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Paper Citation Record · LEDGER

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

As of 20 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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.424219Z digest=sha256:a63fe859f0309bab024c2af733a0fda6ab6d8945fe9bb58079f7df62c7bf589e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.427893Z digest=sha256:264a988150b7770f7e9ddbf87cf253853da91b80933958b061994645ef742fb3

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.431615Z digest=sha256:644a6c9038497ddc5dfea221dd8ed19444d8b02d336bb96fd282b0d117d4dc57

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.435312Z digest=sha256:bd1d283a7755b52d529ba500b0b0f81ac8ceb85efa0d1ae19916dbe2be05d833

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.439062Z digest=sha256:0782d4039f6b9e353e354231502ea4ed64da467545697cf260b695afc752cf5e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.443270Z digest=sha256:302ebeaffcdcddab81c4d57722cff9095c06dd543ddcf982da753e7f8605f0ac

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.446566Z digest=sha256:a89b772749e3bb6f6d55103b5cd58a15ab0410940b90450b222ccecc401aedc7

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.449772Z digest=sha256:860e669f4d0188045ec75a6dd0b4580dac0852ae2ef1080a75af8a9d6291f8fa

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.453888Z digest=sha256:b45e6c38b8e6ef015ab91965f2db0ab069ebb24155450ed02db2d74d45e4a61d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.457262Z digest=sha256:9c54415b1860568eb8ae581d85808bca383bc010f8c6501fab36e88417c6fec9

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.461051Z digest=sha256:4e546ef5bd11bad4641d2ebb365b6f73c7d16ea41ec59d871da7bc3b6a8103b9

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.465075Z digest=sha256:daae3d6e6df58cc42cabf921e0ebdf3241992ad0b0e10acb098d5c2e64d65123

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.470253Z digest=sha256:b68b0ae65d9daddbb3b11d48d5df7de112e649eb02139eab646beca2b106e4a5

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.474066Z digest=sha256:96b3550ddd0ed39eab999dccea25e4ef1dfa4944de95d84459584a1e85b0e898

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.477761Z digest=sha256:3841ee29a3642bc68c4cd750c14634a5cfeac4f6cdcf789544a0e2d38fe50de0

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.481385Z digest=sha256:46803f0ee5d5b433091de3ca657929a7f8c498683ef655745b4d094114f9dea7

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.484555Z digest=sha256:d63ebb123343a975c1aaaed36239c5a435086158d5422d2e609e57e0c1a7a11b

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 2026-08-20T06:33:59.587034+00:00.

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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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.491274Z digest=sha256:ede7105c2691640fb32749822f215bf25eb2c06a83e34ffc8ba5e4d38746d83c

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.494632Z digest=sha256:6a2cb9a1ade00098e9ad6d4c204dc065c0e28feddc672d2a7111d5f95983367d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.497943Z digest=sha256:4b518f3924b314f2398316f07ce21afaf51fdd6bb72d3459b7d95bfe1a55f665

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.500997Z digest=sha256:dfd50dfb2ea2d35b773e5125194a880f0e1d2249d7776ef9310627beb232a333

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.503984Z digest=sha256:91d47bfbfd9549f355e72cd4da902b1766f2ac009d26285911327c70acba82af

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.507141Z digest=sha256:56c5f4b2c4702e060b9bba4165da33dd899234c2d8559a968bd416ea64d70cfb

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.510121Z digest=sha256:c218e5ccf377217ceb00f5954a878e6a8a3581a0924fdd3d42787362eb9d21a9

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.513022Z digest=sha256:9a9f2e42883c155c21160157ceb3b668ff64391960f8fcab8e32afb57d13046d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.517060Z digest=sha256:1511ee4fac3a60d76e07215cd693d86dae3a7aa229d23771427b54930ae103c4

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.520237Z digest=sha256:1152533b7132b582932b2d54fe6d1dc66ec81c5a33c676dd4fcc8e246e5b0736

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.523279Z digest=sha256:c32007ec354e47b29f42f646e90d8555b4bda223449047cd9c684eda284649a5

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.526481Z digest=sha256:1281f8314e860a2663ffb8dbae19479f7544821d8d972e0de6c97ad149ce594f

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.529715Z digest=sha256:8fb17ae9f0fec90a8fef653742794d6ae60ee8c410b6740a0c55c9e7112e276d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.533113Z digest=sha256:8e10b604113bfc7b8956f353e7c05a591c5733887b65769262ca26bd4dc5eb8d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.536205Z digest=sha256:99410c39683460f571f34a6808811cc56d26595753b4ce2ff9c12ee05f355cbd

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.539410Z digest=sha256:7a931dc5a6b29e3ba5a717dbc43a0edad28d82427050f0bf2472a36e966ac840

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.542534Z digest=sha256:f8fe756160c150070ee32281e05da5907b6a8ee4689d390593ec1e919deda791

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.546497Z digest=sha256:140f68f73b34144c9b558589b7468c1525b61daaa9620fe068bc6cfdfb9b58d6

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.549612Z digest=sha256:726023908c39b1250710fae99a02743b97a0b3a33cc25abcd498ddc964928587

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.552820Z digest=sha256:5c3ca064e3a09033befd10d6933bdecaaf8800fb450c6d5c2689bfcd61267b25

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.555817Z digest=sha256:d6f91421736fad7063571e210fee05bf0a4d58dfc2844872fe5f8e6f3053e404

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.558986Z digest=sha256:151abb36a856d6f149d04830cbb13d078a1b19c7c6c087458a977c709110dc5e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.562150Z digest=sha256:aaaecabf2115f83c3da0cf4ee3a1c434465130b4437a593eb564f8c7c0acc749

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.565292Z digest=sha256:a9e4ca3af65b2d03f0d04d63a7719cb50352b51b5d4660f3feff38d03c50443e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.568419Z digest=sha256:e9d8ef27a49bb1eae021e60be502003e10f1b40749ac39ca994baf70e312f7c1

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.571993Z digest=sha256:91d510fe3516a997f47ff27bb1960a4d373f95c70050c4e21a10dd96516e986a

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.575251Z digest=sha256:5fcbaf312749d73c5b431aaec7f7a47abd38ba50796b0a20b2a0f4c49782a8ea

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.578447Z digest=sha256:21d7e26b358dc6d2c51c50b6cf0034695d86f6ded25be035d860557053b2321e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.581643Z digest=sha256:86fe0a4d6249bafc4d23753201385f9eabaa3d2a147cef95b5c431ad0de42cdd

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.584792Z digest=sha256:06b593e9d7073ed9c16593a920424de06616454aba9bde58d994835a659d4b59

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.587779Z digest=sha256:75ea12a61ce6fc607d8ce637bd6e7d7fdb95e964b5e6d91f1ef96c6355001c4e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.590996Z digest=sha256:f189222942ace304b3dd379b58a2bfc595b84d65d9fc057cc19afdb3310977cb

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.594065Z digest=sha256:3cc69fa016edfb4e72ff933305fe7cc4ceec9fc201089060fd3c8f950d6e805e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T05:22:00.597700Z digest=sha256:533b55b9dae4eb8fcf7c11f9908400a1eaaaa9670df789333704aaf1b5c47ebc

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-21T14:29:15.751497Z digest=sha256:62000d27c546fb7f93f3709e57fce339622dfbd594fc21f008e5901ec31b5110

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-09T22:06:47.552043Z digest=sha256:998be63bfc94a3febc7ccf0108cf098939b1a0d7ecb5aab7e939d1673f6fa19a

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 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-05-19T18:01:06.649723Z digest=sha256:599f989325a378c65f6433ff653bf69d954f4b6b93f05120ce71fc9279afbe99

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