Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:22:00.597700Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:22:00.597700Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-21T14:29:15.751497Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-21T14:30:13.855728Z
53 of 53 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 63b4cacb-015e-4d18-8e3f-ed38ce90baf0 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 1
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.
Observation f9fe5d4d-79a7-42da-82f5-761cea92dd6a · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 2
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.
Observation dabea981-b22b-404a-b813-5502eb724c97 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Verification:
Reference 3
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.
Observation 6d60f624-4709-4d96-a194-5a87b2547763 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 4
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.
Observation df2ac0c5-74b3-40c0-8feb-da750c5ea8b6 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 5
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.
Observation de219b37-9077-4525-b0c9-047251927802 · outbound
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
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.
Observation c5af0184-5085-437e-a2ba-8539f6db2a04 · outbound
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
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.
Observation 5d10ff22-e53b-4be4-bf03-1c2e208d4079 · outbound
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
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.
Observation 0dce4497-c296-410c-a9a8-0464b3d732da · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 9
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.
Observation e488479e-af3b-467a-8ae9-18a958e3ea23 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 10
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.
Observation 920522b8-2aec-4d79-aeed-ef708b6e42f4 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 11
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.
Observation 8c5695b6-8173-485a-97d4-78ad4ec63cc2 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 12
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.
Observation fb323f60-7360-498d-97e7-f6cbd10d054e · outbound
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
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.
Observation 48a73b27-621c-4d06-ae5a-6d3d1992563b · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 14
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.
Observation 5024c2e2-3357-4e3b-b7ff-0472e2c3931e · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 15
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.
Observation 19a0d186-4d9e-4a06-93eb-dbb11aa8056b · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 16
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.
Observation a89eaf8b-cc9e-4edc-8098-d7fcc1f9a2c3 · outbound
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
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.
Observation d484d231-6fca-4fce-af42-363d3ec4fa4a · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Figure 6: Coordinator Prompt(for Strategy)
Reference 18
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.
Observation b4b45a5d-93b9-489f-9806-5c4249ff5f84 · outbound
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
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.
Observation 57eef879-9220-4591-9853-195cf7d4bb24 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 20
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.
Observation 06659062-24f7-4247-9359-6d6b0862b6c4 · outbound
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
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.
Observation 3f179724-1071-4e74-9f0e-a0bcccba55d3 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 22
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.
Observation 03aadf30-6042-4562-8105-e559efccb412 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 23
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.
Observation 29b8043b-909f-45fd-8535-bf1ad2069586 · outbound
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
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.
Observation 219f730e-a840-4fc8-a54f-baa5bcdb2f6f · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 25
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.
Observation f0480240-c0f9-4d52-a1d9-f1987477191f · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 26
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.
Observation 9fe284a5-b708-49b0-842f-45894becd494 · outbound
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
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.
Observation 00af16b0-7b58-4cbf-927b-3d5b76ea03f1 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 28
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.
Observation 956dec7e-6495-4a46-94b0-0854f49d911f · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 29
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.
Observation e3352bc0-785a-48f2-8d44-f906e25c20a8 · outbound
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
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.
Observation 42464565-e48a-4e3a-bdf1-f5f1eb3c7b68 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 31
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.
Observation cf2e6efa-7c6b-426b-8e2b-62d94752eba4 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 32
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.
Observation fedb9e77-6b51-43a1-9738-ff0cb83eccc0 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium S2: Use coordinate geometry method for area
Reference 33
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.
Observation d2cc11d0-8ca8-4ab4-9853-76fb32969480 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 34
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.
Observation c7706525-6888-4411-bbcb-ed2b4cde55d8 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 35
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.
Observation 45803ad9-0700-4ecc-afb6-d74710b40a03 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium S3: Apply logarithm properties
Reference 36
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.
Observation 53cf900b-347b-4764-9080-9163fc8f0db9 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 37
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.
Observation a5022397-0888-4c43-b7f6-d869fde22ca3 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 38
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.
Observation bea6ec51-3583-44f8-a501-904c1d024c33 · outbound
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
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.
Observation d8debfd0-bc21-4de2-839c-32cc1477c4f6 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 40
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.
Observation 0f3994f6-b130-4b45-97b7-a599de782839 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium S5: Identify quadratic components
Reference 41
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.
Observation 53c9c1da-b8fa-494b-931d-233afde24e2e · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 42
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.
Observation b39794c7-26b8-46b3-a272-c23965bb28ab · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 43
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.
Observation 972e613b-b4ff-4fed-842d-6ca6e533d8cb · outbound
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
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.
Observation 78520bb7-15b1-4093-a04e-f1086cc8411b · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Each row has 4 chocolates
Reference 45
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.
Observation 7c1db624-15d8-4ff4-b5e6-050e1fc08958 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 46
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.
Observation 60d826d2-1151-47f2-aac8-bbba24520b78 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium John has 12 stickers
Reference 47
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.
Observation 2db837d8-206a-4357-a3ac-0e9fe1aae30b · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 48
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.
Observation a2664e98-ac47-4dac-997a-f3e9d070cbfa · outbound
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
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.
Observation af127cb7-fe1e-4c7b-b4e1-806fc49db3b6 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 50
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.
Observation ccdc2f87-1c04-4dee-b0a9-4db7df0ca343 · outbound
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
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.
Observation 0af133a8-ba4b-4653-b92d-6bf91f6f256d · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 52
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.
Observation 93bbb421-2f72-4467-8e40-b3b0e8d60533 · outbound
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium Unresolved cited work
Reference 53
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.
Observation 5b4c1d5d-7990-4636-9eef-19872ac89187 · inbound
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
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.
Observation 69617526-2b95-4559-b603-a7fb13aa730a · inbound
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
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.
Observation 464c31f0-6435-446b-ad3e-caad6d5c97b5 · inbound
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
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.