{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:H5BU3GHDWMTZL6HO3UIQTWRHV2","short_pith_number":"pith:H5BU3GHD","canonical_record":{"source":{"id":"0810.1381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-08T08:27:47Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8fd28a0097a21e5fefc2a12ef24443b566ffc1e4bf64bbd8ac97db9aef775dbc","abstract_canon_sha256":"8e8b33fdcc91dd417553cd9c6e95a5ed98cff14d84e9d2703e42a54727b5ffc7"},"schema_version":"1.0"},"canonical_sha256":"3f434d98e3b32795f8eedd1109da27aeb44080da5d81b448957c80cd735add0d","source":{"kind":"arxiv","id":"0810.1381","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1381","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1381v1","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1381","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"H5BU3GHDWMTZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"H5BU3GHDWMTZL6HO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"H5BU3GHD","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:H5BU3GHDWMTZL6HO3UIQTWRHV2","target":"record","payload":{"canonical_record":{"source":{"id":"0810.1381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-08T08:27:47Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8fd28a0097a21e5fefc2a12ef24443b566ffc1e4bf64bbd8ac97db9aef775dbc","abstract_canon_sha256":"8e8b33fdcc91dd417553cd9c6e95a5ed98cff14d84e9d2703e42a54727b5ffc7"},"schema_version":"1.0"},"canonical_sha256":"3f434d98e3b32795f8eedd1109da27aeb44080da5d81b448957c80cd735add0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:06.825179Z","signature_b64":"dmBb9CROHoaVMd2WLlh/3kKIwGfahBWB8QeAOy9fPMITWEd2a2dW4+8Kv3yjpoEZ8sAMNPpX8y4xwP6RLpnDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f434d98e3b32795f8eedd1109da27aeb44080da5d81b448957c80cd735add0d","last_reissued_at":"2026-05-18T03:36:06.824579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:06.824579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.1381","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":"MDcKsibgbzHJ8zPxMTOpzNkzGDgexacPU2QTEaSwdR9skbIBn/8zCag8v68innD8kbQZ863YSGhlcXsZapXrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:52:50.457008Z"},"content_sha256":"119815c469ae9355fd4d9e9cab4ec9830c2f80a5d86853b32b07ba7f37fb5fd8","schema_version":"1.0","event_id":"sha256:119815c469ae9355fd4d9e9cab4ec9830c2f80a5d86853b32b07ba7f37fb5fd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:H5BU3GHDWMTZL6HO3UIQTWRHV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Beno\\^it Perthame (INRIA Rocquencourt, Jorge P. Zubelli (UCI), LJLL), Marie Doumic Jauffret (INRIA Rocquencourt)","submitted_at":"2008-10-08T08:27:47Z","abstract_excerpt":"We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We propose a new regularization technique based on a filtering approach. We prove convergence of the algorithm and validate the theoretical results by implementing numerical simulations, based on classical techniques. We compare the results for direct and inverse problems, for the filtering method and for the quasi-reversibility method proposed in [Perthame-Zubelli]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1381","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":"9Q1C8GVpR5yVgcb15OW2AYRbPYFms7qGjh+aVpRB45XMf1/V2n5eeR4ZsyC6ZqilfsG8GdQtT8wFCl6Op2JnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:52:50.457366Z"},"content_sha256":"180bc36f827ee6c860bbf374f74c52d19d129a06f75ca143a2cbdd4e2aba0adc","schema_version":"1.0","event_id":"sha256:180bc36f827ee6c860bbf374f74c52d19d129a06f75ca143a2cbdd4e2aba0adc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5BU3GHDWMTZL6HO3UIQTWRHV2/bundle.json","state_url":"https://pith.science/pith/H5BU3GHDWMTZL6HO3UIQTWRHV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5BU3GHDWMTZL6HO3UIQTWRHV2/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":"2026-06-01T06:52:50Z","links":{"resolver":"https://pith.science/pith/H5BU3GHDWMTZL6HO3UIQTWRHV2","bundle":"https://pith.science/pith/H5BU3GHDWMTZL6HO3UIQTWRHV2/bundle.json","state":"https://pith.science/pith/H5BU3GHDWMTZL6HO3UIQTWRHV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5BU3GHDWMTZL6HO3UIQTWRHV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:H5BU3GHDWMTZL6HO3UIQTWRHV2","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":"8e8b33fdcc91dd417553cd9c6e95a5ed98cff14d84e9d2703e42a54727b5ffc7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-08T08:27:47Z","title_canon_sha256":"8fd28a0097a21e5fefc2a12ef24443b566ffc1e4bf64bbd8ac97db9aef775dbc"},"schema_version":"1.0","source":{"id":"0810.1381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1381","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1381v1","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1381","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"H5BU3GHDWMTZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"H5BU3GHDWMTZL6HO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"H5BU3GHD","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:180bc36f827ee6c860bbf374f74c52d19d129a06f75ca143a2cbdd4e2aba0adc","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":"We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We propose a new regularization technique based on a filtering approach. We prove convergence of the algorithm and validate the theoretical results by implementing numerical simulations, based on classical techniques. We compare the results for direct and inverse problems, for the filtering method and for the quasi-reversibility method proposed in [Perthame-Zubelli].","authors_text":"Beno\\^it Perthame (INRIA Rocquencourt, Jorge P. Zubelli (UCI), LJLL), Marie Doumic Jauffret (INRIA Rocquencourt)","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-08T08:27:47Z","title":"Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1381","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":"sha256:119815c469ae9355fd4d9e9cab4ec9830c2f80a5d86853b32b07ba7f37fb5fd8","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":"8e8b33fdcc91dd417553cd9c6e95a5ed98cff14d84e9d2703e42a54727b5ffc7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-10-08T08:27:47Z","title_canon_sha256":"8fd28a0097a21e5fefc2a12ef24443b566ffc1e4bf64bbd8ac97db9aef775dbc"},"schema_version":"1.0","source":{"id":"0810.1381","kind":"arxiv","version":1}},"canonical_sha256":"3f434d98e3b32795f8eedd1109da27aeb44080da5d81b448957c80cd735add0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f434d98e3b32795f8eedd1109da27aeb44080da5d81b448957c80cd735add0d","first_computed_at":"2026-05-18T03:36:06.824579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:06.824579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dmBb9CROHoaVMd2WLlh/3kKIwGfahBWB8QeAOy9fPMITWEd2a2dW4+8Kv3yjpoEZ8sAMNPpX8y4xwP6RLpnDCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:06.825179Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.1381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:119815c469ae9355fd4d9e9cab4ec9830c2f80a5d86853b32b07ba7f37fb5fd8","sha256:180bc36f827ee6c860bbf374f74c52d19d129a06f75ca143a2cbdd4e2aba0adc"],"state_sha256":"ad271b6c1de7b29deccb2920a8ff132a91b4c78718a917ae264de58ebf185c7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F8Cc1bsOM+V1zPbtcbTLUljjnvI9HMx/Xr805W4gzsFjsNH9TAHGlSDjNDZqcTbDHHVNfG5j0xbXEkgYVMPBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:52:50.459429Z","bundle_sha256":"c0c0e9cf0c15ff8cbf6a3ccd607a7d1a1f1e8ccad5f896a160a4f056c7103be4"}}