{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:AKB3ETP5TKGVKAEFADXV7N3SYJ","short_pith_number":"pith:AKB3ETP5","canonical_record":{"source":{"id":"0903.1649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-09T21:01:44Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4ccb72b1659b69af0fd514c55f765226c809e6e13efb8aef89e8dadd53044f35","abstract_canon_sha256":"aedab0fc02e7cc6cf13b566fe12b3dbdc6998e7309a23018d4657333de8ea1d7"},"schema_version":"1.0"},"canonical_sha256":"0283b24dfd9a8d55008500ef5fb772c252466d923b93961818296b00c3c4c855","source":{"kind":"arxiv","id":"0903.1649","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1649","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1649v2","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1649","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"AKB3ETP5TKGV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKB3ETP5TKGVKAEF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKB3ETP5","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:AKB3ETP5TKGVKAEFADXV7N3SYJ","target":"record","payload":{"canonical_record":{"source":{"id":"0903.1649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-09T21:01:44Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4ccb72b1659b69af0fd514c55f765226c809e6e13efb8aef89e8dadd53044f35","abstract_canon_sha256":"aedab0fc02e7cc6cf13b566fe12b3dbdc6998e7309a23018d4657333de8ea1d7"},"schema_version":"1.0"},"canonical_sha256":"0283b24dfd9a8d55008500ef5fb772c252466d923b93961818296b00c3c4c855","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:43.143128Z","signature_b64":"wWKVwn88ThnmLT6ZuujFll/ESZKeVrhjKyzjUbp+AzrPrDp7XZ0dRsm/mTcHJ8yepyPTukNq1Ey8st3qKI9iBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0283b24dfd9a8d55008500ef5fb772c252466d923b93961818296b00c3c4c855","last_reissued_at":"2026-05-17T23:50:43.142711Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:43.142711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.1649","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":"2026-05-17T23:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XDS4eIo+at1w24JUyaKqMX6iEEmUb7O9a1hRk65hjuMxeudfKOA76XXeu9XDKkvSI0xzLn2Hj+OwKjtDdBjDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:52:19.708230Z"},"content_sha256":"04aff5add29800b54fa616e48d889c3b50e03493f1615ccdd0e8ba3cf9e18508","schema_version":"1.0","event_id":"sha256:04aff5add29800b54fa616e48d889c3b50e03493f1615ccdd0e8ba3cf9e18508"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:AKB3ETP5TKGVKAEFADXV7N3SYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a size-structured two-phase population model with infinite states-at-birth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jozsef Z. Farkas, Peter Hinow","submitted_at":"2009-03-09T21:01:44Z","abstract_excerpt":"In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an \"active\" phase when individuals grow, reproduce and die and a second \"resting\" phase when individuals only grow. Transition between these two phases depends on individuals' size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1649","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":"2026-05-17T23:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7EwOLYwC09jfgjOJrK3AYm1a1enGKivcQpeMvCAUGe9kaD2AdRu9s2ZyZ49Kqe8Q4SPJjVS3HcWd/jjQ9K6KCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:52:19.708587Z"},"content_sha256":"65a29dff3be08ad1fa18e785f364efb5b39e48fa1ce950b62fcc714840d1621a","schema_version":"1.0","event_id":"sha256:65a29dff3be08ad1fa18e785f364efb5b39e48fa1ce950b62fcc714840d1621a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKB3ETP5TKGVKAEFADXV7N3SYJ/bundle.json","state_url":"https://pith.science/pith/AKB3ETP5TKGVKAEFADXV7N3SYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKB3ETP5TKGVKAEFADXV7N3SYJ/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":"2026-07-02T21:52:19Z","links":{"resolver":"https://pith.science/pith/AKB3ETP5TKGVKAEFADXV7N3SYJ","bundle":"https://pith.science/pith/AKB3ETP5TKGVKAEFADXV7N3SYJ/bundle.json","state":"https://pith.science/pith/AKB3ETP5TKGVKAEFADXV7N3SYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKB3ETP5TKGVKAEFADXV7N3SYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:AKB3ETP5TKGVKAEFADXV7N3SYJ","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":"aedab0fc02e7cc6cf13b566fe12b3dbdc6998e7309a23018d4657333de8ea1d7","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-09T21:01:44Z","title_canon_sha256":"4ccb72b1659b69af0fd514c55f765226c809e6e13efb8aef89e8dadd53044f35"},"schema_version":"1.0","source":{"id":"0903.1649","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1649","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1649v2","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1649","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"AKB3ETP5TKGV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKB3ETP5TKGVKAEF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKB3ETP5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:65a29dff3be08ad1fa18e785f364efb5b39e48fa1ce950b62fcc714840d1621a","target":"graph","created_at":"2026-05-17T23:50:43Z","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 this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an \"active\" phase when individuals grow, reproduce and die and a second \"resting\" phase when individuals only grow. Transition between these two phases depends on individuals' size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymp","authors_text":"Jozsef Z. Farkas, Peter Hinow","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-09T21:01:44Z","title":"On a size-structured two-phase population model with infinite states-at-birth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1649","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":"sha256:04aff5add29800b54fa616e48d889c3b50e03493f1615ccdd0e8ba3cf9e18508","target":"record","created_at":"2026-05-17T23:50:43Z","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":"aedab0fc02e7cc6cf13b566fe12b3dbdc6998e7309a23018d4657333de8ea1d7","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-03-09T21:01:44Z","title_canon_sha256":"4ccb72b1659b69af0fd514c55f765226c809e6e13efb8aef89e8dadd53044f35"},"schema_version":"1.0","source":{"id":"0903.1649","kind":"arxiv","version":2}},"canonical_sha256":"0283b24dfd9a8d55008500ef5fb772c252466d923b93961818296b00c3c4c855","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0283b24dfd9a8d55008500ef5fb772c252466d923b93961818296b00c3c4c855","first_computed_at":"2026-05-17T23:50:43.142711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:43.142711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wWKVwn88ThnmLT6ZuujFll/ESZKeVrhjKyzjUbp+AzrPrDp7XZ0dRsm/mTcHJ8yepyPTukNq1Ey8st3qKI9iBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:43.143128Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1649","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04aff5add29800b54fa616e48d889c3b50e03493f1615ccdd0e8ba3cf9e18508","sha256:65a29dff3be08ad1fa18e785f364efb5b39e48fa1ce950b62fcc714840d1621a"],"state_sha256":"adfb58d227af85268c230f389e61851064c57b054dc080d32f10aa774a34a1d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Chl8S/R9Dju6tTih7sriGJWbz80WSqqmAULk7RFTkv41OdXNpkd23BLH6PthAAhArDpwo4WGZ/JucVaRRE8lBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T21:52:19.710488Z","bundle_sha256":"125350cb391316db9390257b0a21964b2f930403b57cf72e41295ca1e39c0910"}}