{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DMBKMEXTTYSQ4QNKZ4JILF4TOE","short_pith_number":"pith:DMBKMEXT","canonical_record":{"source":{"id":"1511.01719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-05T12:48:29Z","cross_cats_sorted":[],"title_canon_sha256":"0151b51c5ed16f540d0dfa6f156c6355c4bd282d36bfe95aa91279f393b150de","abstract_canon_sha256":"d5a28f071048808f050122cf257b849f53b95192dcbc2451704ddee5c7541664"},"schema_version":"1.0"},"canonical_sha256":"1b02a612f39e250e41aacf128597937137125721789f0570fe934fc6878d3d87","source":{"kind":"arxiv","id":"1511.01719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01719","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01719v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01719","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"DMBKMEXTTYSQ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DMBKMEXTTYSQ4QNK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DMBKMEXT","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DMBKMEXTTYSQ4QNKZ4JILF4TOE","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-05T12:48:29Z","cross_cats_sorted":[],"title_canon_sha256":"0151b51c5ed16f540d0dfa6f156c6355c4bd282d36bfe95aa91279f393b150de","abstract_canon_sha256":"d5a28f071048808f050122cf257b849f53b95192dcbc2451704ddee5c7541664"},"schema_version":"1.0"},"canonical_sha256":"1b02a612f39e250e41aacf128597937137125721789f0570fe934fc6878d3d87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:39.975487Z","signature_b64":"458oix2w1yv8/V2jU1dJdRp1CpcMy+lqWhRUgYdl/TxdCxbattntCdS8QoHKs4t0HUdqBUj9Kkd4Ia3/PkPnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b02a612f39e250e41aacf128597937137125721789f0570fe934fc6878d3d87","last_reissued_at":"2026-05-18T01:27:39.974999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:39.974999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01719","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":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSl3QCm9CwmFNUOLoNFRh6rUIx2tpGo+6iChbsiU9AqmCn1dn9V5x8JacyvOn1UdDn8MMp8QLEb+66EMcicdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:15:40.558293Z"},"content_sha256":"ebbbb9c05060895145c8438f03650b2bbd0b38412a7aa37b169294ead5570cff","schema_version":"1.0","event_id":"sha256:ebbbb9c05060895145c8438f03650b2bbd0b38412a7aa37b169294ead5570cff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DMBKMEXTTYSQ4QNKZ4JILF4TOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large time behavior and Lyapunov functionals for a nonlocal differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Danielle Hilhorst (LM-Orsay), Philippe Lauren\\c{c}ot (IMT), Thanh-Nam Nguyen","submitted_at":"2015-11-05T12:48:29Z","abstract_excerpt":"A new approach is used to describe the large time behavior of the non-local differential equation initially studied in [3]. Our approach is based upon the existence of infinitely many Lyapunov functionals and allows us to extend the analysis performed in [3]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01719","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":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPMsJ2fbutOD/9UPh4+yZYrFbNKx4mxbanQg3iDnKZROqve/XRwB4Id9xS8J677Uof938LEPKnO0YojBx/sqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:15:40.559055Z"},"content_sha256":"a54c008a6a6ea7d3a7e6b6b7000263854dcde0fa1e98b638db08abadfc4bcacd","schema_version":"1.0","event_id":"sha256:a54c008a6a6ea7d3a7e6b6b7000263854dcde0fa1e98b638db08abadfc4bcacd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMBKMEXTTYSQ4QNKZ4JILF4TOE/bundle.json","state_url":"https://pith.science/pith/DMBKMEXTTYSQ4QNKZ4JILF4TOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMBKMEXTTYSQ4QNKZ4JILF4TOE/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":"2026-06-10T00:15:40Z","links":{"resolver":"https://pith.science/pith/DMBKMEXTTYSQ4QNKZ4JILF4TOE","bundle":"https://pith.science/pith/DMBKMEXTTYSQ4QNKZ4JILF4TOE/bundle.json","state":"https://pith.science/pith/DMBKMEXTTYSQ4QNKZ4JILF4TOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMBKMEXTTYSQ4QNKZ4JILF4TOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DMBKMEXTTYSQ4QNKZ4JILF4TOE","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":"d5a28f071048808f050122cf257b849f53b95192dcbc2451704ddee5c7541664","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-05T12:48:29Z","title_canon_sha256":"0151b51c5ed16f540d0dfa6f156c6355c4bd282d36bfe95aa91279f393b150de"},"schema_version":"1.0","source":{"id":"1511.01719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01719","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01719v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01719","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"DMBKMEXTTYSQ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DMBKMEXTTYSQ4QNK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DMBKMEXT","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:a54c008a6a6ea7d3a7e6b6b7000263854dcde0fa1e98b638db08abadfc4bcacd","target":"graph","created_at":"2026-05-18T01:27:39Z","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":"A new approach is used to describe the large time behavior of the non-local differential equation initially studied in [3]. Our approach is based upon the existence of infinitely many Lyapunov functionals and allows us to extend the analysis performed in [3].","authors_text":"Danielle Hilhorst (LM-Orsay), Philippe Lauren\\c{c}ot (IMT), Thanh-Nam Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-05T12:48:29Z","title":"Large time behavior and Lyapunov functionals for a nonlocal differential equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01719","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:ebbbb9c05060895145c8438f03650b2bbd0b38412a7aa37b169294ead5570cff","target":"record","created_at":"2026-05-18T01:27:39Z","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":"d5a28f071048808f050122cf257b849f53b95192dcbc2451704ddee5c7541664","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-05T12:48:29Z","title_canon_sha256":"0151b51c5ed16f540d0dfa6f156c6355c4bd282d36bfe95aa91279f393b150de"},"schema_version":"1.0","source":{"id":"1511.01719","kind":"arxiv","version":1}},"canonical_sha256":"1b02a612f39e250e41aacf128597937137125721789f0570fe934fc6878d3d87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b02a612f39e250e41aacf128597937137125721789f0570fe934fc6878d3d87","first_computed_at":"2026-05-18T01:27:39.974999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:39.974999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"458oix2w1yv8/V2jU1dJdRp1CpcMy+lqWhRUgYdl/TxdCxbattntCdS8QoHKs4t0HUdqBUj9Kkd4Ia3/PkPnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:39.975487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebbbb9c05060895145c8438f03650b2bbd0b38412a7aa37b169294ead5570cff","sha256:a54c008a6a6ea7d3a7e6b6b7000263854dcde0fa1e98b638db08abadfc4bcacd"],"state_sha256":"7fb756967508ee92808055b056af6ef52bf6f4cad44233056c72dac8b92a6bee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+78GFE3bnDgXTHOl8cjVKuVQGTps+uR3Lwutac8pCwMayCh+Ptwi6SdCbklyJrQA5s3ZZZPNhuDCyIF29GPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:15:40.562945Z","bundle_sha256":"e5ceb4780c191a9d52b8ecf2377b9144d490e6b8f105a072ab55ac1c0ebf687e"}}