Paper Citation Record · LEDGER

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis

As of 10 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2608.05956.

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

pith.paper-citation-record.v1
2608.05956 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T20:28:42.309781Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact1
verified fuzzy24
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 90abba96-473f-43d3-838c-044333fe0c74 · outbound

This paper cites Improving Factuality and Reasoning in Language Models through Multiagent Debate.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Improving Factuality and Reasoning in Language Models through Multiagent Debate

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T20:28:41.766175Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c921e57d-6388-40a7-bed5-648c8751b13e · outbound

This paper cites Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T20:28:41.771185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e525134-aa3d-4c07-b442-84cde7292f14 · outbound

This paper cites AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T20:28:41.775495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 65e31065-a41c-4184-bace-b033067308db · outbound

This paper cites Agentic Reasoning for Large Language Models.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Agentic Reasoning for Large Language Models

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T20:28:41.780001Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c48dc28-ea3d-453d-a776-1816f2b56e6e · outbound

This paper cites Prescribed- time optimal consensus for switched stochastic multiagent sys- tems: Reinforcement learning strategy,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Prescribed- time optimal consensus for switched stochastic multiagent sys- tems: Reinforcement learning strategy,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.204418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 699324a8-9d24-42c3-a47d-62e9969fbe57 · outbound

This paper cites Event-triggered random delayed impulsive consensus of multi-agent systems with time-varying delay,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Event-triggered random delayed impulsive consensus of multi-agent systems with time-varying delay,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.117505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6ef0038c-e638-4b47-8260-e61b39cdd21f · outbound

This paper cites Behavior reasoning for opponent agents in multi- agent learning systems,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Behavior reasoning for opponent agents in multi- agent learning systems,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.062925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2d888786-07b9-49aa-b92b-a41f2618ad64 · outbound

This paper cites Adaptive trust model for multi-agent teaming based on reinforcement-learning-based fusion,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Adaptive trust model for multi-agent teaming based on reinforcement-learning-based fusion,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.052197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aee9a8c5-58be-452a-bec3-9bd7f24e4d53 · outbound

This paper cites The impact of perceived autonomous agents on dynamic team behaviors,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis The impact of perceived autonomous agents on dynamic team behaviors,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.041592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1b0217c6-0ad0-4110-88bd-401ae3b5275f · outbound

This paper cites Data-driven distributed output consensus control for multi-agent systems with unknown internal state,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Data-driven distributed output consensus control for multi-agent systems with unknown internal state,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.031537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 22978339-7394-43e0-b224-cc19e6840b30 · outbound

This paper cites A survey on neural network interpretability,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis A survey on neural network interpretability,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.021406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bcdb7601-82d0-474f-83fc-87d437bc80b2 · outbound

This paper cites Towards faithfully interpretable NLP systems: How should we define and evaluate faithfulness?.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Towards faithfully interpretable NLP systems: How should we define and evaluate faithfulness?

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:43.010624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3294f4ba-d32b-4236-8b19-c5ec84436d66 · outbound

This paper cites Lan- guage models don’t always say what they think: Unfaithful explanations in chain-of-thought prompting,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Lan- guage models don’t always say what they think: Unfaithful explanations in chain-of-thought prompting,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.999747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4d0e7551-cddf-45d7-8065-03b23fc74714 · outbound

This paper cites Hamiltonian systems and transformation in Hilbert space,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Hamiltonian systems and transformation in Hilbert space,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.988466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d2b0d746-4110-4f57-95d6-4821498d42d4 · outbound

This paper cites Spectral properties of dynamical systems, model reduction and decompositions,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Spectral properties of dynamical systems, model reduction and decompositions,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.977169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7ccb483b-f741-43e8-b924-4279e7c7ce9f · outbound

This paper cites Dynamic mode decomposition of numerical and experimental data,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Dynamic mode decomposition of numerical and experimental data,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.967328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fb260926-ab6d-4a80-92df-a562a0208db0 · outbound

This paper cites Dynamic mode decomposition and its variants,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Dynamic mode decomposition and its variants,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.955962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 415962f9-96a2-4265-bec5-907c1fef47ed · outbound

This paper cites Spectral analysis of nonlinear flows,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Spectral analysis of nonlinear flows,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.900139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 91a49d95-f3b1-4b9a-81aa-b58974bb2eb0 · outbound

This paper cites A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.786809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 73f602fd-1c57-42a8-beb6-619893a5fe40 · outbound

This paper cites On convergence of extended dynamic mode decomposition to the Koopman operator,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis On convergence of extended dynamic mode decomposition to the Koopman operator,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.681240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 98173640-0a1e-48b8-a9d9-b09249ac5537 · outbound

This paper cites Extended dynamic mode decomposition with dictionary learning: A data- driven adaptive spectral decomposition of the Koopman opera- tor,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Extended dynamic mode decomposition with dictionary learning: A data- driven adaptive spectral decomposition of the Koopman opera- tor,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.519953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 48b59e17-9880-447c-b37d-215e0071a51a · outbound

This paper cites Multi-Agent Collaboration Mechanisms: A Survey of LLMs.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Multi-Agent Collaboration Mechanisms: A Survey of LLMs

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T20:28:42.100172Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 080583bb-1d60-4277-935f-ff67671e2596 · outbound

This paper cites Data-driven approximation of the Koopman generator: Model reduction, system identification, and control,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Data-driven approximation of the Koopman generator: Model reduction, system identification, and control,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.509470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation af85d360-d238-40ce-82cf-ad7d1fbb049d · outbound

This paper cites Modern Koopman Theory for Dynamical Systems.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Modern Koopman Theory for Dynamical Systems

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T20:28:42.107981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 010e47c6-a7cc-434b-993e-5fb4d6d95218 · outbound

This paper cites Langchain & langgraph in production: Architec- tures for multi-agent llm systems,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Langchain & langgraph in production: Architec- tures for multi-agent llm systems,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.497220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f69d4ebc-e2a9-463a-bafe-87e9f98487af · outbound

This paper cites Multi-Agent Debate Strategies: Survey, Taxonomy, and Challenges.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Multi-Agent Debate Strategies: Survey, Taxonomy, and Challenges

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-07T20:28:42.359111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 505d4b53-bf42-4b20-8cb1-ddf115bf783d · outbound

This paper cites Consensus problems in networks of agents with switching topology and time-delays,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Consensus problems in networks of agents with switching topology and time-delays,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.485369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5b48ce01-fd4f-4a47-9fec-a63e884d7d18 · outbound

This paper cites Reaching a consensus,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Reaching a consensus,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.473391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 30c6fd0d-a569-4d12-b028-c4f109ad1834 · outbound

This paper cites Opinion dynamics and bounded confidence: Models, analysis and simulation,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Opinion dynamics and bounded confidence: Models, analysis and simulation,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.462747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a51b3546-78c8-4200-b6e4-4a8162cbb27d · outbound

This paper cites Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T20:28:42.302080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bcd0d2e1-fc7d-4e16-bae9-5646fd88ae25 · outbound

This paper cites Opinion dynamics with social confirmation effect: An adaptive Hegselmann-Krause model,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Opinion dynamics with social confirmation effect: An adaptive Hegselmann-Krause model,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.450494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation de742d38-cc66-4666-8e91-22c02fd1c13f · outbound

This paper cites Diffusion maps,.

Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis Diffusion maps,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T20:28:42.438119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

No inbound Pith citation observations are available.