{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Z7UOJNUJLUCC3MKTAP5QQRJ5P6","short_pith_number":"pith:Z7UOJNUJ","canonical_record":{"source":{"id":"1610.08609","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2016-10-27T04:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"6add21e23aa7a950e68315919e7ba6b263f38cee0ef82e4fd8a82c242b52299f","abstract_canon_sha256":"8fdbb8fe0e427c301bf064b5d6c6b8d6a1dabed1b4d0e3b0209c6d663410d6a6"},"schema_version":"1.0"},"canonical_sha256":"cfe8e4b6895d042db15303fb08453d7f81075a3ce782b9e24cbf8b091870e92f","source":{"kind":"arxiv","id":"1610.08609","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08609","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08609v1","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08609","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"pith_short_12","alias_value":"Z7UOJNUJLUCC","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z7UOJNUJLUCC3MKT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z7UOJNUJ","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Z7UOJNUJLUCC3MKTAP5QQRJ5P6","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08609","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2016-10-27T04:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"6add21e23aa7a950e68315919e7ba6b263f38cee0ef82e4fd8a82c242b52299f","abstract_canon_sha256":"8fdbb8fe0e427c301bf064b5d6c6b8d6a1dabed1b4d0e3b0209c6d663410d6a6"},"schema_version":"1.0"},"canonical_sha256":"cfe8e4b6895d042db15303fb08453d7f81075a3ce782b9e24cbf8b091870e92f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:07.751002Z","signature_b64":"Da/5BLFd4Jfq5x8mx/4MO3M0vmn8hIBYhi7HjirGR53Xig8uzSdlNqdQnDsVQbTe/9+/nMeFN1g7MNvibkd9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfe8e4b6895d042db15303fb08453d7f81075a3ce782b9e24cbf8b091870e92f","last_reissued_at":"2026-05-18T01:01:07.750406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:07.750406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08609","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":"2026-05-18T01:01:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"baTAfHO8e/J3ZJ3ESS6EAyXnVRo8RF5WsOtZq6s9/KfZdBzzbPfQyWF7RHNiJDCaSOIbbNIdaao0Ww2NVhFRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:59:44.487123Z"},"content_sha256":"08fda2723fa0210f1e2829260f7a574245d68b56bce21fd27547547caebe100a","schema_version":"1.0","event_id":"sha256:08fda2723fa0210f1e2829260f7a574245d68b56bce21fd27547547caebe100a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Z7UOJNUJLUCC3MKTAP5QQRJ5P6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Systems of Delay Differential Equations: Analysis of a model with feedback","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Alliera, Pablo Amster","submitted_at":"2016-10-27T04:10:29Z","abstract_excerpt":"Self-regulatory models are common in nature, as described e.g. in (\\cite{mur}), (\\cite{ha}) and (\\cite{Gb}).\\\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in the {next} gland, which successively generates another hormone to stimulate the next one and so on. In the end, a final hormone is released which, by increasing its concentration, will inhibit the secretion of previous hormones that allowed the production process. This generates the decay of this hormone to a minimum threshold that re-activates the cycle again"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08609","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":"2026-05-18T01:01:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9h6OXzWCWVuWDr7Cn/DuoChAxwAHvR73e8vICS0nUjVrK+RR1XekhNjjXwUcdAbKoO2PiXPiT+IRFBOdnPrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:59:44.487487Z"},"content_sha256":"fa6d78f867bf2cfdc597e18e615f8557bb7bcef76a31943484d7ca9961163729","schema_version":"1.0","event_id":"sha256:fa6d78f867bf2cfdc597e18e615f8557bb7bcef76a31943484d7ca9961163729"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7UOJNUJLUCC3MKTAP5QQRJ5P6/bundle.json","state_url":"https://pith.science/pith/Z7UOJNUJLUCC3MKTAP5QQRJ5P6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7UOJNUJLUCC3MKTAP5QQRJ5P6/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":"2026-05-31T09:59:44Z","links":{"resolver":"https://pith.science/pith/Z7UOJNUJLUCC3MKTAP5QQRJ5P6","bundle":"https://pith.science/pith/Z7UOJNUJLUCC3MKTAP5QQRJ5P6/bundle.json","state":"https://pith.science/pith/Z7UOJNUJLUCC3MKTAP5QQRJ5P6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7UOJNUJLUCC3MKTAP5QQRJ5P6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z7UOJNUJLUCC3MKTAP5QQRJ5P6","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":"8fdbb8fe0e427c301bf064b5d6c6b8d6a1dabed1b4d0e3b0209c6d663410d6a6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2016-10-27T04:10:29Z","title_canon_sha256":"6add21e23aa7a950e68315919e7ba6b263f38cee0ef82e4fd8a82c242b52299f"},"schema_version":"1.0","source":{"id":"1610.08609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08609","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08609v1","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08609","created_at":"2026-05-18T01:01:07Z"},{"alias_kind":"pith_short_12","alias_value":"Z7UOJNUJLUCC","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z7UOJNUJLUCC3MKT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z7UOJNUJ","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:fa6d78f867bf2cfdc597e18e615f8557bb7bcef76a31943484d7ca9961163729","target":"graph","created_at":"2026-05-18T01:01:07Z","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":"Self-regulatory models are common in nature, as described e.g. in (\\cite{mur}), (\\cite{ha}) and (\\cite{Gb}).\\\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in the {next} gland, which successively generates another hormone to stimulate the next one and so on. In the end, a final hormone is released which, by increasing its concentration, will inhibit the secretion of previous hormones that allowed the production process. This generates the decay of this hormone to a minimum threshold that re-activates the cycle again","authors_text":"Carlos Alliera, Pablo Amster","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2016-10-27T04:10:29Z","title":"Systems of Delay Differential Equations: Analysis of a model with feedback"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08609","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":"sha256:08fda2723fa0210f1e2829260f7a574245d68b56bce21fd27547547caebe100a","target":"record","created_at":"2026-05-18T01:01:07Z","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":"8fdbb8fe0e427c301bf064b5d6c6b8d6a1dabed1b4d0e3b0209c6d663410d6a6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DS","submitted_at":"2016-10-27T04:10:29Z","title_canon_sha256":"6add21e23aa7a950e68315919e7ba6b263f38cee0ef82e4fd8a82c242b52299f"},"schema_version":"1.0","source":{"id":"1610.08609","kind":"arxiv","version":1}},"canonical_sha256":"cfe8e4b6895d042db15303fb08453d7f81075a3ce782b9e24cbf8b091870e92f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfe8e4b6895d042db15303fb08453d7f81075a3ce782b9e24cbf8b091870e92f","first_computed_at":"2026-05-18T01:01:07.750406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:07.750406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Da/5BLFd4Jfq5x8mx/4MO3M0vmn8hIBYhi7HjirGR53Xig8uzSdlNqdQnDsVQbTe/9+/nMeFN1g7MNvibkd9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:07.751002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08fda2723fa0210f1e2829260f7a574245d68b56bce21fd27547547caebe100a","sha256:fa6d78f867bf2cfdc597e18e615f8557bb7bcef76a31943484d7ca9961163729"],"state_sha256":"8963f4b8cd08761f041d1c971981bedcd4593ddeeb79dcde704881127a88b73f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nfYred5hALMWta212MElLhhRqBHkiTlX+Uwfd2B3OWXjfAH+9u1f03JfRN6tZdLyIB9M3/tJdJf10QGso4+GCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:59:44.489569Z","bundle_sha256":"8f66d82897805a5150e14eeed503e7fbc63e484acff93a9fdf7e5e61becace08"}}