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Paper Citation Record · LEDGER

Pseudo-Formalization for Automatic Proof Verification

As of 21 August 2026, this Paper Citation Record lists 75 of 75 outbound references and 0 inbound Pith citation observations for arXiv:2605.20531.

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

pith.paper-citation-record.v1
2605.20531 v2

Coverage vector

measured 75 of 75 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-30T17:17:48.969969Z

measured 75 of 75 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

75 of 75 outbound references displayed

  • verified exact20
  • verified fuzzy39
  • unresolved14
  • parse uncertain1
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 79a42ac6-dfca-4f6f-b3d3-cccc261b3f67 · outbound

This paper cites Learning to Give Checkable Answers with Prover-Verifier Games.

Pseudo-Formalization for Automatic Proof Verification Learning to Give Checkable Answers with Prover-Verifier Games

Reference 1

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arxiv_id, observed 2026-06-30T17:24:57.679420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:1767b5c9da8186ccc617e1001f7722441a071f8ff35064df04a4525444b531a6

Observation 06f618b9-ead7-4000-8ec6-0111dc39c918 · outbound

This paper cites Towards a Lean proof of Fermat’s Last Theorem.https: //imperialcollegelondon.github.io/FLT/blueprint.pdf.

Pseudo-Formalization for Automatic Proof Verification Towards a Lean proof of Fermat’s Last Theorem.https: //imperialcollegelondon.github.io/FLT/blueprint.pdf

Reference 2

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raw_fallback, observed 2026-07-08T09:34:48.611852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:235c6a6dbb63c76130ac2cb910909e8562af555dc5391c442f8d8a297eb10d28

Observation 33f4a043-fb6c-4b9f-bbc3-3c9edc09d1b8 · outbound

This paper cites SPC: Evolving Self-Play Critic via Adversarial Games for LLM Reasoning.

Pseudo-Formalization for Automatic Proof Verification SPC: Evolving Self-Play Critic via Adversarial Games for LLM Reasoning

Reference 3

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arxiv_id, observed 2026-06-30T17:24:57.676445Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:670c9ced5184695c23b8e633693797e3f692be57b2787c41cadba6688cd3cac9

Observation 9e9198fa-0026-468a-a64d-346d3b39dfe2 · outbound

This paper cites Power-free palindromes and reversed primes: S.

Pseudo-Formalization for Automatic Proof Verification Power-free palindromes and reversed primes: S

Reference 4

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raw_fallback, observed 2026-07-08T09:34:48.613939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:dd2b504ac2c84d7751b5f73ba46b4a28801d070f8dc11694f3ead036b6c3aad0

Observation 4faa5e7b-951c-4d9e-8532-36ca13d3e30d · outbound

This paper cites Escaping the cognitive well: Efficient competition math with off-the-shelf models.

Pseudo-Formalization for Automatic Proof Verification Escaping the cognitive well: Efficient competition math with off-the-shelf models

Reference 5

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raw_fallback, observed 2026-07-08T09:34:48.628391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:b9725fdbe8ec452e97b9ac825b485d6b9d6017b25d3112ca46e22e3f11548d57

Observation 4c2df4cf-848f-40fe-bae0-a659cf5d9959 · outbound

This paper cites Escaping the cognitive well: Efficient competition math with off-the-shelf models.arXiv preprint arXiv:2602.16793.

Pseudo-Formalization for Automatic Proof Verification Escaping the cognitive well: Efficient competition math with off-the-shelf models.arXiv preprint arXiv:2602.16793

Reference 6

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arxiv_id, observed 2026-06-30T17:24:57.733457Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:74dff89783da7d23ce5aaeb3d6997448bb957b69d5284594b66494e221c4481a

Observation e1da4547-c12f-46b5-9aa4-3deec5b95f25 · outbound

This paper cites The lean theorem prover (system description).

Pseudo-Formalization for Automatic Proof Verification The lean theorem prover (system description)

Reference 7

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:122b7f9b8cebe3d9264f0a74f4bd0656c4704e5f8377b5dc24f116622fbb05f4

Observation 9e55acf8-9cb7-49a6-9c5f-d5f672e621cd · outbound

This paper cites Finite codimension stability of invariant surfaces.

Pseudo-Formalization for Automatic Proof Verification Finite codimension stability of invariant surfaces

Reference 8

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arxiv_id, observed 2026-06-30T17:24:57.738610Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:1ee5233b9d75d05d7f8fdea46957a03590c2d43f3fc98d8c04970e51f9a7ce9f

Observation 39c4ffc5-576b-44df-b224-7b0f85c0fed2 · outbound

This paper cites Llm critics help catch bugs in mathematics: Towards a better mathematical verifier with natural language feedback.

Pseudo-Formalization for Automatic Proof Verification Llm critics help catch bugs in mathematics: Towards a better mathematical verifier with natural language feedback

Reference 9

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raw_fallback, observed 2026-07-08T09:34:48.601192Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:defb71b453d3f58c3e1870f9d0b5e57a48ea28250ce6d7ee3efa7a29c0664b9a

Observation f7fe30b7-ade9-4403-9a73-e78bc2186db6 · outbound

This paper cites Formal proof – theory and practice.Notices of the American Mathematical Society, 55:1395–1406.

Pseudo-Formalization for Automatic Proof Verification Formal proof – theory and practice.Notices of the American Mathematical Society, 55:1395–1406

Reference 10

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:9bca3b9827aea19d2ecc7e5b1fb9f774dc079fd55ac64220dadff8fe186ea13e

Observation 8d564df2-e49c-4c1e-85d0-fc995836f4ae · outbound

This paper cites Context rot: How increasing input tokens impacts llm performance.URL https://research.

Pseudo-Formalization for Automatic Proof Verification Context rot: How increasing input tokens impacts llm performance.URL https://research

Reference 11

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:15a16be8f71b0f0d81fd39b646939fb928f2052bb9608c5463fd03d9ef742e02

Observation 4fea4ef0-55a9-4eb4-aa2b-a603089081ee · outbound

This paper cites Pessimistic Verification for Open Ended Math Questions.

Pseudo-Formalization for Automatic Proof Verification Pessimistic Verification for Open Ended Math Questions

Reference 12

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local_arxiv, observed 2026-06-30T17:24:57.740882Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:24404bfd8f3d26e6bdcc82c75743b6d493ed0041b5b0fe4c90ff257879d22f45

Observation 68c3ac76-28ca-4797-9cb2-90e292ff2c9b · outbound

This paper cites Winning gold at imo 2025 with a model-agnostic verification- and-refinement pipeline.

Pseudo-Formalization for Automatic Proof Verification Winning gold at imo 2025 with a model-agnostic verification- and-refinement pipeline

Reference 13

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arxiv_id, observed 2026-06-30T17:24:57.722800Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:6d96223898bb9abec4b7db605888de7fd8887b5604d526984d84cfd7dc496359

Observation 1b043fc1-21d6-4cfc-bff1-08db1ed04fdb · outbound

This paper cites Prover-Verifier Games improve legibility of LLM outputs.

Pseudo-Formalization for Automatic Proof Verification Prover-Verifier Games improve legibility of LLM outputs

Reference 14

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arxiv_id, observed 2026-06-30T17:24:57.725305Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:a20d9b86bbb0ced9a8f3a2e08528103423b2136a0fcfc97b43dc5876567138a4

Observation 60145fb5-a19a-4b3e-9cc0-68c9377986fc · outbound

This paper cites PrimeNumberTheoremAnd: A formalization of the prime number theorem and related results in Lean 4.

Pseudo-Formalization for Automatic Proof Verification PrimeNumberTheoremAnd: A formalization of the prime number theorem and related results in Lean 4

Reference 15

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:bb6ea258f7064f3f1f97e2c0501c85d822e693ffece78606bada57f2b1ac7d2b

Observation d99d4411-273a-401a-99ef-61f1760d915d · outbound

This paper cites Let’s verify step by step.

Pseudo-Formalization for Automatic Proof Verification Let’s verify step by step

Reference 16

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:feb57c5d900c3f66689da42e9c8efd89b2c8984c3a7186a4147193d8cd0e3685

Observation 964db1a5-43f5-423c-ae3d-f6a091f29fe5 · outbound

This paper cites Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving.

Pseudo-Formalization for Automatic Proof Verification Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving

Reference 17

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arxiv_id, observed 2026-06-30T17:24:57.728053Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:a3e97b0cd9228ee8d635761cb8341c352c96e96aa957625ae8a3898acd3ec324

Observation dd2ad225-be36-4299-a26d-df495c24f920 · outbound

This paper cites Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction.

Pseudo-Formalization for Automatic Proof Verification Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction

Reference 18

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local_arxiv, observed 2026-06-30T17:24:57.728045Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:42a46bd0546ac2ffcbe83e1e520be492c392292dead88b21d5d1270e62df1700

Observation c53d7d5e-2445-4b4c-af00-473db18c4a4e · outbound

This paper cites Trust, but verify: A self-verification approach to reinforcement learning with verifiable rewards.

Pseudo-Formalization for Automatic Proof Verification Trust, but verify: A self-verification approach to reinforcement learning with verifiable rewards

Reference 19

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:84fada2cf1184c5b4716a62cb311ed0651daee5d256c2da20e8eaef2fd6d931f

Observation 1db0e006-9de9-4d0c-af03-20726d5c20c7 · outbound

This paper cites Towards robust mathematical reasoning.

Pseudo-Formalization for Automatic Proof Verification Towards robust mathematical reasoning

Reference 20

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raw_fallback, observed 2026-07-08T09:34:48.574859Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:8ded171371a070eb3c887e33dcc6caf804899fc8c121b1ce7bc77b87fcf330ca

Observation 079f52f3-3440-42c7-89da-cc5f09f1eb31 · outbound

This paper cites Scaling generative verifiers for natural language mathematical proof verification and selection.arXiv preprint arXiv:2511.13027.

Pseudo-Formalization for Automatic Proof Verification Scaling generative verifiers for natural language mathematical proof verification and selection.arXiv preprint arXiv:2511.13027

Reference 21

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:beb87f8337d7fcc316ed6f1f8b2141e03f46d38f01ff01373a84b01db447cd4c

Observation 27579b8c-6be2-43b7-8c25-91898a9b27ff · outbound

This paper cites The Expressive Power of Transformers with Chain of Thought.

Pseudo-Formalization for Automatic Proof Verification The Expressive Power of Transformers with Chain of Thought

Reference 22

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arxiv_id, observed 2026-06-30T17:24:57.694418Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:7b364e00e9b314af1ba8bed157d6c521d355838704e116098e3c2644ed122834

Observation 070ba25d-d8dd-4f56-8fc1-0fcae0e87647 · outbound

This paper cites The lean 4 theorem prover and programming language.

Pseudo-Formalization for Automatic Proof Verification The lean 4 theorem prover and programming language

Reference 23

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:53e5bcfbfb87c71a040a2ee0e2918f0d0b36c3449553798f03cfb0cf1b04cc1d

Observation 0d1cd5b0-8b56-493c-8826-341f59fb2edd · outbound

This paper cites Springer.

Pseudo-Formalization for Automatic Proof Verification Springer

Reference 24

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:ff0266be0f66addc25c7b57ced912adb1c30bc039b81aed3fa3d5c5c05fa6751

Observation 84390bf3-e4bd-408e-bfe2-e7419dca1b93 · outbound

This paper cites Hard2verify: A step-level verification benchmark for open-ended frontier math.

Pseudo-Formalization for Automatic Proof Verification Hard2verify: A step-level verification benchmark for open-ended frontier math

Reference 25

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arxiv_id, observed 2026-06-30T17:24:57.695934Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:964309c8ff1a97d3c9cad751cf6697b7d586588e85c69d1073b5fc7ba8afc004

Observation 3560a904-2168-44ab-afcd-9634fdd732c9 · outbound

This paper cites Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent.

Pseudo-Formalization for Automatic Proof Verification Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent

Reference 26

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local_arxiv, observed 2026-06-30T17:24:57.720007Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:bd32832b31d53140bd97c5b23518d5a38fec32791300e7740effe50946aabe80

Observation e430d50e-0a77-478a-b85b-4605b2a059a4 · outbound

This paper cites Liquid tensor experiment.Experimental Mathematics, 31(2):349–354.

Pseudo-Formalization for Automatic Proof Verification Liquid tensor experiment.Experimental Mathematics, 31(2):349–354

Reference 27

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:2f7c1eea5e00113cef624debff78b57bbb40b008609630633a0e062aa8972244

Observation 7e38257b-12d9-4832-96ea-81a9518f4c3a · outbound

This paper cites Deepseekmath-v2: Towards self-verifiable mathematical reasoning.

Pseudo-Formalization for Automatic Proof Verification Deepseekmath-v2: Towards self-verifiable mathematical reasoning

Reference 28

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arxiv_id, observed 2026-06-30T17:24:57.686554Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:3c3f1d7ea4a7650c7bee9491417d903d6ee12093c1ff424a0135a8b9fe5113b6

Observation bccfd1ef-cd00-45cc-bdd6-9b3866db07f6 · outbound

This paper cites Heimdall: test-time scaling on the generative verification.

Pseudo-Formalization for Automatic Proof Verification Heimdall: test-time scaling on the generative verification

Reference 29

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arxiv_id, observed 2026-06-30T17:24:57.683949Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:b8379076a194c2aa4b71987bb3c56c04f58c8ecc4b8e24a5876cd64a34b0b52f

Observation 5a95f614-22a4-4992-b31a-f8317bb00329 · outbound

This paper cites A promising path towards autoformalization and general artificial intelli- gence.

Pseudo-Formalization for Automatic Proof Verification A promising path towards autoformalization and general artificial intelli- gence

Reference 30

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raw_fallback, observed 2026-07-08T09:34:48.582404Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:48b0b50894f1cd56964a14d1f3f5ebe2f0556f62a7182f10f014335984535af3

Observation f5cd6e4c-a664-4d03-9427-b80d1d75f41c · outbound

This paper cites From solving to verifying: A unified objective for robust reasoning in llms.

Pseudo-Formalization for Automatic Proof Verification From solving to verifying: A unified objective for robust reasoning in llms

Reference 31

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arxiv_id, observed 2026-06-30T17:24:57.691865Z

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source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:328fe89261eb1355d3bd1b6c3bd4278a528cd1d4fc0ab51f3fe144850ce1de87

Observation 5f649650-5dad-4c81-9a07-fc37db7f083a · outbound

This paper cites Autoformalization with large language models.Advances in neural information processing systems, 35:32353–32368.

Pseudo-Formalization for Automatic Proof Verification Autoformalization with large language models.Advances in neural information processing systems, 35:32353–32368

Reference 32

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raw_fallback, observed 2026-07-08T09:34:48.567222Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:20c355c00f2257529e5b66c8bb1dd9aa94023ad1816b45241344216c99185305

Observation ee2a97a3-8d9a-4e7d-8192-14c56ac69d43 · outbound

This paper cites PENCIL: Long Thoughts with Short Memory.

Pseudo-Formalization for Automatic Proof Verification PENCIL: Long Thoughts with Short Memory

Reference 33

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arxiv_id, observed 2026-06-30T17:24:57.736550Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:01f14eecab3d79dc06196fd6078c11282a8db7fda03f1c3c85393539e3f2d021

Observation d118b28f-2bfd-4ef8-ba05-3ceec6eb8488 · outbound

This paper cites Recursive Models for Long-Horizon Reasoning.

Pseudo-Formalization for Automatic Proof Verification Recursive Models for Long-Horizon Reasoning

Reference 34

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arxiv_id, observed 2026-07-03T02:17:09.880536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:98ec09300125693d953a131b6c0036e4680065adc190d1fe2af6f968d74d45e6

Observation de214421-6c3c-4737-a5c7-ee1450b7fa89 · outbound

This paper cites Loca-bench: Benchmarking language agents under controllable and extreme context growth.

Pseudo-Formalization for Automatic Proof Verification Loca-bench: Benchmarking language agents under controllable and extreme context growth

Reference 35

Resolution
verified exact
arxiv_id, observed 2026-06-30T17:24:57.733896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:beb9e3c9f50d72b3991afd8b73b5db6e403cd79d8a49de6c7170bd0875e31071

Observation aa5b3004-feb1-4f72-9ba2-6db373df0f5d · outbound

This paper cites Generative Verifiers: Reward Modeling as Next-Token Prediction.

Pseudo-Formalization for Automatic Proof Verification Generative Verifiers: Reward Modeling as Next-Token Prediction

Reference 36

Resolution
verified exact
arxiv_id, observed 2026-06-30T17:24:57.743520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:296a69687bcb1b0945b0b9a7c59646c409c721d2bf1a1db9fa5344958e059676

Observation 7bb176e1-23a5-4116-a50b-ee48947e0763 · outbound

This paper cites Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification.

Pseudo-Formalization for Automatic Proof Verification Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification

Reference 37

Resolution
verified exact
arxiv_id, observed 2026-06-30T17:24:57.745979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:a92919f56ca5cf53004061eaa8d8853d4162731ca091fa123e30ffb6708c5efa

Observation a9e30482-a722-4d24-a180-71a0259cf9bf · outbound

This paper cites Processbench: Identifying process errors in mathematical reasoning.

Pseudo-Formalization for Automatic Proof Verification Processbench: Identifying process errors in mathematical reasoning

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.570558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:5911b57a1a74003ed109f8a8baee3a07a327d2086be15ac1e798be2415a778fb

Observation 2227c853-fa29-4adf-93ad-bb36fb991248 · outbound

This paper cites Leanarchitect: Automating blueprint generation for humans and ai.

Pseudo-Formalization for Automatic Proof Verification Leanarchitect: Automating blueprint generation for humans and ai

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.573054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:04d6f1a241bb5c831c87727a1dc5cf3b646d68f1998ff1987f9965bd9c1ef014

Observation ed1d0f70-b0bb-4c89-8511-032d7f79eed1 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 40

Resolution
parse uncertain
raw_fallback, observed 2026-07-08T09:34:48.592887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:7d17f00e0034bbceb785256b8c42b756a4fad787bdc5b4f780f85fffc6d75f96

Observation 22b1fd37-7880-4dd4-a6da-e280683a8ff2 · outbound

This paper cites Definition 3(Block-wise verification algorithm).Let P= (G , T) be a Pseudo-Formal proof with node set V={v 1.

Pseudo-Formalization for Automatic Proof Verification Definition 3(Block-wise verification algorithm).Let P= (G , T) be a Pseudo-Formal proof with node set V={v 1

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.561951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:42c10b3279f17ae8d4e383e2c8133ff8c69aa0e7322ecff8a40d5ac71eb837db

Observation ec8cd8a4-bfd1-445d-9888-62e08dda9fb9 · outbound

This paper cites 1"> Assumptions / Conditions / Definitions. - ... Statement : ... </PROPOSITION_STATEMENT> <LEMMA_STATEMENT id=.

Pseudo-Formalization for Automatic Proof Verification 1"> Assumptions / Conditions / Definitions. - ... Statement : ... </PROPOSITION_STATEMENT> <LEMMA_STATEMENT id=

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.563780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:463ac13a4914735255e9f186ae50557c2e0017d3e3710ae351837bbb9600595b

Observation ebfeb71e-f00c-4bb5-8f94-080653ec0ef2 · outbound

This paper cites These are often the parent or ancestor statements of the Assertion, and can be the same as the global theorem.

Pseudo-Formalization for Automatic Proof Verification These are often the parent or ancestor statements of the Assertion, and can be the same as the global theorem

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.591279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:f4ffab898aa87f2f59a5076ef074ce8de7371c1834ad113e3be2ec3d5a666a24

Observation c4ced01d-5a14-4914-9c74-9484274dba62 · outbound

This paper cites You may assume all established results are correct and use them freely - do NOT re-verify them.

Pseudo-Formalization for Automatic Proof Verification You may assume all established results are correct and use them freely - do NOT re-verify them

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.589475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:49da1cf365d94ac40586c141da6ee2dd7430911871d2cca204ce9a75190e5b9b

Observation 30b040ee-0529-4321-af3a-1440697c556c · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.556410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:025e7389643f2288bdf748a4ba238845038241298b69ff232b3595dbfc7d8499

Observation 86147025-32f8-496f-ac93-b5d700532681 · outbound

This paper cites verdict".

Pseudo-Formalization for Automatic Proof Verification verdict"

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.587625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:b027f5d7ea831537e8967cd71dc8557e5afdb8810f9dd9f7e78d6f16d455b568

Observation fa12f371-a11e-453a-8785-bfab88e9ed27 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.565392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:c883a8eceadd1b2d8167437ae1807eff718211a7f8531772ead1f5c78360338d

Observation 16ec747d-5064-4a9e-bbb0-98404c936936 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.576462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:7236b2c51e65ece7e9c45e899746dc9830d83087b7feab0713af1bab1a35ac02

Observation 48163930-2a9e-4af4-9ccc-aec11feab942 · outbound

This paper cites This rewrite was produced automatically and may contain artifacts that are not present in the original solution.

Pseudo-Formalization for Automatic Proof Verification This rewrite was produced automatically and may contain artifacts that are not present in the original solution

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.559844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:e27c25134ae59e3cfe8061021344b3609bf3d3f3f9219b486987153304ec9609

Observation 1156f372-572c-44a9-9cf5-61863bd02b0c · outbound

This paper cites These may or may not be genuine errors in the original solution.

Pseudo-Formalization for Automatic Proof Verification These may or may not be genuine errors in the original solution

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.552862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:80eacc7bcc94ea74d58249085f18ace54ed60b8b54bd81a7c5b2a15b0ff08010

Observation 2a657d16-6a89-4360-9382-18e67e1885fe · outbound

This paper cites For each flagged issue, decide whether it is a genuine mathematical error in the ORIGINAL solution or a false alarm caused by the rewrite.

Pseudo-Formalization for Automatic Proof Verification For each flagged issue, decide whether it is a genuine mathematical error in the ORIGINAL solution or a false alarm caused by the rewrite

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.634034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:c4784e759d60dcbc9da8ec6c878d80639418e09d1d55f9cd2942ba8fea25297c

Observation 4406ccf3-850d-4fa0-9df5-96c79a2881ee · outbound

This paper cites The potential errors are useful leads, but your final output must be based on the original solution steps.

Pseudo-Formalization for Automatic Proof Verification The potential errors are useful leads, but your final output must be based on the original solution steps

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.637840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:4f8b972afe141d679c67fa8b4598b5b99e6c17a76f6a05daf04fb99679e27d17

Observation 6ffca279-01ba-4b52-abbe-b97f72621341 · outbound

This paper cites For each original step, determine whether that step is correct or incorrect.

Pseudo-Formalization for Automatic Proof Verification For each original step, determine whether that step is correct or incorrect

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.635904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:2ac060d32d9249e207da8f38cd3a9f9edd9ae2d331c12b09bd3dd2f5defd4c96

Observation a90ef981-c9e1-4211-9089-d79efd6c790d · outbound

This paper cites corrected typos in the proof of Theorem 3.

Pseudo-Formalization for Automatic Proof Verification corrected typos in the proof of Theorem 3

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.639648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:0db2e75455c99c751e8c7de467b8085bf7bd52f154f2a3c82ac0da565349fcb0

Observation 9ef97a82-7dee-49b1-99bb-dea06afabd3d · outbound

This paper cites Use this to read the paper as a human reader would, with all theorem/lemma/proposition numbers rendered.

Pseudo-Formalization for Automatic Proof Verification Use this to read the paper as a human reader would, with all theorem/lemma/proposition numbers rendered

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.641413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:220e2da4ff45df29f7a52d091b12160005ead1cc48f66e399b2954838868f547

Observation 1d1ee891-542d-47e2-80b7-aa90a1263a28 · outbound

This paper cites Theorem 19.

Pseudo-Formalization for Automatic Proof Verification Theorem 19

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.626566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:ddbd2b331ebdb79fe75d5313d30047a958407ab278fc340b48f1d838716279bc

Observation f3ee4eae-eacd-48e6-a5db-b8d59c2646b1 · outbound

This paper cites Use it to read the paper as a human would and to identify the rendered numerical or letter labels of every theorem/lemma/proposition/corollary/claim.

Pseudo-Formalization for Automatic Proof Verification Use it to read the paper as a human would and to identify the rendered numerical or letter labels of every theorem/lemma/proposition/corollary/claim

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.630341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:3ac6eabecbad3d9b11c2494523e0a056df2a321de274ead3f85cd1adcde0663e

Observation dc9cceaa-00a3-43f5-9b7d-e2efd0cdc2c3 · outbound

This paper cites Use it to inspect precise notation, equations, and the exact wording of each statement and proof.

Pseudo-Formalization for Automatic Proof Verification Use it to inspect precise notation, equations, and the exact wording of each statement and proof

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.619367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:ed0a7f1d79c5ffa270cf6ffa49c7b88d9900c7f21c4302e54a3faf378d768407

Observation 60ecff44-5eff-43fe-8a9c-0a1016fdbdc4 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.623134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:663b7795f4e8984903bf55cdbc1ccee8cea86a51932b1179ffb3115ee87a757f

Observation c303feaf-1c3a-4cac-8d79-7cb99b093428 · outbound

This paper cites N"> may cite any of the propositions; a <PROPOSITION_PROOF id=.

Pseudo-Formalization for Automatic Proof Verification N"> may cite any of the propositions; a <PROPOSITION_PROOF id=

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.616272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:48d04b9aed7617f72c35e5f2d05fe25cbf882450ead96b4eb79683b6bc042b0a

Observation 66722f31-b946-42a5-a3ac-ab2344ff45e8 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.621412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:178eaac51aae117a50899cd455292a07f153a156b8dcf67b00891093600b4fe5

Observation da423b7d-896e-43c4-b7a4-5c6b37cd1a32 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.558014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:ce6cfa114c807898b8363626f686107dcfc1d1954cbd2cb25e2950bc41297689

Observation 3bc07f58-66a6-45db-b7a0-087107bf9bdd · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 63

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.596086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:63fda0cbff70e2509a3b8cc83ebbb6a087d3ddce090606372b7fba637dff765c

Observation 41d0a687-2680-445f-a304-a0c5e49f61a7 · outbound

This paper cites Requirements for the new rewrite: - Fix every issue listed in the Identified Errors.

Pseudo-Formalization for Automatic Proof Verification Requirements for the new rewrite: - Fix every issue listed in the Identified Errors

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.609667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:18f252fcc6a1ffef909bd3f5a7a3d41afafaf77fe96747cf6470012f9acce861

Observation 42e9014d-e768-4eee-b811-9c449282d405 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 65

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.632067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:388245748f5c0e9106b7b4bae34419892e60e8383c6245332cd5774abf9558cf

Observation ca4d82e6-f84e-401e-ba1c-445b4db9aec0 · outbound

This paper cites These are provided so you can understand the scope of the Assertion.

Pseudo-Formalization for Automatic Proof Verification These are provided so you can understand the scope of the Assertion

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.602877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:dbeed9c4d8c80695f61c37d20eb0f34af36050f8568b9247e66be418a4c74260

Observation 825e9273-8894-4593-a68b-b517076427e0 · outbound

This paper cites You may use them as reference points.

Pseudo-Formalization for Automatic Proof Verification You may use them as reference points

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.604559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:f78f32f57e3d50708b4359ea910016cb1da39e8f8313ec5c4c8ebea956707f40

Observation dd728b64-752c-4ecb-848f-363201d3527c · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 68

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.607797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:e28043dd3e8772f60858e13463b108cd952c5ec5671f0c8012110dade50cdd43

Observation 77d72ab1-3d03-4884-ba24-af01bbeb9351 · outbound

This paper cites Your task is to determine whether the Assertion and its Proposed Proof **faithfully represent** the corresponding part of the Original Paper.

Pseudo-Formalization for Automatic Proof Verification Your task is to determine whether the Assertion and its Proposed Proof **faithfully represent** the corresponding part of the Original Paper

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.554633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:21897b49207488e3e2a948c8394de58f9820ec93665a1bbef02d559417dd0ae9

Observation aa533b57-87e4-44bd-9c75-c60934c4268c · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 70

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.548071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:d518094788069ebb980bed1d3f2374f7c56f17d287f5fb356b4e93bd44503a4e

Observation 350c8eec-560b-45bc-978e-5c2929bb5d66 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 71

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.549566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:88d3587b74688f5037f280e0d34a9b367b07dcaa0770c83aa84fbc763458d53e

Observation 80eb84f7-6a1b-4ed5-a619-289457870ee7 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 72

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.599379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:a1a6a46096172c016dbd2efa444edde12cde66fff6953dcc51ea616a1a0a440e

Observation 384845c5-ab6d-4aae-80e1-b925407a37d6 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 73

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.597717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:74eb23d2dca1b0d568a283338fabe5f94d9bc69cf3e3ce52a17b99ca23391667

Observation 2fef5e53-8c1d-4809-89b2-556a6c2b7ee4 · outbound

This paper cites an unresolved cited work.

Pseudo-Formalization for Automatic Proof Verification Unresolved cited work

Reference 74

Resolution
unresolved
raw_fallback, observed 2026-07-08T09:34:48.546607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:f2c41f6f39558a923ceae7a35e8bc9e64de6c45cd28e405a7022cd5c9479e5fb

Observation 6f331cc3-9cc5-4adc-9980-40f453dd288c · outbound

This paper cites verdict".

Pseudo-Formalization for Automatic Proof Verification verdict"

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T09:34:48.551184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-06-30T17:17:48.969969Z digest=sha256:606444fa2c4fb214ec32c062ddfed79c80ecf64150c6808e011cdfd14b12474f

Pith citing papers

No inbound Pith citation observations are available.