{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3G4V2XKXCZ6BZJB5C5TECCRBJG","short_pith_number":"pith:3G4V2XKX","canonical_record":{"source":{"id":"2504.06769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-04-09T10:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"f48ebaf820d3381160b9ba440cfe5ca0da896b07d17cf640f7d1c4afb1039897","abstract_canon_sha256":"24e44189c79cc2f5d8328a74e16fbe8e145045388764d3d2c2f545e3f5ed3c00"},"schema_version":"1.0"},"canonical_sha256":"d9b95d5d57167c1ca43d1766410a2149a1649a15dacb2c2c215afd6cb573bc7e","source":{"kind":"arxiv","id":"2504.06769","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.06769","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"2504.06769v1","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.06769","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"3G4V2XKXCZ6B","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"pith_short_16","alias_value":"3G4V2XKXCZ6BZJB5","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"pith_short_8","alias_value":"3G4V2XKX","created_at":"2026-07-05T10:46:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3G4V2XKXCZ6BZJB5C5TECCRBJG","target":"record","payload":{"canonical_record":{"source":{"id":"2504.06769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-04-09T10:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"f48ebaf820d3381160b9ba440cfe5ca0da896b07d17cf640f7d1c4afb1039897","abstract_canon_sha256":"24e44189c79cc2f5d8328a74e16fbe8e145045388764d3d2c2f545e3f5ed3c00"},"schema_version":"1.0"},"canonical_sha256":"d9b95d5d57167c1ca43d1766410a2149a1649a15dacb2c2c215afd6cb573bc7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:46:45.575227Z","signature_b64":"bSyRcRXFWPCmggUBfLwbDWQRAxYUkKTj5oRSstC4tWyKBIkZXX/5Mcx1t7N3SdVFFai6boP6XSp/9s58VTmJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9b95d5d57167c1ca43d1766410a2149a1649a15dacb2c2c215afd6cb573bc7e","last_reissued_at":"2026-07-05T10:46:45.574767Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:46:45.574767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.06769","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iObiZk3igb0Pj38xJULl1n2H2w19WqSIZjtyZ5Vo+xpwC8CsSITSxw9MH1K2JH1KQxU/sbMS9Lcb2F2f2gQNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:44:56.746400Z"},"content_sha256":"43dcd0d03c56ab8c0326bfc59d6cb8d16243a3db8cb3db0f2d47f0c3bab4d345","schema_version":"1.0","event_id":"sha256:43dcd0d03c56ab8c0326bfc59d6cb8d16243a3db8cb3db0f2d47f0c3bab4d345"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3G4V2XKXCZ6BZJB5C5TECCRBJG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolutionary dynamics of continuous public goods games in structured populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Attila Szolnoki, Duozi Lin, Jing Luo, Xiaojie Chen","submitted_at":"2025-04-09T10:47:05Z","abstract_excerpt":"Over the past few decades, many works have studied the evolutionary dynamics of continuous games. However, previous works have primarily focused on two-player games with pairwise interactions. Indeed, group interactions rather than pairwise interactions are usually found in real situations. The public goods game serves as a paradigm of multi-player interactions. Notably, various types of benefit functions are typically considered in public goods games, including linear, saturating, and sigmoid functions. Thus far, the evolutionary dynamics of cooperation in continuous public goods games with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06769","kind":"arxiv","version":1},"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/2504.06769/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":"2026-07-05T10:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhMTOmqOS70GqJDnpfRz13phex30HLenv869ipQbUQaQ0J/0EEzm7hrYW+ZLmeH/sOF5e6Ze2GzzavvcElGFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:44:56.746952Z"},"content_sha256":"7465bccd55f5e8ec99e70960b56b3f41217feca1c8470efe8211cc72f6cd4c5f","schema_version":"1.0","event_id":"sha256:7465bccd55f5e8ec99e70960b56b3f41217feca1c8470efe8211cc72f6cd4c5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3G4V2XKXCZ6BZJB5C5TECCRBJG/bundle.json","state_url":"https://pith.science/pith/3G4V2XKXCZ6BZJB5C5TECCRBJG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3G4V2XKXCZ6BZJB5C5TECCRBJG/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":"2026-08-10T12:44:56Z","links":{"resolver":"https://pith.science/pith/3G4V2XKXCZ6BZJB5C5TECCRBJG","bundle":"https://pith.science/pith/3G4V2XKXCZ6BZJB5C5TECCRBJG/bundle.json","state":"https://pith.science/pith/3G4V2XKXCZ6BZJB5C5TECCRBJG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3G4V2XKXCZ6BZJB5C5TECCRBJG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3G4V2XKXCZ6BZJB5C5TECCRBJG","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":"24e44189c79cc2f5d8328a74e16fbe8e145045388764d3d2c2f545e3f5ed3c00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-04-09T10:47:05Z","title_canon_sha256":"f48ebaf820d3381160b9ba440cfe5ca0da896b07d17cf640f7d1c4afb1039897"},"schema_version":"1.0","source":{"id":"2504.06769","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.06769","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"2504.06769v1","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.06769","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"3G4V2XKXCZ6B","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"pith_short_16","alias_value":"3G4V2XKXCZ6BZJB5","created_at":"2026-07-05T10:46:45Z"},{"alias_kind":"pith_short_8","alias_value":"3G4V2XKX","created_at":"2026-07-05T10:46:45Z"}],"graph_snapshots":[{"event_id":"sha256:7465bccd55f5e8ec99e70960b56b3f41217feca1c8470efe8211cc72f6cd4c5f","target":"graph","created_at":"2026-07-05T10:46:45Z","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/2504.06769/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Over the past few decades, many works have studied the evolutionary dynamics of continuous games. However, previous works have primarily focused on two-player games with pairwise interactions. Indeed, group interactions rather than pairwise interactions are usually found in real situations. The public goods game serves as a paradigm of multi-player interactions. Notably, various types of benefit functions are typically considered in public goods games, including linear, saturating, and sigmoid functions. Thus far, the evolutionary dynamics of cooperation in continuous public goods games with t","authors_text":"Attila Szolnoki, Duozi Lin, Jing Luo, Xiaojie Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-04-09T10:47:05Z","title":"Evolutionary dynamics of continuous public goods games in structured populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06769","kind":"arxiv","version":1},"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":"sha256:43dcd0d03c56ab8c0326bfc59d6cb8d16243a3db8cb3db0f2d47f0c3bab4d345","target":"record","created_at":"2026-07-05T10:46:45Z","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":"24e44189c79cc2f5d8328a74e16fbe8e145045388764d3d2c2f545e3f5ed3c00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-04-09T10:47:05Z","title_canon_sha256":"f48ebaf820d3381160b9ba440cfe5ca0da896b07d17cf640f7d1c4afb1039897"},"schema_version":"1.0","source":{"id":"2504.06769","kind":"arxiv","version":1}},"canonical_sha256":"d9b95d5d57167c1ca43d1766410a2149a1649a15dacb2c2c215afd6cb573bc7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9b95d5d57167c1ca43d1766410a2149a1649a15dacb2c2c215afd6cb573bc7e","first_computed_at":"2026-07-05T10:46:45.574767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:46:45.574767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bSyRcRXFWPCmggUBfLwbDWQRAxYUkKTj5oRSstC4tWyKBIkZXX/5Mcx1t7N3SdVFFai6boP6XSp/9s58VTmJAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:46:45.575227Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.06769","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43dcd0d03c56ab8c0326bfc59d6cb8d16243a3db8cb3db0f2d47f0c3bab4d345","sha256:7465bccd55f5e8ec99e70960b56b3f41217feca1c8470efe8211cc72f6cd4c5f"],"state_sha256":"cf4f4d71a6c58bfa568f54d11e866283de2ae205cbea2b177f52f8d7811caabf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lB55xObzDV4ylY5lLtRMOnxSkmJVILhWn3BG1Wyf0pauuyTAAxuHE6XKLIKfV8vEvNBdGiZW8MIzYgK6j9kAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T12:44:56.750205Z","bundle_sha256":"e26bdc719f35d75a4fc62974c6f619f4f67d41b49e156c4f9e7d0fbb5456a5d9"}}