{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VV7NTG2P4T6JMZRTHKYRKRQJOF","short_pith_number":"pith:VV7NTG2P","canonical_record":{"source":{"id":"0909.0392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-09-02T11:35:45Z","cross_cats_sorted":["math.AP","q-bio.QM"],"title_canon_sha256":"a0eeda5d1b3a66287812b78a4c76bf3e98876619051d98801a74bbc020ca16d4","abstract_canon_sha256":"113a69605d6353408dfa2c05bfd19bb2967037ba63f060c5e7865bf20bba4c46"},"schema_version":"1.0"},"canonical_sha256":"ad7ed99b4fe4fc9666333ab1154609716d800e4aa0bea2e3f68af00d33fe441f","source":{"kind":"arxiv","id":"0909.0392","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0392","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0392v1","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0392","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"VV7NTG2P4T6J","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VV7NTG2P4T6JMZRT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VV7NTG2P","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VV7NTG2P4T6JMZRTHKYRKRQJOF","target":"record","payload":{"canonical_record":{"source":{"id":"0909.0392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-09-02T11:35:45Z","cross_cats_sorted":["math.AP","q-bio.QM"],"title_canon_sha256":"a0eeda5d1b3a66287812b78a4c76bf3e98876619051d98801a74bbc020ca16d4","abstract_canon_sha256":"113a69605d6353408dfa2c05bfd19bb2967037ba63f060c5e7865bf20bba4c46"},"schema_version":"1.0"},"canonical_sha256":"ad7ed99b4fe4fc9666333ab1154609716d800e4aa0bea2e3f68af00d33fe441f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:06.776174Z","signature_b64":"t2yhDFvdX/kzGovJegF0jXUju/tQAoxKD+plrYHKozuWAT/Gb+kQBp152NEx1x1txlEyXYzmb0VxeNFXUI5EDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad7ed99b4fe4fc9666333ab1154609716d800e4aa0bea2e3f68af00d33fe441f","last_reissued_at":"2026-05-18T03:36:06.775423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:06.775423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.0392","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":"2026-05-18T03:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uVtSrHWIYKrD9F8sZUDgbAaUeNqMAzCNBBqEkWcDAiG1L2xPPTYhUaA+ty2hpPkJN2tjetqqlc7ZDk4THqf7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:33:44.161209Z"},"content_sha256":"70dd9497085bf83b38b3ceb5773fefe18965b81eef13e9afa96664e48270f1cd","schema_version":"1.0","event_id":"sha256:70dd9497085bf83b38b3ceb5773fefe18965b81eef13e9afa96664e48270f1cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VV7NTG2P4T6JMZRTHKYRKRQJOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Calibration of a Size-Structured Population Model from Experimental Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","q-bio.QM"],"primary_cat":"math.NA","authors_text":"Jorge P. Zubelli (UCI), LJLL), Marie Doumic Jauffret (INRIA Rocquencourt, Pedro Maia (UCI)","submitted_at":"2009-09-02T11:35:45Z","abstract_excerpt":"The aim of this work is twofold. First, we survey the techniques developed in (Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2008) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the data reported in the classical work of Kubitschek [3] concerning Escherichia coli in vitro experiments measured by means of a Coulter tra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0392","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":"2026-05-18T03:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ECkHpN2uJeg/qXXzab5TvgGyjrzv1pv1s9MX+6p9TNpbUjBNHJFHX19D1X26zUNzQ3YUAmYBkFLK0rUbfmb1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:33:44.161813Z"},"content_sha256":"0823b9976b7f9fae32f2594770764f304f325cd7a5cf5d4e66fb3a66e7cd182c","schema_version":"1.0","event_id":"sha256:0823b9976b7f9fae32f2594770764f304f325cd7a5cf5d4e66fb3a66e7cd182c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VV7NTG2P4T6JMZRTHKYRKRQJOF/bundle.json","state_url":"https://pith.science/pith/VV7NTG2P4T6JMZRTHKYRKRQJOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VV7NTG2P4T6JMZRTHKYRKRQJOF/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":"2026-05-27T05:33:44Z","links":{"resolver":"https://pith.science/pith/VV7NTG2P4T6JMZRTHKYRKRQJOF","bundle":"https://pith.science/pith/VV7NTG2P4T6JMZRTHKYRKRQJOF/bundle.json","state":"https://pith.science/pith/VV7NTG2P4T6JMZRTHKYRKRQJOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VV7NTG2P4T6JMZRTHKYRKRQJOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VV7NTG2P4T6JMZRTHKYRKRQJOF","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":"113a69605d6353408dfa2c05bfd19bb2967037ba63f060c5e7865bf20bba4c46","cross_cats_sorted":["math.AP","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-09-02T11:35:45Z","title_canon_sha256":"a0eeda5d1b3a66287812b78a4c76bf3e98876619051d98801a74bbc020ca16d4"},"schema_version":"1.0","source":{"id":"0909.0392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0392","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0392v1","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0392","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"VV7NTG2P4T6J","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VV7NTG2P4T6JMZRT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VV7NTG2P","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:0823b9976b7f9fae32f2594770764f304f325cd7a5cf5d4e66fb3a66e7cd182c","target":"graph","created_at":"2026-05-18T03:36:06Z","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 aim of this work is twofold. First, we survey the techniques developed in (Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2008) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the data reported in the classical work of Kubitschek [3] concerning Escherichia coli in vitro experiments measured by means of a Coulter tra","authors_text":"Jorge P. Zubelli (UCI), LJLL), Marie Doumic Jauffret (INRIA Rocquencourt, Pedro Maia (UCI)","cross_cats":["math.AP","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-09-02T11:35:45Z","title":"On the Calibration of a Size-Structured Population Model from Experimental Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0392","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":"sha256:70dd9497085bf83b38b3ceb5773fefe18965b81eef13e9afa96664e48270f1cd","target":"record","created_at":"2026-05-18T03:36:06Z","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":"113a69605d6353408dfa2c05bfd19bb2967037ba63f060c5e7865bf20bba4c46","cross_cats_sorted":["math.AP","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-09-02T11:35:45Z","title_canon_sha256":"a0eeda5d1b3a66287812b78a4c76bf3e98876619051d98801a74bbc020ca16d4"},"schema_version":"1.0","source":{"id":"0909.0392","kind":"arxiv","version":1}},"canonical_sha256":"ad7ed99b4fe4fc9666333ab1154609716d800e4aa0bea2e3f68af00d33fe441f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad7ed99b4fe4fc9666333ab1154609716d800e4aa0bea2e3f68af00d33fe441f","first_computed_at":"2026-05-18T03:36:06.775423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:06.775423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t2yhDFvdX/kzGovJegF0jXUju/tQAoxKD+plrYHKozuWAT/Gb+kQBp152NEx1x1txlEyXYzmb0VxeNFXUI5EDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:06.776174Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70dd9497085bf83b38b3ceb5773fefe18965b81eef13e9afa96664e48270f1cd","sha256:0823b9976b7f9fae32f2594770764f304f325cd7a5cf5d4e66fb3a66e7cd182c"],"state_sha256":"1d26c89363ee695494db999a4230513a47767bf51e5613f94d74b9246b3c15de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sPH0pLavIKUgZWIL54tbUfkihfx2EYsFMhWjY+FR17ZCDpZq6cucDEFJvDWk45tPa1MSIR7tzC55Ubp6l6YQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:33:44.165151Z","bundle_sha256":"56556a17ac716f02762dd33323527009170f3cb51a62c2b4d5b039f9c6c18787"}}