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Paper Citation Record · LEDGER

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium

As of 8 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 3 inbound Pith citation observations for arXiv:2506.08292.

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

pith.paper-citation-record.v1
2506.08292 v1

Coverage vector

measured 53 of 53 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:22:00.597700Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-21T14:29:15.751497Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-21T14:30:13.855728Z

Reference resolution

53 of 53 outbound references displayed

  • verified exact0
  • verified fuzzy21
  • unresolved19
  • parse uncertain13
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 63b4cacb-015e-4d18-8e3f-ed38ce90baf0 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.152420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.419224Z digest=sha256:c6e928b3d75fbaefc907e6ac0aa46f419eb5634f02640e4060cb7f94e1985889

Observation f9fe5d4d-79a7-42da-82f5-761cea92dd6a · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.141850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.424219Z digest=sha256:d6a1ec78a1fe034e93ec4bc0edf469acb0dd437dac390b50d3a3e876fc3eb6f1

Observation dabea981-b22b-404a-b813-5502eb724c97 · outbound

This paper cites Verification:.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Verification:

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:01.129583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.427893Z digest=sha256:72ede5f906242fd01a115ffd7ade5de8b7c4a33e5983c686af4fdaf3ab24459f

Observation 6d60f624-4709-4d96-a194-5a87b2547763 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.118900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.431615Z digest=sha256:d2f969b68a8daa9b5b6fd7dffac0431f7223f7f6f993c26e30da791823f8dc27

Observation df2ac0c5-74b3-40c0-8feb-da750c5ea8b6 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.108727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.435312Z digest=sha256:c5afb76301fdfbf938376990e9ef554f8ae506494fc546e67c6460c0f45c11c4

Observation de219b37-9077-4525-b0c9-047251927802 · outbound

This paper cites Therefore, any convex combination of strategies does not decrease the utility, satisfying quasi-concavity.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Therefore, any convex combination of strategies does not decrease the utility, satisfying quasi-concavity

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:01.096934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.439062Z digest=sha256:afe24659b42b123e049231a7816e9f19b293affb36c019571f4537838053a7ca

Observation c5af0184-5085-437e-a2ba-8539f6db2a04 · outbound

This paper cites Convexity follows from the quasi-concavity of Ui in πi, implying that any convex combination of best responses is also a best response.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Convexity follows from the quasi-concavity of Ui in πi, implying that any convex combination of best responses is also a best response

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:01.086010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.443270Z digest=sha256:493b35e5c567a82a34940c60dfb059f24433cabc8e57100b74acc9b724831373

Observation 5d10ff22-e53b-4be4-bf03-1c2e208d4079 · outbound

This paper cites This property holds because the payoff function Ui is continuous in (πi, π−i), and the strategy spaces are compact.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium This property holds because the payoff function Ui is continuous in (πi, π−i), and the strategy spaces are compact

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:01.076053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.446566Z digest=sha256:312bcb8713a0ed750f2f2f758078ec77b17bae805e56e2e4770e7a8f30e9b958

Observation 0dce4497-c296-410c-a9a8-0464b3d732da · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.065228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.449772Z digest=sha256:4a1a53f383f49eba20d140927fbe529b1665535e6ac2fa20d23deee2fab70b9e

Observation e488479e-af3b-467a-8ae9-18a958e3ea23 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.055178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.453888Z digest=sha256:bf643311db06a6f4de1cbfcab6d462cfe9ce8846ab10839279006589ca79c658

Observation 920522b8-2aec-4d79-aeed-ef708b6e42f4 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.043960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.457262Z digest=sha256:d96c0eda76096ff9f1d861fc9c185abfbef79124257a022b6fc45c1c1abbcf17

Observation 8c5695b6-8173-485a-97d4-78ad4ec63cc2 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.034229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.461051Z digest=sha256:15403882d40f4fcd3ae58927df36272b00571aaeac1fcea14ad636caef6d5093

Observation fb323f60-7360-498d-97e7-f6cbd10d054e · outbound

This paper cites ∞X k=0 γkri(sk, ak) | s0 = s # , V π i (s) = Eπ.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium ∞X k=0 γkri(sk, ak) | s0 = s # , V π i (s) = Eπ

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:01.024111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.465075Z digest=sha256:b76631c7067776c81fdfb5f834cc0fb60f493626e459a5b5f8bbc5478b3e5749

Observation 48a73b27-621c-4d06-ae5a-6d3d1992563b · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.014226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.470253Z digest=sha256:84ec61fb328d708a1933603bfe526ad27613e1b327c00c953a28de3a4b97a69c

Observation 5024c2e2-3357-4e3b-b7ff-0472e2c3931e · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:01.004342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.474066Z digest=sha256:e01e98aba4ff758b8723dbd7f531e00b1c43e86dc4db253313d28e909a897c2c

Observation 19a0d186-4d9e-4a06-93eb-dbb11aa8056b · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.994238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.477761Z digest=sha256:7a97f3d7c83f441286daa8accf11078f2c836ca8b9b5cff452b2488ef47084e6

Observation a89eaf8b-cc9e-4edc-8098-d7fcc1f9a2c3 · outbound

This paper cites This is a textual or embedded summary of the agent’s partial view of the environment, updated via the belief network.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium This is a textual or embedded summary of the agent’s partial view of the environment, updated via the belief network

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.983955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.481385Z digest=sha256:5468f0c1bd3e66f3783ad8f63a3cde2383db02d70b6ed2f5f4578087bbee6cf1

Observation d484d231-6fca-4fce-af42-363d3ec4fa4a · outbound

This paper cites Figure 6: Coordinator Prompt(for Strategy).

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Figure 6: Coordinator Prompt(for Strategy)

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.972775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.484555Z digest=sha256:b545d2f4781365b256899d67b9df0594a55b72e28f3233da22292544986cfe57

Observation b4b45a5d-93b9-489f-9806-5c4249ff5f84 · outbound

This paper cites If Tom saves $45 per week, how much does Janet save in 5 weeks? S2: Find Janet’s weekly savings relative to Tom’s.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium If Tom saves $45 per week, how much does Janet save in 5 weeks? S2: Find Janet’s weekly savings relative to Tom’s

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.962035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.488058Z digest=sha256:d922379e05bccf051ad456e298c6ed655b2ce449e27b7ef424531d355c1f04b3

Observation 57eef879-9220-4591-9853-195cf7d4bb24 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 20

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.952275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.491274Z digest=sha256:53e22250503b2bba9db285a778ce0dcdda8222902d5c82801fa305bfefa39953

Observation 06659062-24f7-4247-9359-6d6b0862b6c4 · outbound

This paper cites If they increase production by 15% next month, how many cars will they produce in a 30-day month? S3: Calculate production increase.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium If they increase production by 15% next month, how many cars will they produce in a 30-day month? S3: Calculate production increase

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.942598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.494632Z digest=sha256:ec86e3206eef9ec4c6677bd364755bc431b049260f68eeb610e8a4b1302fed72

Observation 3f179724-1071-4e74-9f0e-a0bcccba55d3 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.932395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.497943Z digest=sha256:2fa3274790600f955a041ac5f5ecc1f634eb6792ca0823ee416f66e82b0bcdcd

Observation 03aadf30-6042-4562-8105-e559efccb412 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.922767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.500997Z digest=sha256:85576f76aa26cdd4627368680f0531f53663e9de8b205bbf70b74ddad1b1e6aa

Observation 29b8043b-909f-45fd-8535-bf1ad2069586 · outbound

This paper cites Sarah then gives 1 4 of her marbles to Tom.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Sarah then gives 1 4 of her marbles to Tom

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.913318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.503984Z digest=sha256:ab53cd2852b5e58a90c40b097072a84741c7338b689121780c07214ba08321f7

Observation 219f730e-a840-4fc8-a54f-baa5bcdb2f6f · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 25

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.903643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.507141Z digest=sha256:3f2cef32db99a9fee4545c1398ede2d28251912d6a259f3af261beb51eabaaa1

Observation f0480240-c0f9-4d52-a1d9-f1987477191f · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.894547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.510121Z digest=sha256:8e43b23bcfec1252f5974c7ca5adc1488d5d5d8b24746a92d69cc6ecbdd32c53

Observation 9fe284a5-b708-49b0-842f-45894becd494 · outbound

This paper cites What’s the total distance traveled? S5: Calculate distance for each speed separately using d = r × t.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium What’s the total distance traveled? S5: Calculate distance for each speed separately using d = r × t

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.884970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.513022Z digest=sha256:94d719101d6f3ffdc045385b88f1b72b41b9f0acb17228b29b9fb19fb4f493de

Observation 00af16b0-7b58-4cbf-927b-3d5b76ea03f1 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.875511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.517060Z digest=sha256:d751faa693acef2d3822bae6ab777ed44d2a9f5db89efb34d580a68e931e018c

Observation 956dec7e-6495-4a46-94b0-0854f49d911f · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.866422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.520237Z digest=sha256:dbf1257d98fd360ef11b33e6736f4ca31443bb52dac190050414ca2886e9a0b4

Observation e3352bc0-785a-48f2-8d44-f906e25c20a8 · outbound

This paper cites MATH MATH Problem 1: Q1: In a bag of marbles, 3 7 are blue and 2 5 are red.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium MATH MATH Problem 1: Q1: In a bag of marbles, 3 7 are blue and 2 5 are red

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.855617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.523279Z digest=sha256:300c24b1ce115a24074ee1b62605c4e943b916bd446738c8fd040184a66bc627

Observation 42464565-e48a-4e3a-bdf1-f5f1eb3c7b68 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.846334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.526481Z digest=sha256:f0e712462a7dd02814ead16f70812f17946f50f19e2b3d90998dfe2b2656c7f8

Observation cf2e6efa-7c6b-426b-8e2b-62d94752eba4 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 32

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.836191Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.529715Z digest=sha256:05c53a9654cb63ffc407d59073b27b621bb72f57e324d2948a3871edb0a5c095

Observation fedb9e77-6b51-43a1-9738-ff0cb83eccc0 · outbound

This paper cites S2: Use coordinate geometry method for area.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium S2: Use coordinate geometry method for area

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.827180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.533113Z digest=sha256:62b102bf533171118f1a445d37f4aa9c9f6cdfb953c0000a465a4963f92804d5

Observation d2cc11d0-8ca8-4ab4-9853-76fb32969480 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 34

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.817764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.536205Z digest=sha256:24860dece75d55375c92926cb722746f026618a35fe1ae44ff665b22c398917e

Observation c7706525-6888-4411-bbcb-ed2b4cde55d8 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 35

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.808288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.539410Z digest=sha256:7b02404d9662309a8ec338fa98f9ce228a6781c463337b9de346125edbe57c0d

Observation 45803ad9-0700-4ecc-afb6-d74710b40a03 · outbound

This paper cites S3: Apply logarithm properties.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium S3: Apply logarithm properties

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.798958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.542534Z digest=sha256:53171998c7f908dbf4bb874388bb0eab5785cfbcca8b00a0dcc05efee9a27dad

Observation 53cf900b-347b-4764-9080-9163fc8f0db9 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.789775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.546497Z digest=sha256:4f8ad70127bb47c1cf7bc2c70feae3771e4adfe256bd596a47186921f1a45779

Observation a5022397-0888-4c43-b7f6-d869fde22ca3 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 38

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.780416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.549612Z digest=sha256:c9447141489f836d7d57354cbdc5544ee1a51a08deb332002e4c3cd9e78ad533

Observation bea6ec51-3583-44f8-a501-904c1d024c33 · outbound

This paper cites Find the area of the sector formed by a 40◦ angle at the center.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Find the area of the sector formed by a 40◦ angle at the center

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.770998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.552820Z digest=sha256:288af6b0cc0acf0d2d30092d0fda8dbc81704001fe126cee12183e5900361116

Observation d8debfd0-bc21-4de2-839c-32cc1477c4f6 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 40

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.761297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.555817Z digest=sha256:a719e124d82b9db0ef9856cf3941b31a1ec4684607aadbcbd8df4935f122ba49

Observation 0f3994f6-b130-4b45-97b7-a599de782839 · outbound

This paper cites S5: Identify quadratic components.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium S5: Identify quadratic components

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.751664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.558986Z digest=sha256:a4c739604e47dddc3c354b430721eaf07160a9c5fee06faa344ea312a3ae22a8

Observation 53c9c1da-b8fa-494b-931d-233afde24e2e · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 42

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.741236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.562150Z digest=sha256:5cbc835c0666004088509c09c886b31cbdf889abc0faa578d909cbf74fac12af

Observation b39794c7-26b8-46b3-a272-c23965bb28ab · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 43

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.731043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.565292Z digest=sha256:0f227a0e270ec273f8d30faf6b14be539a18248a4bd485729873059d3075dc36

Observation 972e613b-b4ff-4fed-842d-6ca6e533d8cb · outbound

This paper cites SVAMP SV AMP Problem 1: Q1: There are 56 books on the shelf.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium SVAMP SV AMP Problem 1: Q1: There are 56 books on the shelf

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.721521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.568419Z digest=sha256:2290ac66d2bd3e054bee9bfa1584991062a94940595d1ee933d0a699cfbf11ad

Observation 78520bb7-15b1-4093-a04e-f1086cc8411b · outbound

This paper cites Each row has 4 chocolates.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Each row has 4 chocolates

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.711187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.571993Z digest=sha256:3e1ba091e708244a2360f6aa74b9a3ee16871cf393667e899404f5746dbd6249

Observation 7c1db624-15d8-4ff4-b5e6-050e1fc08958 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 46

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.701604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.575251Z digest=sha256:b05aa2cb10d82afa0aaa14831a3e2fec83e7da5d28532b70b0b1195b39e3dd13

Observation 60d826d2-1151-47f2-aac8-bbba24520b78 · outbound

This paper cites John has 12 stickers.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium John has 12 stickers

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.691936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.578447Z digest=sha256:7bbc3d35e4f63e655d2aa2e808f932271fac43e642c3ae285c5ca12e7897149d

Observation 2db837d8-206a-4357-a3ac-0e9fe1aae30b · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 48

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.682311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.581643Z digest=sha256:d2e6983b1554e4d1c18b8b51d4bdcfdb6b7e5b8e1f704cfe62089b2e29b1675c

Observation a2664e98-ac47-4dac-997a-f3e9d070cbfa · outbound

This paper cites ( 2 7 ) are roses and ( 3 7 ) are tulips.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium ( 2 7 ) are roses and ( 3 7 ) are tulips

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.671792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.584792Z digest=sha256:ca4f902cb5f06114cc5f4865d5a7682a5065af551243d087aae1ae63b70b29a8

Observation af127cb7-fe1e-4c7b-b4e1-806fc49db3b6 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 50

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.661609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.587779Z digest=sha256:740f163fe4fa72e69dac7464cf86c48cb79a41e6e9569d313517f25a353d3a0c

Observation ccdc2f87-1c04-4dee-b0a9-4db7df0ca343 · outbound

This paper cites If there are 23 children, how many boxes of 10 pencils should the teacher buy? S5: Calculate total need.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium If there are 23 children, how many boxes of 10 pencils should the teacher buy? S5: Calculate total need

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:00.651760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.590996Z digest=sha256:b3a5fcaada522b93b53a5c0037f12a443d81adef6f04c1f484c80c4da0eddf3b

Observation 0af133a8-ba4b-4653-b92d-6bf91f6f256d · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 52

Resolution
parse uncertain
raw_fallback, observed 2026-08-07T05:22:00.639635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.594065Z digest=sha256:6d9c94fa85377a9877c2dca048f49dcf602acde499bf830ace0bb99b53464198

Observation 93bbb421-2f72-4467-8e40-b3b0e8d60533 · outbound

This paper cites an unresolved cited work.

From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:00.628792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:22:00.597700Z digest=sha256:50c9f8ff89c2eda824b2aced101227be22459d1b5b8ea81b0a8eccee221005ac

Pith citing papers

Observation 5b4c1d5d-7990-4636-9eef-19872ac89187 · inbound

Learning from Self-Debate: Preparing Reasoning Models for Multi-Agent Debate cites this paper.

Learning from Self-Debate: Preparing Reasoning Models for Multi-Agent Debate From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium

Reference 24

Resolution
verified exact
arxiv_id, observed 2026-05-21T14:30:13.858122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-05-21T14:29:15.751497Z digest=sha256:55307662dd567e47e8365810370940ef460548261fb323d4587d9b093899d8ca

Observation 69617526-2b95-4559-b603-a7fb13aa730a · inbound

Strategic Heterogeneous Multi-Agent Architecture for Cost-Effective Code Vulnerability Detection cites this paper.

Strategic Heterogeneous Multi-Agent Architecture for Cost-Effective Code Vulnerability Detection From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium

Reference 25

Resolution
verified exact
arxiv_id, observed 2026-05-11T14:16:28.635337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-05-09T22:06:47.552043Z digest=sha256:c5bec852a7a399b044839904816fa6e240aadaf916bbc7c04cab3d18643bc490

Observation 464c31f0-6435-446b-ad3e-caad6d5c97b5 · inbound

TeamTR: Trust-Region Fine-Tuning for Multi-Agent LLM Coordination cites this paper.

TeamTR: Trust-Region Fine-Tuning for Multi-Agent LLM Coordination From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium

Reference 47

Resolution
verified exact
arxiv_id, observed 2026-05-19T18:02:42.284745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-05-19T18:01:06.649723Z digest=sha256:9d4fd577e1bc0827fafa37598a84e7f1315664c1cfd16834dbf7bbf477e8e092