{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6N2S2TM2PQF7BP4LKY4TWRRD3J","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":"cae9ddf319d0d8c51c90fece1b9b4efb998ed9a3eec81dc09d6c8a6586a7a0fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-28T11:49:26Z","title_canon_sha256":"45f47c99b215d81323d8b56be9c7758ba5015413a1fee392afdd37025a38a9e9"},"schema_version":"1.0","source":{"id":"1509.08282","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08282","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08282v3","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08282","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"6N2S2TM2PQF7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6N2S2TM2PQF7BP4L","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6N2S2TM2","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:2210e9433d99227fa7189c0416fa4e9fcd517b41a76d4eab6d48e80dd47f8680","target":"graph","created_at":"2026-05-18T00:53:24Z","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":"This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by which these are generated relies fundamentally on the hybrid structure of the flow: invariant manifolds of the continuous dynamics govern small oscillations, while discr","authors_text":"Alexandre Vidal, Jonathan E. Rubin, Jonathan Touboul, Justyna Signerska-Rynkowska","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-28T11:49:26Z","title":"Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08282","kind":"arxiv","version":3},"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":"sha256:5a5e009b3547e6a27a3a1b7b422cfaf8c044b015b57661ea6d4429393bf61ee1","target":"record","created_at":"2026-05-18T00:53:24Z","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":"cae9ddf319d0d8c51c90fece1b9b4efb998ed9a3eec81dc09d6c8a6586a7a0fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-28T11:49:26Z","title_canon_sha256":"45f47c99b215d81323d8b56be9c7758ba5015413a1fee392afdd37025a38a9e9"},"schema_version":"1.0","source":{"id":"1509.08282","kind":"arxiv","version":3}},"canonical_sha256":"f3752d4d9a7c0bf0bf8b56393b4623da5b967898861a1334b1b897b0afd0a1b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3752d4d9a7c0bf0bf8b56393b4623da5b967898861a1334b1b897b0afd0a1b4","first_computed_at":"2026-05-18T00:53:24.614353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:24.614353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/eGHN7chCa1yF3cU5h0y0F8lGRLmI3RGJTQyxUOqWeqpgyWO5zKFN3WpK6PbrEHe/pUD1ZA8qNc4bzDlnfU6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:24.614810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08282","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a5e009b3547e6a27a3a1b7b422cfaf8c044b015b57661ea6d4429393bf61ee1","sha256:2210e9433d99227fa7189c0416fa4e9fcd517b41a76d4eab6d48e80dd47f8680"],"state_sha256":"0643659c61ff676c2c3718e4a50b629279c6dc7104e748cbc1f32a1f6f064649"}