{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RJWNVCRTH6BQQQ7S3K56YL7523","short_pith_number":"pith:RJWNVCRT","canonical_record":{"source":{"id":"1903.06968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T18:24:47Z","cross_cats_sorted":[],"title_canon_sha256":"1b9fe95b165271fb7da08acc7cfd089403e8967e391c20f14cf1a781016f98db","abstract_canon_sha256":"13816f08f03403759c4a7ad9e6f5d65aab3c70918fea540bbe9708556770dc87"},"schema_version":"1.0"},"canonical_sha256":"8a6cda8a333f830843f2dabbec2ffdd6fdb0e0fe145f57fedcef0128f092ba60","source":{"kind":"arxiv","id":"1903.06968","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06968","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06968v1","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06968","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"RJWNVCRTH6BQ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RJWNVCRTH6BQQQ7S","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RJWNVCRT","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RJWNVCRTH6BQQQ7S3K56YL7523","target":"record","payload":{"canonical_record":{"source":{"id":"1903.06968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T18:24:47Z","cross_cats_sorted":[],"title_canon_sha256":"1b9fe95b165271fb7da08acc7cfd089403e8967e391c20f14cf1a781016f98db","abstract_canon_sha256":"13816f08f03403759c4a7ad9e6f5d65aab3c70918fea540bbe9708556770dc87"},"schema_version":"1.0"},"canonical_sha256":"8a6cda8a333f830843f2dabbec2ffdd6fdb0e0fe145f57fedcef0128f092ba60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:06.612092Z","signature_b64":"NTzCRh7MyIpj4R21pxnrNPSkstQA9R+ag3STHxWY3D/vMYtqlfxKqYE2ERTtztAGXn0d9mxNPwMyxLJRomVHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a6cda8a333f830843f2dabbec2ffdd6fdb0e0fe145f57fedcef0128f092ba60","last_reissued_at":"2026-05-17T23:51:06.611469Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:06.611469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.06968","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":"2026-05-17T23:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXa51a4qeX09yH9U9cr6Fz6kWCVoPeVNkwZpv7IH8gArfg0QPcLSk6hObfKn+BWxatYymOmnaPO0Zykshd/uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:13:58.085372Z"},"content_sha256":"477511547113ae9e2976103bfa40f513002def5b452caabd1337881086a80dbb","schema_version":"1.0","event_id":"sha256:477511547113ae9e2976103bfa40f513002def5b452caabd1337881086a80dbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RJWNVCRTH6BQQQ7S3K56YL7523","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Creation of discontinuities in circle maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anne C. Skeldon, Gianne Derks, Paul A. Glendinning","submitted_at":"2019-03-16T18:24:47Z","abstract_excerpt":"Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and `threshold' systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake regulation, we consider how structural transitions in circle maps occur. In particular we describe how maps evolve near the creation of a discontinuity.\n  We show that the natural way to create discontinuities in the maps associated with both threshold systems and Cherry flows results in a square root singularity in the map as the discontinuity is approached fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06968","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":"2026-05-17T23:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DvYNIiMN8allbIPrhHS6bl1P70+KDTXApNqZmxTHiGECygXGu+XzOrLRk8w6wpl79a7CjBLaBYg6g+EXCnf9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:13:58.085768Z"},"content_sha256":"61962e177851335a96f4106156a960d8e7286483ea903a24af795273a42f7625","schema_version":"1.0","event_id":"sha256:61962e177851335a96f4106156a960d8e7286483ea903a24af795273a42f7625"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RJWNVCRTH6BQQQ7S3K56YL7523/bundle.json","state_url":"https://pith.science/pith/RJWNVCRTH6BQQQ7S3K56YL7523/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RJWNVCRTH6BQQQ7S3K56YL7523/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":"2026-06-24T16:13:58Z","links":{"resolver":"https://pith.science/pith/RJWNVCRTH6BQQQ7S3K56YL7523","bundle":"https://pith.science/pith/RJWNVCRTH6BQQQ7S3K56YL7523/bundle.json","state":"https://pith.science/pith/RJWNVCRTH6BQQQ7S3K56YL7523/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RJWNVCRTH6BQQQ7S3K56YL7523/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RJWNVCRTH6BQQQ7S3K56YL7523","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":"13816f08f03403759c4a7ad9e6f5d65aab3c70918fea540bbe9708556770dc87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T18:24:47Z","title_canon_sha256":"1b9fe95b165271fb7da08acc7cfd089403e8967e391c20f14cf1a781016f98db"},"schema_version":"1.0","source":{"id":"1903.06968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06968","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06968v1","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06968","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"RJWNVCRTH6BQ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RJWNVCRTH6BQQQ7S","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RJWNVCRT","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:61962e177851335a96f4106156a960d8e7286483ea903a24af795273a42f7625","target":"graph","created_at":"2026-05-17T23:51:06Z","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":"Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and `threshold' systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake regulation, we consider how structural transitions in circle maps occur. In particular we describe how maps evolve near the creation of a discontinuity.\n  We show that the natural way to create discontinuities in the maps associated with both threshold systems and Cherry flows results in a square root singularity in the map as the discontinuity is approached fr","authors_text":"Anne C. Skeldon, Gianne Derks, Paul A. Glendinning","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T18:24:47Z","title":"Creation of discontinuities in circle maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06968","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":"sha256:477511547113ae9e2976103bfa40f513002def5b452caabd1337881086a80dbb","target":"record","created_at":"2026-05-17T23:51:06Z","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":"13816f08f03403759c4a7ad9e6f5d65aab3c70918fea540bbe9708556770dc87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T18:24:47Z","title_canon_sha256":"1b9fe95b165271fb7da08acc7cfd089403e8967e391c20f14cf1a781016f98db"},"schema_version":"1.0","source":{"id":"1903.06968","kind":"arxiv","version":1}},"canonical_sha256":"8a6cda8a333f830843f2dabbec2ffdd6fdb0e0fe145f57fedcef0128f092ba60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a6cda8a333f830843f2dabbec2ffdd6fdb0e0fe145f57fedcef0128f092ba60","first_computed_at":"2026-05-17T23:51:06.611469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:06.611469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NTzCRh7MyIpj4R21pxnrNPSkstQA9R+ag3STHxWY3D/vMYtqlfxKqYE2ERTtztAGXn0d9mxNPwMyxLJRomVHAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:06.612092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:477511547113ae9e2976103bfa40f513002def5b452caabd1337881086a80dbb","sha256:61962e177851335a96f4106156a960d8e7286483ea903a24af795273a42f7625"],"state_sha256":"31dbade37674bba9bbb79909bad570bd146a6e39bf7de3ff719f73909db2cf8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rCsoC8iGO0pivdpvV6vc2xCtQHTe+vtatDgcZDRRHCf58Pj+6HCfE9ENE9ZO3YLNUjh9wwes/y5wIhrBGB9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:13:58.087815Z","bundle_sha256":"ddb02bc54796c69541573aa46e11b3e69e97cb034767e134d2f4ea1a0beee6ec"}}