Paper Citation Record · LEDGER

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game

As of 19 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2607.08692.

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

pith.paper-citation-record.v1
2607.08692 v1

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-10T03:06:20.668165Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

44 of 44 outbound references displayed

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unresolved2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 990a7447-1fe4-4912-a6a0-9b6a249fc089 · outbound

This paper cites The Lean 4 theorem prover and program- ming language,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game The Lean 4 theorem prover and program- ming language,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.786963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5107d4d5-6f5f-4130-a473-dd6233971c6c · outbound

This paper cites Pok ´emon tcg tournament metagame aggregates,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Pok ´emon tcg tournament metagame aggregates,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.809270Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e13365a8-73a7-42a5-b2e6-cb6e03f4e385 · outbound

This paper cites Limitless tcg tournament platform,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Limitless tcg tournament platform,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.772605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ca64c18c-3da6-43c7-9b57-2f7565ff7b27 · outbound

This paper cites Programming a computer for playing chess,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Programming a computer for playing chess,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.752685Z

Source-reported events for the cited work

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Observation 831da710-a31a-4e89-8f58-516aca0ddbcf · outbound

This paper cites On the complexity of some two-person perfect- information games,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game On the complexity of some two-person perfect- information games,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.807747Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0ca026b4-3b8b-4b95-b19a-1d8197d62e6c · outbound

This paper cites Computing a perfect strategy for n×nchess requires time exponential inn,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Computing a perfect strategy for n×nchess requires time exponential inn,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.770517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 77b73f19-12e0-45d2-b767-bd48f40a851d · outbound

This paper cites Heads-up limit hold’em poker is solved,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Heads-up limit hold’em poker is solved,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.768241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1cf7c41e-ede0-4169-b6ad-d961171f1b64 · outbound

This paper cites Superhuman AI for heads-up no-limit poker: Libratus beats top professionals,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Superhuman AI for heads-up no-limit poker: Libratus beats top professionals,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.807553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 410e2ded-f81e-4317-bfd6-b51ae91f3214 · outbound

This paper cites Superhuman AI for multiplayer poker,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Superhuman AI for multiplayer poker,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.809492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4cd428be-2df7-4134-abb8-d4518e57a6fe · outbound

This paper cites A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.811294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1fc6eab7-05fd-4735-9e1e-969ba5955790 · outbound

This paper cites Grandmaster level in StarCraft II using multi-agent reinforcement learning,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Grandmaster level in StarCraft II using multi-agent reinforcement learning,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.815153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6b0d2404-73b4-4300-b005-817e437b4a2f · outbound

This paper cites Ensemble determinization in Monte Carlo tree search for the imperfect information card game Magic: The gathering,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Ensemble determinization in Monte Carlo tree search for the imperfect information card game Magic: The gathering,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.829053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 638d259e-313f-4467-ab51-3558ba0b6e93 · outbound

This paper cites Monte Carlo search applied to card selection in Magic: The Gathering,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Monte Carlo search applied to card selection in Magic: The Gathering,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.831419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 02efcdfe-f935-4255-9ae1-3b63717839a2 · outbound

This paper cites Monte Carlo tree search experi- ments in Hearthstone,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Monte Carlo tree search experi- ments in Hearthstone,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.787394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3a2d38db-6d0e-4a29-a413-4f36a45a2dd7 · outbound

This paper cites Improving Hearthstone AI by combining MCTS and supervised learning algorithms,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Improving Hearthstone AI by combining MCTS and supervised learning algorithms,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.743190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1a7ca4e9-c227-49c3-997c-0dc6406f6e65 · outbound

This paper cites Deckbuilding in Magic: The Gathering using a genetic algorithm,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Deckbuilding in Magic: The Gathering using a genetic algorithm,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.819282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1851711f-501b-454e-84e3-d0b40843d335 · outbound

This paper cites Introducing the Hearthstone-AI Competition.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Introducing the Hearthstone-AI Competition

Reference 17

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Source-reported events for the cited work

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Observation da74614c-36dc-4240-9ea3-75043290c9c3 · outbound

This paper cites Summarizing strategy card game AI competition,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Summarizing strategy card game AI competition,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.779714Z

Source-reported events for the cited work

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Observation 39477bdc-2147-4e70-b071-85953d2321f6 · outbound

This paper cites Formal proof — the four-color theorem,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Formal proof — the four-color theorem,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.795447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b353f006-d17f-499d-925d-81c80ad16f59 · outbound

This paper cites A formally verified proof of the prime number theorem,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game A formally verified proof of the prime number theorem,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.803945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 04a7abc1-30bc-45c3-9b26-e0dde1920e0d · outbound

This paper cites The Lean mathematical library,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game The Lean mathematical library,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.790393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e1f2d558-73e0-47e0-8984-6a17ff3b37ba · outbound

This paper cites A formal proof of the kepler conjecture,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game A formal proof of the kepler conjecture,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.825017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 56b61b91-0851-4506-a21d-eab219b90c41 · outbound

This paper cites Towards formal verification of card game mechanics,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Towards formal verification of card game mechanics,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.789485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a9c32300-4d35-4490-9174-284488d58844 · outbound

This paper cites The logic of animal conflict,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game The logic of animal conflict,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.785412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ad6bfebd-c08b-4af4-ab9f-b0fe85f4ede3 · outbound

This paper cites Evolutionary stable strategies and game dynamics,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Evolutionary stable strategies and game dynamics,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.799545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 492945af-ac84-45aa-800a-612fe3b320d7 · outbound

This paper cites an unresolved cited work.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-07-10T03:06:43.793552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8247819f-50e7-4b2d-82cc-d51656926727 · outbound

This paper cites Pok ´emon trading card game — rules & resources,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Pok ´emon trading card game — rules & resources,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.783002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 028eee78-b3d8-4154-a7e4-1b3ce0efe33c · outbound

This paper cites Play pok ´emon tournament rules handbook,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Play pok ´emon tournament rules handbook,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.805659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 05c7a84e-2d7b-493b-8345-83f7dda3e904 · outbound

This paper cites Probable inference, the law of succession, and statistical inference.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Probable inference, the law of succession, and statistical inference

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.794062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a09d84a6-f51f-4745-bff4-504df536295e · outbound

This paper cites Judgment under uncertainty: Heuristics and biases.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Judgment under uncertainty: Heuristics and biases

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.827012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4d50ac9b-2a4b-4fab-bc3d-69cb6eba94db · outbound

This paper cites Prospect theory: An analysis of decision under risk.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Prospect theory: An analysis of decision under risk

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.791328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 46e72142-1c17-4ea4-a256-ffd25bec5089 · outbound

This paper cites A simple model of herd behavior,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game A simple model of herd behavior,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.744868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1e360908-2bf9-4943-aa05-3714d4289304 · outbound

This paper cites A theory of fads, fashion, custom, and cultural change as informational cascades,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game A theory of fads, fashion, custom, and cultural change as informational cascades,

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.821268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 094afe5c-de83-4fd1-8a73-d73341a9e27e · outbound

This paper cites Quantal response equilibria for normal form games.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Quantal response equilibria for normal form games

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.813150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ec303de0-31c0-470b-89a1-24891228a231 · outbound

This paper cites Unraveling in guessing games: An experimental study,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Unraveling in guessing games: An experimental study,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.781276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3049b37b-bf0f-40ae-a14b-2771bf70289b · outbound

This paper cites Nisan, T.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Nisan, T

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.803477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 183b0f6a-ef4d-4153-a193-329ae966bb99 · outbound

This paper cites Equilibrium points inn-person games,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Equilibrium points inn-person games,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.761041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 35d24b0d-aff0-4f55-a6d9-89f6a9db8b9e · outbound

This paper cites Zur Theorie der Gesellschaftsspiele,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Zur Theorie der Gesellschaftsspiele,

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.795640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3c0dfe31-0554-47b9-bb49-c09020740041 · outbound

This paper cites Parameter estimation in large dynamic paired com- parison experiments,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Parameter estimation in large dynamic paired com- parison experiments,

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.817211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 52c23e51-4407-44ab-89c7-cf8546e3920d · outbound

This paper cites TrueSkill: A Bayesian skill rating system,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game TrueSkill: A Bayesian skill rating system,

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.823233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 96f53689-2796-42d9-bd90-c6e2fd47ab40 · outbound

This paper cites Hofbauer and K.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Hofbauer and K

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.767734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3eeafd7a-525e-478e-a31d-9d2abf79d495 · outbound

This paper cites an unresolved cited work.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-07-10T03:06:43.766170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cff8dace-ff3b-45f9-b07b-f3407d2a7dd4 · outbound

This paper cites Analysis of swiss-system tournament pair- ings,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Analysis of swiss-system tournament pair- ings,

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T03:06:43.797553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 225a38bc-b206-44a0-a1c1-ac6d9602c732 · outbound

This paper cites Formally verified Pok ´emon TCG metagame analysis: Tournament data, matchup matrices, and Lean 4 proof artifact,.

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game Formally verified Pok ´emon TCG metagame analysis: Tournament data, matchup matrices, and Lean 4 proof artifact,

Reference 44

Resolution: verified exact; doi, observed 2026-07-10T03:06:43.379791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.