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Paper Citation Record · LEDGER

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning

As of 9 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2604.06805.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2604.06805 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T17:47:52.178172Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

13 of 13 outbound references displayed

  • verified exact2
  • verified fuzzy5
  • unresolved2
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch4

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d52fee8b-5627-4d93-a978-107567403e53 · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Training Verifiers to Solve Math Word Problems

Reference 1

Resolution
metadata mismatch
local_arxiv, observed 2026-05-11T06:05:59.729169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:8ce6f4eed33714fff49552af954acb4f1638bf46155bd2abfa5bf6eb876e2605

Observation b25e12df-8949-4cff-814f-311ca9b235dc · outbound

This paper cites Ryo Kamoi, Yusen Zhang, Nan Zhang, and et al.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Ryo Kamoi, Yusen Zhang, Nan Zhang, and et al

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T08:59:19.724234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:215be4370f88f7071a3ff4f1d3a811bda990f9a7183d54c06e628de9e4a5c833

Observation f8658823-6fed-4db5-bc8f-bd4e74737b42 · outbound

This paper cites Confidence Matters: Revisiting Intrinsic Self-Correction Capabilities of Large Language Models.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Confidence Matters: Revisiting Intrinsic Self-Correction Capabilities of Large Language Models

Reference 3

Resolution
metadata mismatch
arxiv_id, observed 2026-05-11T06:05:59.735875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:9b0625bc81538617ee1d0cae780e3c528ee5315ede1f600cfda9ce8cc2af7fd2

Observation bc0592de-1e2e-492b-8de7-288e3e533c76 · outbound

This paper cites Arkil Patel, Satwik Bhattamishra, and Navin Goyal.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Arkil Patel, Satwik Bhattamishra, and Navin Goyal

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T08:59:19.730604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:945e40f28d59e62cd7387b86df85ff8479e1bdc719ee19393549a6f77bd572f4

Observation 3ee1f462-1e49-4f80-b036-0d27f3cf7e36 · outbound

This paper cites Atom of thoughts for markov llm test-time scaling.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Atom of thoughts for markov llm test-time scaling

Reference 5

Resolution
metadata mismatch
arxiv_id, observed 2026-05-11T06:05:59.723063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:1629fce2ea38bb0ad66aabf73f7bd06ab8aa1d287dd33bba3277326adfca1b16

Observation 43c9548e-df1c-40c8-a155-f381de00f66a · outbound

This paper cites InAdvances in Neural Information Processing Systems, volume 35, pages 24824–24837.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning InAdvances in Neural Information Processing Systems, volume 35, pages 24824–24837

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T08:59:19.717944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:5c6b36305487a191f45fc4932246ba14a2b3a58fafebe73f402225674b664976

Observation eae4aad8-1207-431d-9476-241e010f42ab · outbound

This paper cites Confidence v.s. Critique: A Decomposition of Self-Correction Capability for LLMs.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Confidence v.s. Critique: A Decomposition of Self-Correction Capability for LLMs

Reference 7

Resolution
verified exact
arxiv_id, observed 2026-05-11T06:05:59.711053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:210bf8f3c432f68cb08e0c5042aa16ee1261e0da65f6c1aa87504dad2fdee81e

Observation 9904c2e2-dc86-43d1-bd53-eaca08c06d7f · outbound

This paper cites A Survey of Large Language Models.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning A Survey of Large Language Models

Reference 8

Resolution
metadata mismatch
local_arxiv, observed 2026-05-11T06:05:59.680001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:52d1f42873b946c764ed6527efe639bfdcb98e13d99efa66e10f951f3dddd948

Observation 6bfd0c08-9f82-42ed-b0b2-5ddb8006fa01 · outbound

This paper cites InAI for Math Work- shop @ ICML 2024.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning InAI for Math Work- shop @ ICML 2024

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T08:59:19.721110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:306326b7bc2e1e59309e70f9449bb688328e6897b72d97c49b0c67528a37424f

Observation 8ef8b222-abbd-48e9-8cbf-f9673183f8aa · outbound

This paper cites A datasets A.1 Mathematical Reasoning Datasets We evaluate CLoT on four mathematical QA datasets and one multiple-choice dataset.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning A datasets A.1 Mathematical Reasoning Datasets We evaluate CLoT on four mathematical QA datasets and one multiple-choice dataset

Reference 10

Resolution
verified exact
arxiv_id, observed 2026-05-11T06:05:59.693279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:cc9d2747f706f963206976a5b510daf1c630aea366e22b44dceaa95a455cde5b

Observation ca43f399-2d92-4b51-b956-29980fd1ebfa · outbound

This paper cites an unresolved cited work.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-05-17T08:59:19.733896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:b7fa1123fe2545f575703bcb052a1f2ed98d2f1c2468d78eef40f170c38bcaa1

Observation d8b3b74e-fa79-4cc7-bb06-a34633edbbb0 · outbound

This paper cites an unresolved cited work.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-05-17T08:59:19.736952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:b1d80a61544b4ad217cffebcfaa831352a576d04ef3ea5b4cf91b5c6b09175c7

Observation 1beeefc0-b935-422c-aa28-b742724e8779 · outbound

This paper cites This helps evaluate CLoT’s performance when the solution space is constrained by predefined options.

Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning This helps evaluate CLoT’s performance when the solution space is constrained by predefined options

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T08:59:19.727439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T17:47:52.178172Z digest=sha256:90e5b0689211842c3278047d61c752d85a0f9178d232ab02543968e6bc93af2b

Pith citing papers

No inbound Pith citation observations are available.