{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XQ56GEUSLQ5D3VQQZP2MQT3BNH","short_pith_number":"pith:XQ56GEUS","canonical_record":{"source":{"id":"1706.07789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-06-23T17:52:32Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"6271812837c79049a103611f48115c82850c8967b8f1e43887bba0d82f647fdf","abstract_canon_sha256":"8856a3122751a3aa610502ef49fffe2215b896a26ebfdf163707c81b069ce1c2"},"schema_version":"1.0"},"canonical_sha256":"bc3be312925c3a3dd610cbf4c84f6169da386c4e5cd9814f24f074f59269c35b","source":{"kind":"arxiv","id":"1706.07789","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07789","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07789v2","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07789","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"XQ56GEUSLQ5D","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XQ56GEUSLQ5D3VQQ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XQ56GEUS","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XQ56GEUSLQ5D3VQQZP2MQT3BNH","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07789","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-06-23T17:52:32Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"6271812837c79049a103611f48115c82850c8967b8f1e43887bba0d82f647fdf","abstract_canon_sha256":"8856a3122751a3aa610502ef49fffe2215b896a26ebfdf163707c81b069ce1c2"},"schema_version":"1.0"},"canonical_sha256":"bc3be312925c3a3dd610cbf4c84f6169da386c4e5cd9814f24f074f59269c35b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:13.543495Z","signature_b64":"6pH9k4Pf4RYlX7zT467jlBq2cjzb3fjpX8Z9qm6HLB9kksLNPgWZiL0c7osOTZBlyedRrsqDYTQj+6ZMtdUXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc3be312925c3a3dd610cbf4c84f6169da386c4e5cd9814f24f074f59269c35b","last_reissued_at":"2026-05-18T00:21:13.543097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:13.543097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07789","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":"2026-05-18T00:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"piv/uovzzwfsqgeyl9y4YYWF9Zf7+4eD3YjqzBJVL96UOlMGe3OLh7aZG2xbt9c8IFG7xAymSV083Hx214PQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:54:31.460213Z"},"content_sha256":"3713d3c45e28f395a5a3770fcdc8550fbbec811704fa70a34b23e75ffaf29094","schema_version":"1.0","event_id":"sha256:3713d3c45e28f395a5a3770fcdc8550fbbec811704fa70a34b23e75ffaf29094"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XQ56GEUSLQ5D3VQQZP2MQT3BNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phenotypic switching of populations of cells in a stochastic environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"q-bio.PE","authors_text":"Peter G. Hufton, Tobias Galla, Yen Ting Lin","submitted_at":"2017-06-23T17:52:32Z","abstract_excerpt":"In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise deterministic Markov processes. We show that optimal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07789","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":""},"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":"2026-05-18T00:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bxz4igVSoTdnffwxCRVa8tYrJ+kOqKLXZeGW163Dt2AX47U5gYMLtQFmSAKRRIfV0dkZ5mYh43BTh8Y+un66DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:54:31.460567Z"},"content_sha256":"dca3d7e203f7df5c77580ae9b842e89cc67001f890cb26d1c0ebc6f5d4627b4a","schema_version":"1.0","event_id":"sha256:dca3d7e203f7df5c77580ae9b842e89cc67001f890cb26d1c0ebc6f5d4627b4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQ56GEUSLQ5D3VQQZP2MQT3BNH/bundle.json","state_url":"https://pith.science/pith/XQ56GEUSLQ5D3VQQZP2MQT3BNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQ56GEUSLQ5D3VQQZP2MQT3BNH/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":"2026-06-21T09:54:31Z","links":{"resolver":"https://pith.science/pith/XQ56GEUSLQ5D3VQQZP2MQT3BNH","bundle":"https://pith.science/pith/XQ56GEUSLQ5D3VQQZP2MQT3BNH/bundle.json","state":"https://pith.science/pith/XQ56GEUSLQ5D3VQQZP2MQT3BNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQ56GEUSLQ5D3VQQZP2MQT3BNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XQ56GEUSLQ5D3VQQZP2MQT3BNH","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":"8856a3122751a3aa610502ef49fffe2215b896a26ebfdf163707c81b069ce1c2","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-06-23T17:52:32Z","title_canon_sha256":"6271812837c79049a103611f48115c82850c8967b8f1e43887bba0d82f647fdf"},"schema_version":"1.0","source":{"id":"1706.07789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07789","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07789v2","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07789","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"XQ56GEUSLQ5D","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XQ56GEUSLQ5D3VQQ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XQ56GEUS","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:dca3d7e203f7df5c77580ae9b842e89cc67001f890cb26d1c0ebc6f5d4627b4a","target":"graph","created_at":"2026-05-18T00:21:13Z","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":"In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise deterministic Markov processes. We show that optimal ","authors_text":"Peter G. Hufton, Tobias Galla, Yen Ting Lin","cross_cats":["physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-06-23T17:52:32Z","title":"Phenotypic switching of populations of cells in a stochastic environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07789","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":"sha256:3713d3c45e28f395a5a3770fcdc8550fbbec811704fa70a34b23e75ffaf29094","target":"record","created_at":"2026-05-18T00:21:13Z","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":"8856a3122751a3aa610502ef49fffe2215b896a26ebfdf163707c81b069ce1c2","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-06-23T17:52:32Z","title_canon_sha256":"6271812837c79049a103611f48115c82850c8967b8f1e43887bba0d82f647fdf"},"schema_version":"1.0","source":{"id":"1706.07789","kind":"arxiv","version":2}},"canonical_sha256":"bc3be312925c3a3dd610cbf4c84f6169da386c4e5cd9814f24f074f59269c35b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc3be312925c3a3dd610cbf4c84f6169da386c4e5cd9814f24f074f59269c35b","first_computed_at":"2026-05-18T00:21:13.543097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:13.543097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6pH9k4Pf4RYlX7zT467jlBq2cjzb3fjpX8Z9qm6HLB9kksLNPgWZiL0c7osOTZBlyedRrsqDYTQj+6ZMtdUXAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:13.543495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3713d3c45e28f395a5a3770fcdc8550fbbec811704fa70a34b23e75ffaf29094","sha256:dca3d7e203f7df5c77580ae9b842e89cc67001f890cb26d1c0ebc6f5d4627b4a"],"state_sha256":"03d9d5038b928b2f24abab21783bc2164405314dcbc5543fc3fefe9f4c90126a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/g33wj7Ym9FtDECvgbEmOpr3w5ySzgQrJ8rbaJvwtHbrFGcqYhh3UYoWe/VAEldCU2Iy8g4DfdAAkottZPxCCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:54:31.462592Z","bundle_sha256":"a58f5d1647e45948e5dc5e3891bb2ec75dad0f44dfd2862f458ac39047fd3406"}}