{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3RACWTCYGME2ZMOFSHS7XOT2PW","short_pith_number":"pith:3RACWTCY","canonical_record":{"source":{"id":"2512.07588","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2025-12-08T14:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"6251a4445d745db41c807e1a89cdb677b557e2d136301b27a0dab0aaef731edf","abstract_canon_sha256":"477ad875bc80cd25a2740d76c4ff9ff8dc6ce99ab17adc9f1de8cd27bca39e13"},"schema_version":"1.0"},"canonical_sha256":"dc402b4c583309acb1c591e5fbba7a7db6ebab283821850080415d3e6066d532","source":{"kind":"arxiv","id":"2512.07588","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.07588","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"2512.07588v2","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.07588","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"3RACWTCYGME2","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"pith_short_16","alias_value":"3RACWTCYGME2ZMOF","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"pith_short_8","alias_value":"3RACWTCY","created_at":"2026-05-29T02:05:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3RACWTCYGME2ZMOFSHS7XOT2PW","target":"record","payload":{"canonical_record":{"source":{"id":"2512.07588","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2025-12-08T14:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"6251a4445d745db41c807e1a89cdb677b557e2d136301b27a0dab0aaef731edf","abstract_canon_sha256":"477ad875bc80cd25a2740d76c4ff9ff8dc6ce99ab17adc9f1de8cd27bca39e13"},"schema_version":"1.0"},"canonical_sha256":"dc402b4c583309acb1c591e5fbba7a7db6ebab283821850080415d3e6066d532","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:38.229494Z","signature_b64":"dx3wpVXcitTHyzQ8UhV/NDh+qNbimzhaFmgBapAQywRXZVdTT0DNzFq9TWO96EYeo1xFrpkwKJ3eVjDc664/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc402b4c583309acb1c591e5fbba7a7db6ebab283821850080415d3e6066d532","last_reissued_at":"2026-05-29T02:05:38.228954Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:38.228954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.07588","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o3nCGRAizHBYWGjxKnUP9aoiTVoZ216gVvgVxl8bTQU/WOpxbxRnhBGpomPB4kIzHkGSEAtHkd67VQGGHFoXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T15:15:52.029745Z"},"content_sha256":"3c650d95379d8cdc65e65ec504b4a327e4f46073133e6bde39432f6685596c00","schema_version":"1.0","event_id":"sha256:3c650d95379d8cdc65e65ec504b4a327e4f46073133e6bde39432f6685596c00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3RACWTCYGME2ZMOFSHS7XOT2PW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Agent-Centric Dynamical Systems Perspective on Multi-Agent Reinforcement Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.MA","authors_text":"James Rudd-Jones, Mar\\'ia P\\'erez-Ortiz, Mirco Musolesi","submitted_at":"2025-12-08T14:30:25Z","abstract_excerpt":"Analysing learning in Multi-Agent Reinforcement Learning (MARL) environments is challenging, in particular with respect to \\textit{individual} decision-making. Practitioners frequently struggle to compare training runs due to the inherent stochasticity in algorithms arising from random dithering exploration, environment transition noise, and stochastic gradient updates to name a few. Traditional analytical approaches, such as replicator dynamics, oft rely on mean-field approximations to remove stochastic effects, but this simplification, whilst able to provide general overall trends, can lead "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.07588","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.07588/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ho4x7itYHJnGqB6xtUpfAc0lKZbogSayhm/lKOZr7ootKpGECxUjWisjPCS/KtkOCmP/iROB6V8TsY6Jrzw0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T15:15:52.030116Z"},"content_sha256":"d9251208b32f1e6f0a58a17f35eb06efbc96b6100ac86a07000d2e27581daebd","schema_version":"1.0","event_id":"sha256:d9251208b32f1e6f0a58a17f35eb06efbc96b6100ac86a07000d2e27581daebd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RACWTCYGME2ZMOFSHS7XOT2PW/bundle.json","state_url":"https://pith.science/pith/3RACWTCYGME2ZMOFSHS7XOT2PW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RACWTCYGME2ZMOFSHS7XOT2PW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T15:15:52Z","links":{"resolver":"https://pith.science/pith/3RACWTCYGME2ZMOFSHS7XOT2PW","bundle":"https://pith.science/pith/3RACWTCYGME2ZMOFSHS7XOT2PW/bundle.json","state":"https://pith.science/pith/3RACWTCYGME2ZMOFSHS7XOT2PW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RACWTCYGME2ZMOFSHS7XOT2PW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3RACWTCYGME2ZMOFSHS7XOT2PW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"477ad875bc80cd25a2740d76c4ff9ff8dc6ce99ab17adc9f1de8cd27bca39e13","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2025-12-08T14:30:25Z","title_canon_sha256":"6251a4445d745db41c807e1a89cdb677b557e2d136301b27a0dab0aaef731edf"},"schema_version":"1.0","source":{"id":"2512.07588","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.07588","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"2512.07588v2","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.07588","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"3RACWTCYGME2","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"pith_short_16","alias_value":"3RACWTCYGME2ZMOF","created_at":"2026-05-29T02:05:38Z"},{"alias_kind":"pith_short_8","alias_value":"3RACWTCY","created_at":"2026-05-29T02:05:38Z"}],"graph_snapshots":[{"event_id":"sha256:d9251208b32f1e6f0a58a17f35eb06efbc96b6100ac86a07000d2e27581daebd","target":"graph","created_at":"2026-05-29T02:05:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.07588/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Analysing learning in Multi-Agent Reinforcement Learning (MARL) environments is challenging, in particular with respect to \\textit{individual} decision-making. Practitioners frequently struggle to compare training runs due to the inherent stochasticity in algorithms arising from random dithering exploration, environment transition noise, and stochastic gradient updates to name a few. Traditional analytical approaches, such as replicator dynamics, oft rely on mean-field approximations to remove stochastic effects, but this simplification, whilst able to provide general overall trends, can lead ","authors_text":"James Rudd-Jones, Mar\\'ia P\\'erez-Ortiz, Mirco Musolesi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2025-12-08T14:30:25Z","title":"An Agent-Centric Dynamical Systems Perspective on Multi-Agent Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.07588","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3c650d95379d8cdc65e65ec504b4a327e4f46073133e6bde39432f6685596c00","target":"record","created_at":"2026-05-29T02:05:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"477ad875bc80cd25a2740d76c4ff9ff8dc6ce99ab17adc9f1de8cd27bca39e13","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2025-12-08T14:30:25Z","title_canon_sha256":"6251a4445d745db41c807e1a89cdb677b557e2d136301b27a0dab0aaef731edf"},"schema_version":"1.0","source":{"id":"2512.07588","kind":"arxiv","version":2}},"canonical_sha256":"dc402b4c583309acb1c591e5fbba7a7db6ebab283821850080415d3e6066d532","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc402b4c583309acb1c591e5fbba7a7db6ebab283821850080415d3e6066d532","first_computed_at":"2026-05-29T02:05:38.228954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:38.228954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dx3wpVXcitTHyzQ8UhV/NDh+qNbimzhaFmgBapAQywRXZVdTT0DNzFq9TWO96EYeo1xFrpkwKJ3eVjDc664/BQ==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:38.229494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.07588","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c650d95379d8cdc65e65ec504b4a327e4f46073133e6bde39432f6685596c00","sha256:d9251208b32f1e6f0a58a17f35eb06efbc96b6100ac86a07000d2e27581daebd"],"state_sha256":"ceaba56c6698b59dc11e88054dccf212291174dd84e29ffe7c4b30192f128644"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLhFqVS4P4oWxHZRH/PdsfZZv4NHZHawHap1EB663iYvl64iIvTTB8w2A8t8rx1r5hrG4LzuiLkZD6e/Hc5zDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T15:15:52.032589Z","bundle_sha256":"a10e53f5be45169bd699a96cf94e0cbd14896939cb49a79187cbbd5f232e7615"}}