{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3ABDCMUFQK6TJKRA6MVAFL2JHG","short_pith_number":"pith:3ABDCMUF","canonical_record":{"source":{"id":"1310.1054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:34:32Z","cross_cats_sorted":[],"title_canon_sha256":"c9d03a109264968412b64c2e39e05c930e99b33ffcb8baa6a24971a771e81d2e","abstract_canon_sha256":"d5c166fdf38fc870a6361893167d6691bdd8dbdca5da65a0bfe933df3f8c28a8"},"schema_version":"1.0"},"canonical_sha256":"d80231328582bd34aa20f32a02af49399f1370f06cd6494284ea60f7377684c5","source":{"kind":"arxiv","id":"1310.1054","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1054","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1054v2","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1054","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"3ABDCMUFQK6T","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3ABDCMUFQK6TJKRA","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3ABDCMUF","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3ABDCMUFQK6TJKRA6MVAFL2JHG","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:34:32Z","cross_cats_sorted":[],"title_canon_sha256":"c9d03a109264968412b64c2e39e05c930e99b33ffcb8baa6a24971a771e81d2e","abstract_canon_sha256":"d5c166fdf38fc870a6361893167d6691bdd8dbdca5da65a0bfe933df3f8c28a8"},"schema_version":"1.0"},"canonical_sha256":"d80231328582bd34aa20f32a02af49399f1370f06cd6494284ea60f7377684c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:32.321307Z","signature_b64":"V/k9HBV6YMylOTJxj/rIkjyb83gqSJ9VyL+Q8DcKQ9QF8Mm5rRHLL5MNt9Us6N9xHm0V4okXcKfITRUR0qr8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d80231328582bd34aa20f32a02af49399f1370f06cd6494284ea60f7377684c5","last_reissued_at":"2026-05-18T03:06:32.320795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:32.320795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1054","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":"2026-05-18T03:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+JQrPWuq4Nz7sEyp0n+pBeZQS+RUwt/sS4yjzxrGAX3oqlOS6w2uwvijPk5Y/Q3mgrsMuqbUdlkeGvnNFO6sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:27:43.792993Z"},"content_sha256":"e4f8fce4386d646c7ee8cdda0a03f85de8e210736eb6f5d93fa3f05451914812","schema_version":"1.0","event_id":"sha256:e4f8fce4386d646c7ee8cdda0a03f85de8e210736eb6f5d93fa3f05451914812"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3ABDCMUFQK6TJKRA6MVAFL2JHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Border collision bifurcations of stroboscopic maps in periodically driven spiking models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Albert Granados, Fr\\'ed\\'erique Cl\\'ement, Martin Krupa","submitted_at":"2013-10-03T18:34:32Z","abstract_excerpt":"In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is monotonic, possesses an attracting subthreshold equilibrium point and is forced by means of periodic pulsatile (square wave) function.\\\\ In contrast to classical methods, in our approach we use the stroboscopic map (time-$T$ return map) instead of the so-called firing-map. It becomes a discontinuous map potentially defined in an infinite number of partitions. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1054","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":"2026-05-18T03:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xCR2poHrNdITAax0JZ7cgxTXevUQeSInDSqkaukiFHPiPc45Uhiksb5fYSEN/UF5pDC9XSh9oaVyav+HArIcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:27:43.793540Z"},"content_sha256":"afc486154c73648e1364f04ecbcd5f1d528bc50e09ef6573a92db5e4123ed90d","schema_version":"1.0","event_id":"sha256:afc486154c73648e1364f04ecbcd5f1d528bc50e09ef6573a92db5e4123ed90d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ABDCMUFQK6TJKRA6MVAFL2JHG/bundle.json","state_url":"https://pith.science/pith/3ABDCMUFQK6TJKRA6MVAFL2JHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ABDCMUFQK6TJKRA6MVAFL2JHG/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":"2026-06-07T10:27:43Z","links":{"resolver":"https://pith.science/pith/3ABDCMUFQK6TJKRA6MVAFL2JHG","bundle":"https://pith.science/pith/3ABDCMUFQK6TJKRA6MVAFL2JHG/bundle.json","state":"https://pith.science/pith/3ABDCMUFQK6TJKRA6MVAFL2JHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ABDCMUFQK6TJKRA6MVAFL2JHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3ABDCMUFQK6TJKRA6MVAFL2JHG","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":"d5c166fdf38fc870a6361893167d6691bdd8dbdca5da65a0bfe933df3f8c28a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:34:32Z","title_canon_sha256":"c9d03a109264968412b64c2e39e05c930e99b33ffcb8baa6a24971a771e81d2e"},"schema_version":"1.0","source":{"id":"1310.1054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1054","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1054v2","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1054","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"3ABDCMUFQK6T","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3ABDCMUFQK6TJKRA","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3ABDCMUF","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:afc486154c73648e1364f04ecbcd5f1d528bc50e09ef6573a92db5e4123ed90d","target":"graph","created_at":"2026-05-18T03:06:32Z","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":"In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is monotonic, possesses an attracting subthreshold equilibrium point and is forced by means of periodic pulsatile (square wave) function.\\\\ In contrast to classical methods, in our approach we use the stroboscopic map (time-$T$ return map) instead of the so-called firing-map. It becomes a discontinuous map potentially defined in an infinite number of partitions. ","authors_text":"Albert Granados, Fr\\'ed\\'erique Cl\\'ement, Martin Krupa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:34:32Z","title":"Border collision bifurcations of stroboscopic maps in periodically driven spiking models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1054","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:e4f8fce4386d646c7ee8cdda0a03f85de8e210736eb6f5d93fa3f05451914812","target":"record","created_at":"2026-05-18T03:06:32Z","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":"d5c166fdf38fc870a6361893167d6691bdd8dbdca5da65a0bfe933df3f8c28a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-03T18:34:32Z","title_canon_sha256":"c9d03a109264968412b64c2e39e05c930e99b33ffcb8baa6a24971a771e81d2e"},"schema_version":"1.0","source":{"id":"1310.1054","kind":"arxiv","version":2}},"canonical_sha256":"d80231328582bd34aa20f32a02af49399f1370f06cd6494284ea60f7377684c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d80231328582bd34aa20f32a02af49399f1370f06cd6494284ea60f7377684c5","first_computed_at":"2026-05-18T03:06:32.320795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:32.320795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V/k9HBV6YMylOTJxj/rIkjyb83gqSJ9VyL+Q8DcKQ9QF8Mm5rRHLL5MNt9Us6N9xHm0V4okXcKfITRUR0qr8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:32.321307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4f8fce4386d646c7ee8cdda0a03f85de8e210736eb6f5d93fa3f05451914812","sha256:afc486154c73648e1364f04ecbcd5f1d528bc50e09ef6573a92db5e4123ed90d"],"state_sha256":"b85c0221b6964e13fad25417b9218a7b60f273663badca079ee53cd1d5cc24bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ietXUxkPpSx77jvkApXLKnPn+Gau2IDagdVIzgL3LEbq2JU5Gon91x1U+N/GLXPJvo3nrSOXH9AL1j8QHqyoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:27:43.796196Z","bundle_sha256":"454527fdac69c1cfd3471ce9ef796413ed69a2b085051eb1dfe89929e4c136a2"}}