{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VYA6HBBVPECPPZWLLILOAGMATM","short_pith_number":"pith:VYA6HBBV","canonical_record":{"source":{"id":"1302.4196","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-18T09:35:19Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"a0db84daa4785c11a412f3f151e5ef01d857d8b43048b883b7276a989cd83a52","abstract_canon_sha256":"23e0a2dad43372dea3f0b8ade1238af7421acc14ca1cae8ead34697632e737dd"},"schema_version":"1.0"},"canonical_sha256":"ae01e384357904f7e6cb5a16e019809b3a8667ab533baf2d1f0072a61cf65982","source":{"kind":"arxiv","id":"1302.4196","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4196","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4196v2","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4196","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"VYA6HBBVPECP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VYA6HBBVPECPPZWL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VYA6HBBV","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VYA6HBBVPECPPZWLLILOAGMATM","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4196","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-18T09:35:19Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"a0db84daa4785c11a412f3f151e5ef01d857d8b43048b883b7276a989cd83a52","abstract_canon_sha256":"23e0a2dad43372dea3f0b8ade1238af7421acc14ca1cae8ead34697632e737dd"},"schema_version":"1.0"},"canonical_sha256":"ae01e384357904f7e6cb5a16e019809b3a8667ab533baf2d1f0072a61cf65982","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:44.333210Z","signature_b64":"PhNT5KeO4HtlcnwTND0xaOqnaYxeFf2is5nSWvu8/u2wzZ/MTfIxqzBETc0J0umv7b6aMY0JqUu4pvHBtrLBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae01e384357904f7e6cb5a16e019809b3a8667ab533baf2d1f0072a61cf65982","last_reissued_at":"2026-05-18T02:56:44.332524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:44.332524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4196","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":"2026-05-18T02:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IDY/k3G9tfXGP4LdiYAYONLZoBeCfVhGQ0jLckKwPeUOKKuS8kEiWfK6s8uvUOA+D5sa98K5kIUcf7oYgryMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:51:39.111661Z"},"content_sha256":"046ab7d3ececfa742ff21ad49876c13430d188298da7ea81e19786559e26116c","schema_version":"1.0","event_id":"sha256:046ab7d3ececfa742ff21ad49876c13430d188298da7ea81e19786559e26116c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VYA6HBBVPECPPZWLLILOAGMATM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic periodicity of flows in time-depending networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.AP","authors_text":"Britta Dorn, Fatih Bayazit, Marjeta Kramar Fijav\\v{z}","submitted_at":"2013-02-18T09:35:19Z","abstract_excerpt":"We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the solutions under certain natural conditions on the network. We further apply our theory to a model used for air traffic flow management."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4196","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":"2026-05-18T02:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpfBCvUmG5SBXfqNUpj7rm5Sn9w8dhi/jkbtHAqu0aMFIOFKMeeO7uoGfYlueYzdO/KVgmUhCHXf/G1/YHItAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:51:39.112033Z"},"content_sha256":"1019e35e999c3ecf672ddc88a34fc1b863460aaf1728c317ed7999ac8a163164","schema_version":"1.0","event_id":"sha256:1019e35e999c3ecf672ddc88a34fc1b863460aaf1728c317ed7999ac8a163164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYA6HBBVPECPPZWLLILOAGMATM/bundle.json","state_url":"https://pith.science/pith/VYA6HBBVPECPPZWLLILOAGMATM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYA6HBBVPECPPZWLLILOAGMATM/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":"2026-06-24T03:51:39Z","links":{"resolver":"https://pith.science/pith/VYA6HBBVPECPPZWLLILOAGMATM","bundle":"https://pith.science/pith/VYA6HBBVPECPPZWLLILOAGMATM/bundle.json","state":"https://pith.science/pith/VYA6HBBVPECPPZWLLILOAGMATM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYA6HBBVPECPPZWLLILOAGMATM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VYA6HBBVPECPPZWLLILOAGMATM","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":"23e0a2dad43372dea3f0b8ade1238af7421acc14ca1cae8ead34697632e737dd","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-18T09:35:19Z","title_canon_sha256":"a0db84daa4785c11a412f3f151e5ef01d857d8b43048b883b7276a989cd83a52"},"schema_version":"1.0","source":{"id":"1302.4196","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4196","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4196v2","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4196","created_at":"2026-05-18T02:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"VYA6HBBVPECP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VYA6HBBVPECPPZWL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VYA6HBBV","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:1019e35e999c3ecf672ddc88a34fc1b863460aaf1728c317ed7999ac8a163164","target":"graph","created_at":"2026-05-18T02:56:44Z","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 linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the solutions under certain natural conditions on the network. We further apply our theory to a model used for air traffic flow management.","authors_text":"Britta Dorn, Fatih Bayazit, Marjeta Kramar Fijav\\v{z}","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-18T09:35:19Z","title":"Asymptotic periodicity of flows in time-depending networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4196","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":"sha256:046ab7d3ececfa742ff21ad49876c13430d188298da7ea81e19786559e26116c","target":"record","created_at":"2026-05-18T02:56:44Z","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":"23e0a2dad43372dea3f0b8ade1238af7421acc14ca1cae8ead34697632e737dd","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-18T09:35:19Z","title_canon_sha256":"a0db84daa4785c11a412f3f151e5ef01d857d8b43048b883b7276a989cd83a52"},"schema_version":"1.0","source":{"id":"1302.4196","kind":"arxiv","version":2}},"canonical_sha256":"ae01e384357904f7e6cb5a16e019809b3a8667ab533baf2d1f0072a61cf65982","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae01e384357904f7e6cb5a16e019809b3a8667ab533baf2d1f0072a61cf65982","first_computed_at":"2026-05-18T02:56:44.332524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:44.332524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PhNT5KeO4HtlcnwTND0xaOqnaYxeFf2is5nSWvu8/u2wzZ/MTfIxqzBETc0J0umv7b6aMY0JqUu4pvHBtrLBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:44.333210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4196","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:046ab7d3ececfa742ff21ad49876c13430d188298da7ea81e19786559e26116c","sha256:1019e35e999c3ecf672ddc88a34fc1b863460aaf1728c317ed7999ac8a163164"],"state_sha256":"0ff34b26c6b0ef790b031e73fb05f85bc5417f910dacc7e907cae89148bffea3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DKAe/gXUrZNUMX8wg6M31wBEGWgtR4pIkRFd3UUJ61qymm8sKux4s+qbGy6NZ91ESls7yMdOoKJ1FdpQIXGcAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T03:51:39.113971Z","bundle_sha256":"b4b9efe0e3e153fe3db35668f04d1b47d10601d7f4594e41ec8c82c2c9d66691"}}