{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:W6XPLZXFSETZFG4TS473ZI3YAM","short_pith_number":"pith:W6XPLZXF","canonical_record":{"source":{"id":"1609.05738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-09-19T14:15:07Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"53d70344dc6a61b04d3718d5d8d96923c522d0b86bcb792d7d5db936685c9fc8","abstract_canon_sha256":"fd95da22d7dab97a9eef1eadfe3104d34e35b6b3f375957d626d9dcc634e59e3"},"schema_version":"1.0"},"canonical_sha256":"b7aef5e6e59127929b93973fbca378030c5ec9a677f7355bdcd1be65d29fc5bd","source":{"kind":"arxiv","id":"1609.05738","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05738","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05738v1","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05738","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"W6XPLZXFSETZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W6XPLZXFSETZFG4T","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W6XPLZXF","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:W6XPLZXFSETZFG4TS473ZI3YAM","target":"record","payload":{"canonical_record":{"source":{"id":"1609.05738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-09-19T14:15:07Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"53d70344dc6a61b04d3718d5d8d96923c522d0b86bcb792d7d5db936685c9fc8","abstract_canon_sha256":"fd95da22d7dab97a9eef1eadfe3104d34e35b6b3f375957d626d9dcc634e59e3"},"schema_version":"1.0"},"canonical_sha256":"b7aef5e6e59127929b93973fbca378030c5ec9a677f7355bdcd1be65d29fc5bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:25.456515Z","signature_b64":"bfyFiYO6FNdt6EmV13SPE0hJy8DHn7ZtVfabx5LnAWQGo5+SwX4YOWsm+HMgT7pXFIKHoZAwm2HQfY7p9F4rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7aef5e6e59127929b93973fbca378030c5ec9a677f7355bdcd1be65d29fc5bd","last_reissued_at":"2026-05-18T01:04:25.455902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:25.455902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.05738","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":"2026-05-18T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oX8F94YercS3U4gqnCZ8gWIwv74vW+nrBiI0/gIK1VZ1mjZVIXeE/2FR7T/BwWsHfO2A5QfotKIESikgwB2oCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:44:55.288142Z"},"content_sha256":"a96b81d58a02d0270d40837b60bf01a56c0db5098837b08fff6b556284401b25","schema_version":"1.0","event_id":"sha256:a96b81d58a02d0270d40837b60bf01a56c0db5098837b08fff6b556284401b25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:W6XPLZXFSETZFG4TS473ZI3YAM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The quasispecies distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"q-bio.PE","authors_text":"Joseba Dalmau, Rapha\\\"el Cerf","submitted_at":"2016-09-19T14:15:07Z","abstract_excerpt":"The quasispecies model was introduced in 1971 by Manfred Eigen to discuss the first stages of life on Earth. It provides an appealing mathematical framework to study the evolution of populations in biology, for instance viruses. We present briefly the model and we focus on its stationary solutions. These formulae have a surprisingly rich combinatorial structure, involving for instance the Eulerian and Stirling numbers, as well as the up--down coefficients of permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05738","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":"2026-05-18T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"toJb7jVuaEUaFEKAwv7HGEwojICHPi9pg6xzp5zGHWZuR3CbvKMDjJBaYOBr+cZsPz+Us+LJUGFkdrzPWTuvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:44:55.288502Z"},"content_sha256":"367e3f2c4999198e79d71cdd5ce23f055d7bb51f214a53086f2dc14272b63d0b","schema_version":"1.0","event_id":"sha256:367e3f2c4999198e79d71cdd5ce23f055d7bb51f214a53086f2dc14272b63d0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6XPLZXFSETZFG4TS473ZI3YAM/bundle.json","state_url":"https://pith.science/pith/W6XPLZXFSETZFG4TS473ZI3YAM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6XPLZXFSETZFG4TS473ZI3YAM/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":"2026-05-28T10:44:55Z","links":{"resolver":"https://pith.science/pith/W6XPLZXFSETZFG4TS473ZI3YAM","bundle":"https://pith.science/pith/W6XPLZXFSETZFG4TS473ZI3YAM/bundle.json","state":"https://pith.science/pith/W6XPLZXFSETZFG4TS473ZI3YAM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6XPLZXFSETZFG4TS473ZI3YAM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W6XPLZXFSETZFG4TS473ZI3YAM","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":"fd95da22d7dab97a9eef1eadfe3104d34e35b6b3f375957d626d9dcc634e59e3","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-09-19T14:15:07Z","title_canon_sha256":"53d70344dc6a61b04d3718d5d8d96923c522d0b86bcb792d7d5db936685c9fc8"},"schema_version":"1.0","source":{"id":"1609.05738","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05738","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05738v1","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05738","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"W6XPLZXFSETZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W6XPLZXFSETZFG4T","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W6XPLZXF","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:367e3f2c4999198e79d71cdd5ce23f055d7bb51f214a53086f2dc14272b63d0b","target":"graph","created_at":"2026-05-18T01:04:25Z","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":"The quasispecies model was introduced in 1971 by Manfred Eigen to discuss the first stages of life on Earth. It provides an appealing mathematical framework to study the evolution of populations in biology, for instance viruses. We present briefly the model and we focus on its stationary solutions. These formulae have a surprisingly rich combinatorial structure, involving for instance the Eulerian and Stirling numbers, as well as the up--down coefficients of permutations.","authors_text":"Joseba Dalmau, Rapha\\\"el Cerf","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-09-19T14:15:07Z","title":"The quasispecies distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05738","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:a96b81d58a02d0270d40837b60bf01a56c0db5098837b08fff6b556284401b25","target":"record","created_at":"2026-05-18T01:04:25Z","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":"fd95da22d7dab97a9eef1eadfe3104d34e35b6b3f375957d626d9dcc634e59e3","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-09-19T14:15:07Z","title_canon_sha256":"53d70344dc6a61b04d3718d5d8d96923c522d0b86bcb792d7d5db936685c9fc8"},"schema_version":"1.0","source":{"id":"1609.05738","kind":"arxiv","version":1}},"canonical_sha256":"b7aef5e6e59127929b93973fbca378030c5ec9a677f7355bdcd1be65d29fc5bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7aef5e6e59127929b93973fbca378030c5ec9a677f7355bdcd1be65d29fc5bd","first_computed_at":"2026-05-18T01:04:25.455902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:25.455902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bfyFiYO6FNdt6EmV13SPE0hJy8DHn7ZtVfabx5LnAWQGo5+SwX4YOWsm+HMgT7pXFIKHoZAwm2HQfY7p9F4rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:25.456515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05738","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a96b81d58a02d0270d40837b60bf01a56c0db5098837b08fff6b556284401b25","sha256:367e3f2c4999198e79d71cdd5ce23f055d7bb51f214a53086f2dc14272b63d0b"],"state_sha256":"4014511f71e7535ff5357f3bfab6149842eb7310cde1c2da186a825665af4d35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ok5s5xoRhG0Sql/B/CquCfxmrDqs2S4iGz9h3AbPGb9v4oJ4uQdpFRc7FRqknXnw7Q310uRtcqTP1JNX7vVIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:44:55.290429Z","bundle_sha256":"ad98e9eeebf74dad1be49fc528cab8859e09351c66690a669b11697105d58804"}}