{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4W2C4RQR5B666WW3WLYSQPXRXB","short_pith_number":"pith:4W2C4RQR","canonical_record":{"source":{"id":"1202.2951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-02-14T07:05:35Z","cross_cats_sorted":["cond-mat.stat-mech","q-bio.PE"],"title_canon_sha256":"53b6821b8c38f1e12db9ce47718a86bb8be104e40450c947f3328e759b7e1a2c","abstract_canon_sha256":"e9e8a23face94ee0dfa9499a0fb084f4430b76038f5a058601349cb8593fb0a9"},"schema_version":"1.0"},"canonical_sha256":"e5b42e4611e87def5adbb2f1283ef1b856649dcfb6b056c846d330f3d7b8a371","source":{"kind":"arxiv","id":"1202.2951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2951","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2951v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2951","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"4W2C4RQR5B66","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4W2C4RQR5B666WW3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4W2C4RQR","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4W2C4RQR5B666WW3WLYSQPXRXB","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-02-14T07:05:35Z","cross_cats_sorted":["cond-mat.stat-mech","q-bio.PE"],"title_canon_sha256":"53b6821b8c38f1e12db9ce47718a86bb8be104e40450c947f3328e759b7e1a2c","abstract_canon_sha256":"e9e8a23face94ee0dfa9499a0fb084f4430b76038f5a058601349cb8593fb0a9"},"schema_version":"1.0"},"canonical_sha256":"e5b42e4611e87def5adbb2f1283ef1b856649dcfb6b056c846d330f3d7b8a371","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:24.544568Z","signature_b64":"Yr3sBEpylSiSRVSgSzcDmnjewZBojCCUdL7PaTJVJnlPDC5XerVjM9YET6FWK1Lji8Z9eS9hIaohHUh+LdfCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5b42e4611e87def5adbb2f1283ef1b856649dcfb6b056c846d330f3d7b8a371","last_reissued_at":"2026-05-18T04:02:24.544031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:24.544031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2951","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":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uIL0aZxmnpjG87Aol63LMX/fXtN0+QiSlA0ey5QhtUsa+k8fYS5uC7+wPXI9qOA3YjQalLY9ZmIqNAO1lE7zBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:41:59.944375Z"},"content_sha256":"d3d11a4c961a24e4ea2c096eeaa0658f98fb4ec28c8f5d24a4b59b1e0e9d419b","schema_version":"1.0","event_id":"sha256:d3d11a4c961a24e4ea2c096eeaa0658f98fb4ec28c8f5d24a4b59b1e0e9d419b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4W2C4RQR5B666WW3WLYSQPXRXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Species Diversity in Rock-Paper-Scissors Game Coupling with Levy Flight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","q-bio.PE"],"primary_cat":"physics.bio-ph","authors_text":"Dong Wang, Jing Zhang, Qian Zhuang, Zengru Di","submitted_at":"2012-02-14T07:05:35Z","abstract_excerpt":"Rock-paper-scissors (RPS) game is a nice model to study the biodiversity in ecosystem. However, the previous studies only consider the nearest- neighbor- interaction among the species. In this paper, taking the long range migration into account, the effects of the interplay between nearest-neighbor-interaction and long-range-interaction of Levy flight obey the power law distance distribution with the exponent h (-0.3<h<-0.1) in spatial RPS game is investigated. Taking the probability of long range Levy flight and the power exponent as parameters, the coexistence conditions of three species are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2951","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":""},"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":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Vps6r7geNTNe5PTFzMikkw69kelhZJ1P89AabMcNxfXp9gHwi0HErJWwkUOjpsLC0CZG9/2P6azcv/uysmUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:41:59.944717Z"},"content_sha256":"5e4e1ef01bfb0fa509e5d7b2ca0c733f3bb2ed7c957fa7ab53935d3c561838fa","schema_version":"1.0","event_id":"sha256:5e4e1ef01bfb0fa509e5d7b2ca0c733f3bb2ed7c957fa7ab53935d3c561838fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4W2C4RQR5B666WW3WLYSQPXRXB/bundle.json","state_url":"https://pith.science/pith/4W2C4RQR5B666WW3WLYSQPXRXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4W2C4RQR5B666WW3WLYSQPXRXB/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":"2026-06-23T06:41:59Z","links":{"resolver":"https://pith.science/pith/4W2C4RQR5B666WW3WLYSQPXRXB","bundle":"https://pith.science/pith/4W2C4RQR5B666WW3WLYSQPXRXB/bundle.json","state":"https://pith.science/pith/4W2C4RQR5B666WW3WLYSQPXRXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4W2C4RQR5B666WW3WLYSQPXRXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4W2C4RQR5B666WW3WLYSQPXRXB","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":"e9e8a23face94ee0dfa9499a0fb084f4430b76038f5a058601349cb8593fb0a9","cross_cats_sorted":["cond-mat.stat-mech","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-02-14T07:05:35Z","title_canon_sha256":"53b6821b8c38f1e12db9ce47718a86bb8be104e40450c947f3328e759b7e1a2c"},"schema_version":"1.0","source":{"id":"1202.2951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2951","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2951v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2951","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"4W2C4RQR5B66","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4W2C4RQR5B666WW3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4W2C4RQR","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:5e4e1ef01bfb0fa509e5d7b2ca0c733f3bb2ed7c957fa7ab53935d3c561838fa","target":"graph","created_at":"2026-05-18T04:02:24Z","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"},"paper":{"abstract_excerpt":"Rock-paper-scissors (RPS) game is a nice model to study the biodiversity in ecosystem. However, the previous studies only consider the nearest- neighbor- interaction among the species. In this paper, taking the long range migration into account, the effects of the interplay between nearest-neighbor-interaction and long-range-interaction of Levy flight obey the power law distance distribution with the exponent h (-0.3<h<-0.1) in spatial RPS game is investigated. Taking the probability of long range Levy flight and the power exponent as parameters, the coexistence conditions of three species are","authors_text":"Dong Wang, Jing Zhang, Qian Zhuang, Zengru Di","cross_cats":["cond-mat.stat-mech","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-02-14T07:05:35Z","title":"Species Diversity in Rock-Paper-Scissors Game Coupling with Levy Flight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2951","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:d3d11a4c961a24e4ea2c096eeaa0658f98fb4ec28c8f5d24a4b59b1e0e9d419b","target":"record","created_at":"2026-05-18T04:02:24Z","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":"e9e8a23face94ee0dfa9499a0fb084f4430b76038f5a058601349cb8593fb0a9","cross_cats_sorted":["cond-mat.stat-mech","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-02-14T07:05:35Z","title_canon_sha256":"53b6821b8c38f1e12db9ce47718a86bb8be104e40450c947f3328e759b7e1a2c"},"schema_version":"1.0","source":{"id":"1202.2951","kind":"arxiv","version":1}},"canonical_sha256":"e5b42e4611e87def5adbb2f1283ef1b856649dcfb6b056c846d330f3d7b8a371","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5b42e4611e87def5adbb2f1283ef1b856649dcfb6b056c846d330f3d7b8a371","first_computed_at":"2026-05-18T04:02:24.544031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:24.544031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yr3sBEpylSiSRVSgSzcDmnjewZBojCCUdL7PaTJVJnlPDC5XerVjM9YET6FWK1Lji8Z9eS9hIaohHUh+LdfCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:24.544568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3d11a4c961a24e4ea2c096eeaa0658f98fb4ec28c8f5d24a4b59b1e0e9d419b","sha256:5e4e1ef01bfb0fa509e5d7b2ca0c733f3bb2ed7c957fa7ab53935d3c561838fa"],"state_sha256":"19fba5de9dbb02eb975c0493e8220c30429061caab0b15248445625e265bc652"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6R/DQaavx0XACS/Qe+H/R/u16kXvPbNBb6S+PNF59diCqG47jbroBptcpv/mQWzRRIEo2NOsQyDEM1ffi+lDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:41:59.946642Z","bundle_sha256":"982128e6b06d82d9709a28faa66a9e8e5ca8fbd3890f5ad3a5c5741cb8887035"}}