{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YYRBUHJ3IWD2D2YTCIWW4ULNPV","short_pith_number":"pith:YYRBUHJ3","canonical_record":{"source":{"id":"1210.0018","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-28T20:02:45Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"17d7959bf53ef3780de04475b1f0ef7b814cb3800e973a6eb6610e2cf2fc0a5e","abstract_canon_sha256":"93d13eeb51e460f68557fb65dd36988285074a84054d9c5af5a3e1faae02b8f9"},"schema_version":"1.0"},"canonical_sha256":"c6221a1d3b4587a1eb13122d6e516d7d4730b67946eeb4d1045e623e3df4a01c","source":{"kind":"arxiv","id":"1210.0018","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0018","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0018v4","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0018","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"YYRBUHJ3IWD2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YYRBUHJ3IWD2D2YT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YYRBUHJ3","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YYRBUHJ3IWD2D2YTCIWW4ULNPV","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0018","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-28T20:02:45Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"17d7959bf53ef3780de04475b1f0ef7b814cb3800e973a6eb6610e2cf2fc0a5e","abstract_canon_sha256":"93d13eeb51e460f68557fb65dd36988285074a84054d9c5af5a3e1faae02b8f9"},"schema_version":"1.0"},"canonical_sha256":"c6221a1d3b4587a1eb13122d6e516d7d4730b67946eeb4d1045e623e3df4a01c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:49.844740Z","signature_b64":"ubaA2YNcLnFucBrU7a8oMCodZgB1zYL1l1ZUDeFccokI3BxkEEM2L6XAhS32xxyqGk05pHMppQVgimkt4Gw9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6221a1d3b4587a1eb13122d6e516d7d4730b67946eeb4d1045e623e3df4a01c","last_reissued_at":"2026-05-18T02:45:49.844343Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:49.844343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0018","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrRmyLSenLTER1KAMF1ucxoaZLys/upVy0ACLGa807qyUg+urgvEENPlNl1fu6i/vScH4ieeHv85a7heB2EUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:42:37.426658Z"},"content_sha256":"ed28252470fab081b9dd119adde50c32c4008466969d9f2af0548ead343541b9","schema_version":"1.0","event_id":"sha256:ed28252470fab081b9dd119adde50c32c4008466969d9f2af0548ead343541b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YYRBUHJ3IWD2D2YTCIWW4ULNPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Survival of the Scarcer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alan Gabel, Baruch Meerson, S. Redner","submitted_at":"2012-09-28T20:02:45Z","abstract_excerpt":"We investigate extinction dynamics in the paradigmatic model of two competing species A and B that reproduce (A-->2A, B-->2B), self-regulate by annihilation (2A-->0, 2B-->0), and compete (A+B-->A, A+B-->B). For a finite system that is in the well-mixed limit, a quasi-stationary state arises which describes coexistence of the two species. Because of discrete noise, both species eventually become extinct in time that is exponentially long in the quasi-stationary population size. For a sizable range of asymmetries in the growth and competition rates, the paradoxical situation arises in which the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0018","kind":"arxiv","version":4},"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":"2026-05-18T02:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I07pgtvGsa9k0i97iP79QAZdKOO3vqy5xBZHpOP6/Hz8uktp/j3myQFdKdL4anZ+bRXvHkyEuLnxVXQ0VR2kAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:42:37.427194Z"},"content_sha256":"459473d6bb0d1ed2aee4f8f00cecff6152d3a4bc6d27a6f6a8dd0d25a5c1ff24","schema_version":"1.0","event_id":"sha256:459473d6bb0d1ed2aee4f8f00cecff6152d3a4bc6d27a6f6a8dd0d25a5c1ff24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYRBUHJ3IWD2D2YTCIWW4ULNPV/bundle.json","state_url":"https://pith.science/pith/YYRBUHJ3IWD2D2YTCIWW4ULNPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYRBUHJ3IWD2D2YTCIWW4ULNPV/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":"2026-06-05T00:42:37Z","links":{"resolver":"https://pith.science/pith/YYRBUHJ3IWD2D2YTCIWW4ULNPV","bundle":"https://pith.science/pith/YYRBUHJ3IWD2D2YTCIWW4ULNPV/bundle.json","state":"https://pith.science/pith/YYRBUHJ3IWD2D2YTCIWW4ULNPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYRBUHJ3IWD2D2YTCIWW4ULNPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YYRBUHJ3IWD2D2YTCIWW4ULNPV","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":"93d13eeb51e460f68557fb65dd36988285074a84054d9c5af5a3e1faae02b8f9","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-28T20:02:45Z","title_canon_sha256":"17d7959bf53ef3780de04475b1f0ef7b814cb3800e973a6eb6610e2cf2fc0a5e"},"schema_version":"1.0","source":{"id":"1210.0018","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0018","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0018v4","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0018","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"YYRBUHJ3IWD2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YYRBUHJ3IWD2D2YT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YYRBUHJ3","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:459473d6bb0d1ed2aee4f8f00cecff6152d3a4bc6d27a6f6a8dd0d25a5c1ff24","target":"graph","created_at":"2026-05-18T02:45:49Z","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":"We investigate extinction dynamics in the paradigmatic model of two competing species A and B that reproduce (A-->2A, B-->2B), self-regulate by annihilation (2A-->0, 2B-->0), and compete (A+B-->A, A+B-->B). For a finite system that is in the well-mixed limit, a quasi-stationary state arises which describes coexistence of the two species. Because of discrete noise, both species eventually become extinct in time that is exponentially long in the quasi-stationary population size. For a sizable range of asymmetries in the growth and competition rates, the paradoxical situation arises in which the ","authors_text":"Alan Gabel, Baruch Meerson, S. Redner","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-28T20:02:45Z","title":"Survival of the Scarcer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0018","kind":"arxiv","version":4},"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:ed28252470fab081b9dd119adde50c32c4008466969d9f2af0548ead343541b9","target":"record","created_at":"2026-05-18T02:45:49Z","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":"93d13eeb51e460f68557fb65dd36988285074a84054d9c5af5a3e1faae02b8f9","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-28T20:02:45Z","title_canon_sha256":"17d7959bf53ef3780de04475b1f0ef7b814cb3800e973a6eb6610e2cf2fc0a5e"},"schema_version":"1.0","source":{"id":"1210.0018","kind":"arxiv","version":4}},"canonical_sha256":"c6221a1d3b4587a1eb13122d6e516d7d4730b67946eeb4d1045e623e3df4a01c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6221a1d3b4587a1eb13122d6e516d7d4730b67946eeb4d1045e623e3df4a01c","first_computed_at":"2026-05-18T02:45:49.844343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:49.844343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ubaA2YNcLnFucBrU7a8oMCodZgB1zYL1l1ZUDeFccokI3BxkEEM2L6XAhS32xxyqGk05pHMppQVgimkt4Gw9Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:49.844740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0018","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed28252470fab081b9dd119adde50c32c4008466969d9f2af0548ead343541b9","sha256:459473d6bb0d1ed2aee4f8f00cecff6152d3a4bc6d27a6f6a8dd0d25a5c1ff24"],"state_sha256":"640891e5283c252cbd1cfcf789a70e5463681c97227b4c006f5860ebbf89deb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5byphi9izPwYKRjJsVdVgvNgGgUpcySRhBpafcWH4Ah9PS3PZj83+qxc7nXZ79QmpahruOnO6AIoH4obVYklAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:42:37.429790Z","bundle_sha256":"c2f5bafd442946d15e6cc2d1af965df7a194d26c59a6a4280418f027bbc112c0"}}