{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PBC6SBVRGSOHM6QHBPPWKOIV3U","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":"5d92583878383e73fba80f7eef4218ec18713f36634c8df5b8ed0e217570cf36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-14T12:44:57Z","title_canon_sha256":"a2188a3f31f49b7f26fb52c8c952a823f0a6f8b26e567a5243b6715e9854fddc"},"schema_version":"1.0","source":{"id":"1610.04434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04434","created_at":"2026-05-18T01:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04434v1","created_at":"2026-05-18T01:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04434","created_at":"2026-05-18T01:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"PBC6SBVRGSOH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PBC6SBVRGSOHM6QH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PBC6SBVR","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:da1570c2d94a55a49201d980a6c2882d9d85e4ca54ac9d02c3ffd0d7e11359b4","target":"graph","created_at":"2026-05-18T01:02:15Z","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":"We investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and $\\mu$-almost periodic functions. Special attention is paid to the properties of a firing map and its displacement, which give information about the spiking behaviour of the system under consideration. We provide conditions under which such maps are well-defined for every $t \\in \\mathbb R$ and are uniformly continuous. Moreover, we show that the LIF model with a Stepanov almost periodic input has a uniformly almost periodic displacement map. We also show that in the case of a $\\mu$-almost periodic drive","authors_text":"Adam Nawrocki, Justyna Signerska-Rynkowska, Piotr Kasprzak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-14T12:44:57Z","title":"Integrate-and-fire models with an almost periodic input function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04434","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:a4ac520586519d637460567dbdca505650eb0aa422639fd0963b9819e4c8a9ce","target":"record","created_at":"2026-05-18T01:02:15Z","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":"5d92583878383e73fba80f7eef4218ec18713f36634c8df5b8ed0e217570cf36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-14T12:44:57Z","title_canon_sha256":"a2188a3f31f49b7f26fb52c8c952a823f0a6f8b26e567a5243b6715e9854fddc"},"schema_version":"1.0","source":{"id":"1610.04434","kind":"arxiv","version":1}},"canonical_sha256":"7845e906b1349c767a070bdf653915dd2ddaa0f9ebe480436cad0498722ae2ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7845e906b1349c767a070bdf653915dd2ddaa0f9ebe480436cad0498722ae2ee","first_computed_at":"2026-05-18T01:02:15.242645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:15.242645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SCYagxYYYdf3Lz3kVX/iua8BM+ovKVkKtpPTdWRZZO/ESQtNMED5kHXFvvWKcfecT6gUFFjIRHtOoN0yma+gAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:15.243277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4ac520586519d637460567dbdca505650eb0aa422639fd0963b9819e4c8a9ce","sha256:da1570c2d94a55a49201d980a6c2882d9d85e4ca54ac9d02c3ffd0d7e11359b4"],"state_sha256":"ca0b4482df1ceb3a5e1dd725c9781b803e5da0648c4a64f668a2c5b80a9b4a41"}