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Paper Citation Record · LEDGER

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

As of 18 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 4 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 57 of 57 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:51:00.846673Z

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 2026-08-18T06:34:40.430872+00:00.

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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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.424219Z digest=sha256:758e94e2e77643a8cbcd46c05fbada1e5f4e20ad5460aa7299db5fdbdfaea003

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.427893Z digest=sha256:29d0ce0d83d5a0697e00792d2256ebd310111d871a55d22453870a840a52e785

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.431615Z digest=sha256:2055b3a3ef61381357e2f7cb0f0480be8870bf856e35616bdf1beb491bfd9043

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.435312Z digest=sha256:0e29f053fc7f1ec45e7b2a8f8aacdd905d551b8a8111210513b2b384d1ff4e79

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.439062Z digest=sha256:60e3d9bf6dcb3df7ab783f8e727f68155b4a44ab429d356d3b506f0ceba12cd8

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.443270Z digest=sha256:65c77536b076f655d38b2cc7e33623640719ca372c1dd9fc723c5c21ada1e3ff

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.446566Z digest=sha256:76fdd1530caf8f6b5939850c5649643028a1e204852970807db5153fbebe4b93

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.449772Z digest=sha256:5faa83c64dddf86b70c3de87200af78f67a1b9f09181cf2b1571808f37f01462

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.453888Z digest=sha256:c7ac4e90e782064a93c97d966b571deab466971691383d50b22d2e706904fc6e

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.457262Z digest=sha256:9c392c5d21bc549f5d31e67afaa7db5d92e246fd7896f893a7b51d601bc1f4ed

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.461051Z digest=sha256:4f8453ff0a059bba830a8afa61d394bff27a77bee4240ee223dc2069df1bcd7e

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.465075Z digest=sha256:aaf8a1fecf9200f8e3a7d7a1362bad78aa92c4714e6ac69744bebd26922f3b11

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.470253Z digest=sha256:8c979d6cff32fa5ce089073b5fc43c7590aedbcc2922a7734b1483b2debe8a5d

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.474066Z digest=sha256:4bc68c566ee3361fd4d9afb6fbbdcfda3843499dde53bb31a883246625210f50

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.477761Z digest=sha256:6b82ef8af3d4137f8fc82cd90963ae4ebc9b8470ad645782929e88baa69133e9

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.481385Z digest=sha256:83a68d8be1894a0f589d981f513fcfd51f8307749886bdd7e0ff63dc2343e488

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.484555Z digest=sha256:384d5d744d8eb96f5dd664060dcdb499d2792257d954ed10729ed7d2d5e4a509

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.488058Z digest=sha256:ccd112e1384bbe0dd1f74c68949ab91ad51acd46477bbb8cb8b77c6eb315ead1

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.491274Z digest=sha256:017d134140b9b81eff3e7e01e62e0f817b2d85f656a97a17f1f5d948dd4f4f8a

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.494632Z digest=sha256:ce89be28dc420b991c23ac0412ab8ef4f98b4f401ed91964d36cb2c7cf6cdf3c

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.497943Z digest=sha256:5f13d4d3e56c1f7782f794cc4e4397958bb9d94e2a17e05bd2aca949418beeda

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.500997Z digest=sha256:3561fb94b1c070dcb39843b90c1a2006b2a5968f0cac58d1dd766ee283868c64

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.503984Z digest=sha256:29a6ae30659c236bcda056f7287d92168fe3e2cb59fe2fca9e6c1e8287bfaa87

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.507141Z digest=sha256:83181a6b2c3b1b8347ceac25ea1b20428c179c8f51db41ea8c6eaae9db819d7b

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.510121Z digest=sha256:bb70c87198e6c32d317bfdea5eff6077bfd870cb9343f2c493c766f872618ef2

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.513022Z digest=sha256:3906dcbedc0e85a9252ba5dac40d8023e396987f0acd8c0f4047eeff35968bae

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.517060Z digest=sha256:f7f6b60a3ef50bb5c919c85cd866ce3228e6e42ba2b1b048902b522b18e4f418

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.520237Z digest=sha256:b4619dbf27bfa64661762c2c9f214ad0cfe1c99198e308a15764475836a22812

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.523279Z digest=sha256:d7c9a6227d2b9198c6884e4a52dd8d2636c459deed81b82e2074bcb464a949f9

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.526481Z digest=sha256:7fe9b73b1ccbcfce3db392350b9243e642eb953ab16de926f1ddfb15d481f652

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.529715Z digest=sha256:285bdd32077f6b1b4f1166b38e6854a2aab06f8d559ee8c10cbc75b8a2cdbd95

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.533113Z digest=sha256:69dcb4261707d4d47672f2135e06b28d18a2ff8bd752b7492557ff748f717977

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.536205Z digest=sha256:87c757695575d803cb58a294db57e76c9e0e8473cc1935f42010ef9a238f8027

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.539410Z digest=sha256:ec765e1118652bf922bfaea3e27690a638c6fcc8d87e9ce3b952b2ca932692d6

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.542534Z digest=sha256:9c330bf3ad21e0fa81b6629c0726c8df8eaa31214327480d8243dcc331009cb9

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.546497Z digest=sha256:c1e92538e01408176f0a5fa2fbdcbffe262ecd4e5c9cb568201faa278e16ba38

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.549612Z digest=sha256:23cdb6f85a0504be54be03948d82f7324510748c643244c238e46b162d7e13c5

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.552820Z digest=sha256:86a35795c3a91d9213aa23f11920f4e0076491a843379f4f052d406532688851

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.555817Z digest=sha256:cd1e713dae2ee228bf49d395f9e575ba757480d884a4b68786ad46a6b08b8f7c

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.558986Z digest=sha256:ebc334db54209adf7247e54bd6027d4d42b3775f7e40efe0fd810b260451fe1b

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.562150Z digest=sha256:1b09c743b3bec7fcc2ae93599e4d78ecbeb86662623a77be03051fbbf8c4c490

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.565292Z digest=sha256:00bbd5e39c35fc47b41dd86b427f3249ba1f0d324dc31f68c698859364def916

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.568419Z digest=sha256:100da8d5dcead3d49110fb17327eb75bf507de6be0ae573c113d548cc47e10f6

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.571993Z digest=sha256:b45a5ea4f890dfb6895c9e57dbc2ace5286c859511d8925999462c1d70ba2e43

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.575251Z digest=sha256:4e76010f79b944df87421c50b717cad6573ddda1b42ddbb542134beca4efa772

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.578447Z digest=sha256:03a6fce29e38eb7ab8e8100b46c624f29ea2783c08ffadcb44743fceb850adbc

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.581643Z digest=sha256:d2f51a8aab7379217ddb795ee2524cdf4c0c7eebcd2c5a61d8293e5d7976e563

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.584792Z digest=sha256:7a7632d0a9de5a545c89aae10f9204ce2da907196244bb139aac68d16f03f6df

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.587779Z digest=sha256:d5771107c500e1a8230379963396a709e144bca79f57a15a6e7bee2f524145dd

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.590996Z digest=sha256:615fbdd0c4dc23c3e9d1deb09f2d6af3eb9922112303b1c940864cb71b5303ac

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.594065Z digest=sha256:d5b70de573b3733c39c7f7babf3858455458ae8a7055a5009050c818c8b0d6d6

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-07T05:22:00.597700Z digest=sha256:63bd83e7ff3bdcba6aaccbdb93042363593bb6657dda44b934142f1e636ccf61

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-05-21T14:29:15.751497Z digest=sha256:969cdd7a59519439ab98d27a81163f71df30f146aa7ae76583c1ba1c0949fa0b

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-05-09T22:06:47.552043Z digest=sha256:5726618b0552f783b2954cd5ba3c1007fcd3d5a50fa296c03e2b7611573ce66b

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 2026-08-18T06:34:40.430872+00:00.

source=arxiv_source observed=2026-05-19T18:01:06.649723Z digest=sha256:6c0f030bc50583808bc43a888e11dedf932d5350c669ebb2ed36b50ec72ade56

Observation 923c76ed-ae96-40bb-8589-f6399fc8674f · inbound

Group Perspective Matters: Regulating Debate Relationships Can Mitigate Blind Conformity in Multi-Agent Debate cites this paper.

Group Perspective Matters: Regulating Debate Relationships Can Mitigate Blind Conformity in Multi-Agent Debate From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium

Reference 28

Resolution
unresolved
no resolver link, observed 2026-08-15T14:51:00.846673Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T14:51:00.846673Z digest=sha256:0dd1bee4d6f71c605e9ac82adf5ef4023bdf6c25ea04dc7fa4a0bc156c3da537