{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LOHUQGWZLQNN4S3GSHOKAM3LG3","short_pith_number":"pith:LOHUQGWZ","canonical_record":{"source":{"id":"1304.6570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-04-24T13:11:17Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"1f4f977a1a06f4e10453c2bfe39e08222b1f3a80922e3e3fd9abb3481570ea31","abstract_canon_sha256":"82b0ea3ca05777994e5349fa393285bf9264f2c421f75ec7b07145574d370e15"},"schema_version":"1.0"},"canonical_sha256":"5b8f481ad95c1ade4b6691dca0336b36db8aea1fc4a2e5d74e76088a4a657a7b","source":{"kind":"arxiv","id":"1304.6570","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6570","created_at":"2026-05-18T01:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6570v1","created_at":"2026-05-18T01:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6570","created_at":"2026-05-18T01:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"LOHUQGWZLQNN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LOHUQGWZLQNN4S3G","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LOHUQGWZ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LOHUQGWZLQNN4S3GSHOKAM3LG3","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-04-24T13:11:17Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"1f4f977a1a06f4e10453c2bfe39e08222b1f3a80922e3e3fd9abb3481570ea31","abstract_canon_sha256":"82b0ea3ca05777994e5349fa393285bf9264f2c421f75ec7b07145574d370e15"},"schema_version":"1.0"},"canonical_sha256":"5b8f481ad95c1ade4b6691dca0336b36db8aea1fc4a2e5d74e76088a4a657a7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:22.559398Z","signature_b64":"2LIZ+ihDCEJFRQtODQPNHlnL09/8sA/erDDY4rT4l6rr8BpywkGTFoMwlGvge3tHB/86aHUrVMk+/7rTH15+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b8f481ad95c1ade4b6691dca0336b36db8aea1fc4a2e5d74e76088a4a657a7b","last_reissued_at":"2026-05-18T01:50:22.558626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:22.558626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6570","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":"2026-05-18T01:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ZosJF3p73cnCnOmsHbFjUXxB/5fWB8LnCUrFm+lgDm+5GNicECIo0ABsXCw04MeMua4JzLWZEadnCCFA8VyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:42:12.440450Z"},"content_sha256":"a7d822c70692991c2191159870d983756f0f471f8d2b3f06c7559121527b7f96","schema_version":"1.0","event_id":"sha256:a7d822c70692991c2191159870d983756f0f471f8d2b3f06c7559121527b7f96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LOHUQGWZLQNN4S3GSHOKAM3LG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"q-bio.MN","authors_text":"Hodjat Pendar, Rahul V. Kulkarni, Thierry Platini","submitted_at":"2013-04-24T13:11:17Z","abstract_excerpt":"Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations, hence there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6570","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":"2026-05-18T01:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwRwlnlrE0uCPxSoWpjuvLY5F2QwculuSic4/tuyk/jwxUnDN6Om+hPfEHTr9yeZP2pasQ3Btdrg/WKPSyifCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:42:12.441062Z"},"content_sha256":"1d935193fb18d32aa27c2c533276a693ac59093624fa97eeb15cd9d6a37bf70d","schema_version":"1.0","event_id":"sha256:1d935193fb18d32aa27c2c533276a693ac59093624fa97eeb15cd9d6a37bf70d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOHUQGWZLQNN4S3GSHOKAM3LG3/bundle.json","state_url":"https://pith.science/pith/LOHUQGWZLQNN4S3GSHOKAM3LG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOHUQGWZLQNN4S3GSHOKAM3LG3/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":"2026-05-27T09:42:12Z","links":{"resolver":"https://pith.science/pith/LOHUQGWZLQNN4S3GSHOKAM3LG3","bundle":"https://pith.science/pith/LOHUQGWZLQNN4S3GSHOKAM3LG3/bundle.json","state":"https://pith.science/pith/LOHUQGWZLQNN4S3GSHOKAM3LG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOHUQGWZLQNN4S3GSHOKAM3LG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LOHUQGWZLQNN4S3GSHOKAM3LG3","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":"82b0ea3ca05777994e5349fa393285bf9264f2c421f75ec7b07145574d370e15","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-04-24T13:11:17Z","title_canon_sha256":"1f4f977a1a06f4e10453c2bfe39e08222b1f3a80922e3e3fd9abb3481570ea31"},"schema_version":"1.0","source":{"id":"1304.6570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6570","created_at":"2026-05-18T01:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6570v1","created_at":"2026-05-18T01:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6570","created_at":"2026-05-18T01:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"LOHUQGWZLQNN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LOHUQGWZLQNN4S3G","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LOHUQGWZ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:1d935193fb18d32aa27c2c533276a693ac59093624fa97eeb15cd9d6a37bf70d","target":"graph","created_at":"2026-05-18T01:50:22Z","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":"Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations, hence there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expres","authors_text":"Hodjat Pendar, Rahul V. Kulkarni, Thierry Platini","cross_cats":["physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-04-24T13:11:17Z","title":"Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6570","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:a7d822c70692991c2191159870d983756f0f471f8d2b3f06c7559121527b7f96","target":"record","created_at":"2026-05-18T01:50:22Z","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":"82b0ea3ca05777994e5349fa393285bf9264f2c421f75ec7b07145574d370e15","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-04-24T13:11:17Z","title_canon_sha256":"1f4f977a1a06f4e10453c2bfe39e08222b1f3a80922e3e3fd9abb3481570ea31"},"schema_version":"1.0","source":{"id":"1304.6570","kind":"arxiv","version":1}},"canonical_sha256":"5b8f481ad95c1ade4b6691dca0336b36db8aea1fc4a2e5d74e76088a4a657a7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b8f481ad95c1ade4b6691dca0336b36db8aea1fc4a2e5d74e76088a4a657a7b","first_computed_at":"2026-05-18T01:50:22.558626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:22.558626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2LIZ+ihDCEJFRQtODQPNHlnL09/8sA/erDDY4rT4l6rr8BpywkGTFoMwlGvge3tHB/86aHUrVMk+/7rTH15+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:22.559398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7d822c70692991c2191159870d983756f0f471f8d2b3f06c7559121527b7f96","sha256:1d935193fb18d32aa27c2c533276a693ac59093624fa97eeb15cd9d6a37bf70d"],"state_sha256":"022be3d35ebcdc737e515bc8b43b7813f1c6771ca824ddab3a929ae17371b29d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+yAf5PfpV8XmfkKUbD4uaICCRzzajA29KKQwWrAKz9CmXQ0LYdP+gltbFwsiEkMq/eMM85XJDJ5NDtKEYYTSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:42:12.444374Z","bundle_sha256":"b90d0ce526b1e85a738b9f92611395360159820ac514aae2bb2c3ded76aa1987"}}