Pith Number

pith:QIJUMINM

pith:2026:QIJUMINMVLUQZCVCUSBKH44OLO

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Where Does Reasoning Break? Step-Level Hallucination Detection via Hidden-State Transport Geometry

Ali Baheri, Tyler Alvarez

Hidden-state trajectories expose the exact step where LLM reasoning first breaks via transport geometry.

arxiv:2605.13772 v1 · 2026-05-13 · cs.CL · cs.AI

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Claims

C1strongest claim

We prove that contrastive PCA is the optimal projection for a transport-separation objective between first error and correct states, and that single-pass first error localization holds whenever the first error creates a positive transport margin over preceding correct transitions.

C2weakest assumption

The assumption that the first error creates a positive transport margin over preceding correct transitions (stated in the abstract) and that a stable manifold of locally coherent transitions exists for correct reasoning.

C3one line summary

Hallucination is detected as a transport-cost excursion in hidden-state trajectories, localized via contrastive PCA in a teacher model and distilled to a BiLSTM student.

References

27 extracted · 27 resolved · 5 Pith anchors

[1] Abid, A., Zhang, M. J., Bagaria, V . K., and Zou, J. Exploring patterns enriched in a dataset with contrastive principal component analysis.Nature Communications, 9(1):2134, 2018. doi: 10.1038/ s41467 2018

[2] Geometry-aware uncertainty quantification via conformal prediction on man- ifolds 2026 · doi:10.48550/arxiv.2602.16015

[3] Azaria, A. and Mitchell, T. The internal state of an LLM knows when it’s lying. InFindings of the Asso- ciation for Computational Linguistics: EMNLP 2023, pp. 967–976, Singapore, 2023 2023

[4] Merlean: An agentic framework for autoformalization in quantum computation 2026 · doi:10.48550/arxiv.2602

[5] Baheri, A. and Alm, C. O. LLMs-augmented contex- tual bandit. InNeurIPS 2023 Workshop on Foundation Models for Decision Making, 2023. FMDM@NeurIPS 2023 2023

Receipt and verification

First computed	2026-05-18T02:44:15.980810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82134621acaae90c8aa2a482a3f38e5bb70ec344c9d65f0533d90fe77489a6f4

Aliases

arxiv: 2605.13772 · arxiv_version: 2605.13772v1 · doi: 10.48550/arxiv.2605.13772 · pith_short_12: QIJUMINMVLUQ · pith_short_16: QIJUMINMVLUQZCVC · pith_short_8: QIJUMINM

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QIJUMINMVLUQZCVCUSBKH44OLO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 82134621acaae90c8aa2a482a3f38e5bb70ec344c9d65f0533d90fe77489a6f4

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2026-05-13T16:48:48Z",
    "title_canon_sha256": "d550e2ba716eb4453dcb5a3ef08eff2aca7e1dc83f0f84a33e5d634919dd7086"
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