite and can be estimated from data. (b) Violation rate of the nested property as a function of λ. As predicted by Proposition 3.3, increasing λ beyond the empirical scale of κ(X) drives the violation rate to 0. (3)). See Appendix D for impl… view at source ↗

**Figure 5.** Figure 5: Coverage and efficiency across target confidence levels 1 − α under no-false and no-miss objectives on GSM8K dataset. Subfigure (a) and (b) report the achieved empirical coverage as a function of the target coverage, with the dashed gray line indicating the ideal calibration line. Subfigure (c) and (d) report the corresponding efficiency, measured by the retained node ratio, where lower values indicate mor… view at source ↗

**Figure 6.** Figure 6: Coverage and efficiency across target confidence levels 1 − α under no-false and no-miss objectives on MATH dataset. Subfigure (a) and (b) report the achieved empirical coverage as a function of the target coverage, with the dashed gray line indicating the ideal calibration line. Subfigure (c) and (d) report the corresponding efficiency, measured by the retained node ratio, where lower values indicate more… view at source ↗

read the original abstract

Large language models (LLMs) increasingly perform multi-step reasoning, where intermediate claims form implicit directed acyclic graphs whose node correctness is structurally conditioned on their ancestors. This makes factuality uncertainty structural, rather than a trivial accumulation of node-wise errors, and necessitates inference-time uncertainty quantification over the reasoning structure. While conformal prediction (CP) offers flexible user-specified factuality control, existing work remains post-hoc and cannot intervene during generation. To fill the gap between CP's flexibility and its post-hoc limitation, we propose an \emph{Inference-Time Conformal Reasoning (ITCR)} framework that integrates CP directly into reasoning graph generation. ITCR learns a structure-level factuality uncertainty function that aggregates claim-level factuality signals over reasoning graphs without complex modeling assumptions. We then design the non-conformity score based on graph-level factuality uncertainty and calibrate the conformal threshold to decide when to stop generation. We theoretically show such generation is nested, yielding valid coverage guarantees for factuality control. Experiments over multiple datasets and coverage objectives demonstrate empirically valid coverage. In downstream reasoning tasks, inference-time calibrated graphs yield more accurate generation than post-hoc pruned graphs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper puts conformal calibration inside the generation of LLM reasoning graphs instead of after the fact, but the abstract leaves the non-conformity definition and nesting argument unshown.

read the letter

The main point for you is that this work tries to run conformal prediction during the actual step-by-step generation of reasoning graphs rather than pruning afterward. They learn a structure-level factuality uncertainty function that pools claim-level signals, turn that into a non-conformity score, calibrate a threshold at inference time, and stop when the threshold is reached. The claim is that the generation process is nested, so the usual coverage guarantee still applies, and that this produces more accurate final outputs than post-hoc methods.

What the paper does cleanly is name the structural nature of factuality uncertainty in multi-step reasoning: correctness at one node depends on its ancestors, so simple per-claim scores are not enough. The motivation for moving CP inside the loop is reasonable, and the high-level construction follows standard conformal steps without obvious circularity.

The soft spots are the missing pieces that would let us check the guarantee. The abstract does not give the explicit form of the structure-level aggregator or the argument that shows the generation remains nested under the stopping rule. Without those, it is not possible to verify whether the coverage holds under the exchangeability conditions conformal prediction needs or whether the aggregator really avoids complex modeling assumptions. The experiments are described only at the level of “multiple datasets and coverage objectives” with no numbers, ablations, or dataset details, so the size of the accuracy gain over post-hoc pruning cannot be judged.

This is for people working on reliable multi-step LLM outputs who already know conformal prediction. A reader who wants a concrete method for user-specified factuality during generation would get value once the derivations are filled in. I would send it to a serious referee because the framing addresses a real limitation of existing post-hoc approaches and the basic construction is standard enough that the details can be checked in review.

Referee Report

2 major / 2 minor

Summary. The paper proposes an Inference-Time Conformal Reasoning (ITCR) framework that integrates conformal prediction directly into LLM reasoning-graph generation. It learns a structure-level factuality uncertainty function to aggregate claim-level signals, defines a graph-level non-conformity score, calibrates a stopping threshold at inference time, and claims that the resulting generation process is nested, thereby inheriting valid coverage guarantees for user-specified factuality levels. Experiments on multiple datasets are said to confirm empirical validity, and downstream reasoning tasks are reported to show higher accuracy than post-hoc pruning.

Significance. If the nesting argument and coverage guarantees hold without hidden modeling assumptions, the work would provide a principled way to enforce factuality control during generation rather than after the fact, which is a meaningful advance over existing post-hoc conformal methods for structured LLM outputs.

major comments (2)

[Abstract / §3] Abstract and §3 (theoretical section): the claim that 'such generation is nested, yielding valid coverage guarantees' is load-bearing for the central contribution, yet the manuscript supplies neither the explicit definition of the structure-level non-conformity score nor the proof that the stopping rule produces nested sets. Without these, it is impossible to verify whether the coverage guarantee follows from standard conformal arguments or requires additional unstated assumptions on the learned aggregator.
[§4] §4 (experiments): the abstract asserts 'empirically valid coverage' across datasets and objectives, but no tables, coverage plots, or ablation results on the learned uncertainty function are referenced. This prevents assessment of whether the empirical validity is robust or sensitive to the choice of aggregator.

minor comments (2)

[§2] Notation for the reasoning graph (nodes as claims, edges as dependencies) should be introduced with a small diagram or formal definition early in §2 to clarify the structural conditioning.
[Abstract / §3] The phrase 'without complex modeling assumptions' for the structure-level aggregator is repeated but never operationalized; a concrete functional form or pseudocode would help.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below. Where the manuscript is missing explicit details, we will revise to include them.

read point-by-point responses

Referee: [Abstract / §3] Abstract and §3 (theoretical section): the claim that 'such generation is nested, yielding valid coverage guarantees' is load-bearing for the central contribution, yet the manuscript supplies neither the explicit definition of the structure-level non-conformity score nor the proof that the stopping rule produces nested sets. Without these, it is impossible to verify whether the coverage guarantee follows from standard conformal arguments or requires additional unstated assumptions on the learned aggregator.

Authors: We agree that the explicit definition of the structure-level non-conformity score and the proof of nesting are essential to substantiate the coverage claim. The manuscript states in §3 that a graph-level non-conformity score is defined from the learned structure-level uncertainty function and that the stopping rule yields nested sets, but does not spell out the mathematical form or the nesting argument in the main text. In revision we will add the precise definition of the non-conformity score (aggregating claim-level signals via the learned function without further modeling assumptions) and include the short proof that the resulting generation process is nested, thereby inheriting standard conformal coverage guarantees. We will also state any assumptions on the aggregator explicitly. revision: yes
Referee: [§4] §4 (experiments): the abstract asserts 'empirically valid coverage' across datasets and objectives, but no tables, coverage plots, or ablation results on the learned uncertainty function are referenced. This prevents assessment of whether the empirical validity is robust or sensitive to the choice of aggregator.

Authors: We acknowledge that the current draft does not sufficiently reference the supporting experimental material. The experiments section contains results on multiple datasets and coverage objectives, but explicit pointers to coverage plots, tables, and ablations on the uncertainty-function aggregator are missing. In revision we will add these references in both the abstract and §4, including ablations that vary the aggregator to demonstrate robustness. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper applies conformal prediction to structure-level uncertainty over reasoning graphs, asserting that the generation process is nested and therefore inherits standard CP coverage. No equations, self-citations, or fitted quantities are shown that reduce the coverage claim to a definitional tautology or to a parameter fit renamed as a prediction. The nesting argument is presented as a theoretical property of the proposed stopping rule rather than an input smuggled in via prior self-work. The structure-level aggregator is described as learned without complex assumptions, but this is an assertion of modeling choice, not a circular reduction. The derivation chain remains self-contained against external CP benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract relies on standard conformal prediction theory and the modeling choice that graph-level uncertainty can be aggregated from claim-level signals without further assumptions; no free parameters or invented entities are explicitly introduced in the provided text.

axioms (1)

standard math Conformal prediction yields valid coverage under appropriate exchangeability or nestedness conditions on the non-conformity scores.
This is the foundational assumption invoked when the abstract claims valid coverage guarantees from the calibrated threshold.

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discussion (0)

Reference graph

Works this paper leans on

15 extracted references · 7 canonical work pages · 2 internal anchors

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Dey, N., Ding, J., Ferrell, J., Kapper, C., Lovig, M., Plan- chon, E., and Williams, J

URL https://openreview.net/forum? id=3Pf3Wg6o-A4. Dey, N., Ding, J., Ferrell, J., Kapper, C., Lovig, M., Plan- chon, E., and Williams, J. P. Conformal prediction for text infilling and part-of-speech prediction.The New England Journal of Statistics in Data Science, 2022. Fontana, M., Zeni, G., and Vantini, S. Conformal prediction: a unified review of theo...

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URLhttps://proceedings.mlr.press/ v179/giovannotti22a.html. Grattafiori, A., Dubey, A., Jauhri, A., Pandey, A., Kadian, A., Al-Dahle, A., Letman, A., Mathur, A., Schelten, A., Vaughan, A., et al. The llama 3 herd of models, 2024. URLhttps://arxiv.org/abs/2407.21783. Guan, L. Localized conformal prediction: A generalized in- ference framework for conformal...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s41586-025-09422-z 2024
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Holtzman, A., Buys, J., Du, L., Forbes, M., and Choi, Y

URL https://openreview.net/forum? id=7Bywt2mQsCe. Holtzman, A., Buys, J., Du, L., Forbes, M., and Choi, Y . The curious case of neural text degeneration. In International Conference on Learning Representations,
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Huang, J., Xi, H., Zhang, L., Yao, H., Qiu, Y ., and Wei, H

URL https://openreview.net/forum? id=rygGQyrFvH. Huang, J., Xi, H., Zhang, L., Yao, H., Qiu, Y ., and Wei, H. Conformal prediction for deep classifier via label ranking. InInternational Conference on Machine Learning, pp. 20331–20347. PMLR, 2024. Jiang, S., Shakeri, Z., Chan, A., Sanjabi, M., Firooz, H., Xia, Y ., Akyildiz, B., Sun, Y ., Li, J., Wang, Q.,...

work page doi:10.20944/preprints202512.2242.v1 2024
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GraphMind: Theorem Selection and Conclusion Generation Framework with Dynamic GNN for LLM Reasoning

URL https://aclanthology.org/2024. naacl-long.210/. Li, Y ., Zhou, Y ., Wang, X., GuoChen, and Qin, C. Graph- mind: Theorem selection and conclusion generation framework with dynamic gnn for llm reasoning, 2025. URLhttps://arxiv.org/abs/2511.19078. Liao, R., Urtasun, R., and Zemel, R. A {pac}-bayesian approach to generalization bounds for graph neural net...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.patcog 2024
[6]

findings-acl.3/

URL https://aclanthology.org/2023. findings-acl.3/. Romano, Y ., Sesia, M., and Candes, E. Classification with valid and adaptive coverage.Advances in neural informa- tion processing systems, 33:3581–3591, 2020. Rouzrokh, P., Faghani, S., Gamble, C. U., Shariatnia, M., and Erickson, B. J. Conflare: Conformal large language model retrieval, 2024. URL https...

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V ovk, V .The Basic Conformal Prediction Framework, pp

URL https://openreview.net/forum? id=rJXMpikCZ. V ovk, V .The Basic Conformal Prediction Framework, pp. 3–
[8]

ISBN 978-0-12-398537-8

Elsevier, 1 edition, 2014. ISBN 978-0-12-398537-8. doi: 10.1016/B978-0-12-398537-8.00001-8. V ovk, V . Cross-conformal predictors.Annals of Mathemat- ics and Artificial Intelligence, 74(1–2):9–28, June 2015. ISSN 1012-2443. doi: 10.1007/s10472-013-9368-4. V ovk, V ., Gammerman, A., and Shafer, G.Algorithmic learning in a random world. Springer, 2005. 12 I...

work page doi:10.1016/b978-0-12-398537-8.00001-8 2014
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Wang, S., Guo, X., Tie, Y ., Lee, I., Qi, L., and Guan, L

URL https://openreview.net/forum? id=0e1Kn76HM1. Wang, S., Guo, X., Tie, Y ., Lee, I., Qi, L., and Guan, L. Graph-based safe support vector machine for multiple classes.IEEE Access, 6:28097–28107, 2018. Wang, T., Zhou, Z., and Luo, R. Enhancing trustworthiness of graph neural networks with rank-based conformal train- ing. InProceedings of the AAAI Confere...

work page doi:10.18653/v1/2024.findings-emnlp 2018
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findings-emnlp.404/

URL https://aclanthology.org/2024. findings-emnlp.404/. Wei, J., Wang, X., Schuurmans, D., Bosma, M., Xia, F., Chi, E., Le, Q. V ., Zhou, D., et al. Chain-of-thought prompting elicits reasoning in large language models.Advances in neural information processing systems, 35:24824–24837, 2022. Wu, H., Xu, B., Shu, Y ., Yang, M., and Qin, C. Thinking with not...

work page arXiv 2024
[11]

a" depends on subclaim

Graph Description: - Represent dependency relationships between subclaims as a directed graph. - Each subclaim is a vertex in the graph. - An edge (b -> a) exists if subclaim "a" depends on subclaim "b". - Subclaims that are a priori (e.g., assumptions or definitions) should not have any ancestors.,→
[12]

- A value of 1 at position i in row j indicates that subclaim j depends on subclaim i

Output Format: - Provide your graph as an adjacency list of size NUM x NUM, where NUM is the number of subclaims.,→ - A template adjacency list with all entries zero will be included at the end of the prompt as reference.,→ - Replace 0s with 1s where relevant dependencies exist. - A value of 1 at position i in row j indicates that subclaim j depends on su...
[13]

- Each row must contain exactly NUM integers

Rules: - The adjacency list must be square with exactly NUM rows and NUM columns. - Each row must contain exactly NUM integers. - Output must consist solely of the adjacency list (e.g., [[0,1,0],[0,0,1],[0,0,0]]). - Do not include explanations, commentary, or any other formatting
[14]

- Always represent dependencies, even if the subclaims are incorrect

Dependencies: - Consider explicit and implicit dependencies between subclaims. - Always represent dependencies, even if the subclaims are incorrect. Now provide your adjacency list for the following question and subclaims: Question: <QUESTION TEXT> NUM = <N> Subclaims:
[15]

subclaim

<subclaim 2> ... N. <subclaim N> Template: [[0,0,...,0], [0,0,...,0], ... 16 Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models [0,0,...,0]] C. Implementation of Thinking via Inference-Time Calibration For reproducibility, we report the prompt templates used for (i) step generation, and (ii) Step intervene. Step gen...

[1] [1]

Dey, N., Ding, J., Ferrell, J., Kapper, C., Lovig, M., Plan- chon, E., and Williams, J

URL https://openreview.net/forum? id=3Pf3Wg6o-A4. Dey, N., Ding, J., Ferrell, J., Kapper, C., Lovig, M., Plan- chon, E., and Williams, J. P. Conformal prediction for text infilling and part-of-speech prediction.The New England Journal of Statistics in Data Science, 2022. Fontana, M., Zeni, G., and Vantini, S. Conformal prediction: a unified review of theo...

2022

[2] [2]

The Llama 3 Herd of Models

URLhttps://proceedings.mlr.press/ v179/giovannotti22a.html. Grattafiori, A., Dubey, A., Jauhri, A., Pandey, A., Kadian, A., Al-Dahle, A., Letman, A., Mathur, A., Schelten, A., Vaughan, A., et al. The llama 3 herd of models, 2024. URLhttps://arxiv.org/abs/2407.21783. Guan, L. Localized conformal prediction: A generalized in- ference framework for conformal...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s41586-025-09422-z 2024

[3] [3]

Holtzman, A., Buys, J., Du, L., Forbes, M., and Choi, Y

URL https://openreview.net/forum? id=7Bywt2mQsCe. Holtzman, A., Buys, J., Du, L., Forbes, M., and Choi, Y . The curious case of neural text degeneration. In International Conference on Learning Representations,

[4] [4]

Huang, J., Xi, H., Zhang, L., Yao, H., Qiu, Y ., and Wei, H

URL https://openreview.net/forum? id=rygGQyrFvH. Huang, J., Xi, H., Zhang, L., Yao, H., Qiu, Y ., and Wei, H. Conformal prediction for deep classifier via label ranking. InInternational Conference on Machine Learning, pp. 20331–20347. PMLR, 2024. Jiang, S., Shakeri, Z., Chan, A., Sanjabi, M., Firooz, H., Xia, Y ., Akyildiz, B., Sun, Y ., Li, J., Wang, Q.,...

work page doi:10.20944/preprints202512.2242.v1 2024

[5] [5]

GraphMind: Theorem Selection and Conclusion Generation Framework with Dynamic GNN for LLM Reasoning

URL https://aclanthology.org/2024. naacl-long.210/. Li, Y ., Zhou, Y ., Wang, X., GuoChen, and Qin, C. Graph- mind: Theorem selection and conclusion generation framework with dynamic gnn for llm reasoning, 2025. URLhttps://arxiv.org/abs/2511.19078. Liao, R., Urtasun, R., and Zemel, R. A {pac}-bayesian approach to generalization bounds for graph neural net...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.patcog 2024

[6] [6]

findings-acl.3/

URL https://aclanthology.org/2023. findings-acl.3/. Romano, Y ., Sesia, M., and Candes, E. Classification with valid and adaptive coverage.Advances in neural informa- tion processing systems, 33:3581–3591, 2020. Rouzrokh, P., Faghani, S., Gamble, C. U., Shariatnia, M., and Erickson, B. J. Conflare: Conformal large language model retrieval, 2024. URL https...

work page doi:10.1016/j.patcog.2021.108507 2023

[7] [7]

V ovk, V .The Basic Conformal Prediction Framework, pp

URL https://openreview.net/forum? id=rJXMpikCZ. V ovk, V .The Basic Conformal Prediction Framework, pp. 3–

[8] [8]

ISBN 978-0-12-398537-8

Elsevier, 1 edition, 2014. ISBN 978-0-12-398537-8. doi: 10.1016/B978-0-12-398537-8.00001-8. V ovk, V . Cross-conformal predictors.Annals of Mathemat- ics and Artificial Intelligence, 74(1–2):9–28, June 2015. ISSN 1012-2443. doi: 10.1007/s10472-013-9368-4. V ovk, V ., Gammerman, A., and Shafer, G.Algorithmic learning in a random world. Springer, 2005. 12 I...

work page doi:10.1016/b978-0-12-398537-8.00001-8 2014

[9] [9]

Wang, S., Guo, X., Tie, Y ., Lee, I., Qi, L., and Guan, L

URL https://openreview.net/forum? id=0e1Kn76HM1. Wang, S., Guo, X., Tie, Y ., Lee, I., Qi, L., and Guan, L. Graph-based safe support vector machine for multiple classes.IEEE Access, 6:28097–28107, 2018. Wang, T., Zhou, Z., and Luo, R. Enhancing trustworthiness of graph neural networks with rank-based conformal train- ing. InProceedings of the AAAI Confere...

work page doi:10.18653/v1/2024.findings-emnlp 2018

[10] [10]

findings-emnlp.404/

URL https://aclanthology.org/2024. findings-emnlp.404/. Wei, J., Wang, X., Schuurmans, D., Bosma, M., Xia, F., Chi, E., Le, Q. V ., Zhou, D., et al. Chain-of-thought prompting elicits reasoning in large language models.Advances in neural information processing systems, 35:24824–24837, 2022. Wu, H., Xu, B., Shu, Y ., Yang, M., and Qin, C. Thinking with not...

work page arXiv 2024

[11] [11]

a" depends on subclaim

Graph Description: - Represent dependency relationships between subclaims as a directed graph. - Each subclaim is a vertex in the graph. - An edge (b -> a) exists if subclaim "a" depends on subclaim "b". - Subclaims that are a priori (e.g., assumptions or definitions) should not have any ancestors.,→

[12] [12]

- A value of 1 at position i in row j indicates that subclaim j depends on subclaim i

Output Format: - Provide your graph as an adjacency list of size NUM x NUM, where NUM is the number of subclaims.,→ - A template adjacency list with all entries zero will be included at the end of the prompt as reference.,→ - Replace 0s with 1s where relevant dependencies exist. - A value of 1 at position i in row j indicates that subclaim j depends on su...

[13] [13]

- Each row must contain exactly NUM integers

Rules: - The adjacency list must be square with exactly NUM rows and NUM columns. - Each row must contain exactly NUM integers. - Output must consist solely of the adjacency list (e.g., [[0,1,0],[0,0,1],[0,0,0]]). - Do not include explanations, commentary, or any other formatting

[14] [14]

- Always represent dependencies, even if the subclaims are incorrect

Dependencies: - Consider explicit and implicit dependencies between subclaims. - Always represent dependencies, even if the subclaims are incorrect. Now provide your adjacency list for the following question and subclaims: Question: <QUESTION TEXT> NUM = <N> Subclaims:

[15] [15]

subclaim

<subclaim 2> ... N. <subclaim N> Template: [[0,0,...,0], [0,0,...,0], ... 16 Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models [0,0,...,0]] C. Implementation of Thinking via Inference-Time Calibration For reproducibility, we report the prompt templates used for (i) step generation, and (ii) Step intervene. Step gen...