{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GJACHHSSBMXKHAUADWQ7KHQSZK","short_pith_number":"pith:GJACHHSS","schema_version":"1.0","canonical_sha256":"3240239e520b2ea382801da1f51e12caa33593301ba4d47b6d62e5047988f315","source":{"kind":"arxiv","id":"1302.5904","version":2},"attestation_state":"computed","paper":{"title":"Dynamics of large cooperative pulsed-coupled networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras","submitted_at":"2013-02-24T13:35:33Z","abstract_excerpt":"We study the deterministic dynamics of networks N composed by m non identical, mutually pulse-coupled cells. We assume weighted, asymmetric and positive (cooperative) interactions among the cells, and arbitrarily large values of m. We consider two cases of the network's graph: the complete graph, and the existence of a large core (i.e. a large complete subgraph). First, we prove that the system periodically eventually synchronizes with a natural \"spiking period\" \\ p >=1, and that if the cells are mutually structurally identical or similar, then the synchronization is complete (p= 1) . Second, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.5904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-24T13:35:33Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"3cbb03e2ffd6c966f0b9d9fae8501e55ba7ecfe4032fa569c1b0bc27c7f5f186","abstract_canon_sha256":"5fb4b2c45fa62e71531d665edab89107994c25dc31080cc4ff412c6e19830174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.551164Z","signature_b64":"R6mM+viTLCiGfyperJq/ezjYJ0N4tSoQz+joS2km8dzshY/x2yekvvvCx7fnsoVcdnaFx2Pd57S1T3SXD2iTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3240239e520b2ea382801da1f51e12caa33593301ba4d47b6d62e5047988f315","last_reissued_at":"2026-05-18T01:11:55.550834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.550834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of large cooperative pulsed-coupled networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras","submitted_at":"2013-02-24T13:35:33Z","abstract_excerpt":"We study the deterministic dynamics of networks N composed by m non identical, mutually pulse-coupled cells. We assume weighted, asymmetric and positive (cooperative) interactions among the cells, and arbitrarily large values of m. We consider two cases of the network's graph: the complete graph, and the existence of a large core (i.e. a large complete subgraph). First, we prove that the system periodically eventually synchronizes with a natural \"spiking period\" \\ p >=1, and that if the cells are mutually structurally identical or similar, then the synchronization is complete (p= 1) . Second, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5904","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.5904","created_at":"2026-05-18T01:11:55.550888+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5904v2","created_at":"2026-05-18T01:11:55.550888+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5904","created_at":"2026-05-18T01:11:55.550888+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJACHHSSBMXK","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJACHHSSBMXKHAUA","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJACHHSS","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK","json":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK.json","graph_json":"https://pith.science/api/pith-number/GJACHHSSBMXKHAUADWQ7KHQSZK/graph.json","events_json":"https://pith.science/api/pith-number/GJACHHSSBMXKHAUADWQ7KHQSZK/events.json","paper":"https://pith.science/paper/GJACHHSS"},"agent_actions":{"view_html":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK","download_json":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK.json","view_paper":"https://pith.science/paper/GJACHHSS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5904&json=true","fetch_graph":"https://pith.science/api/pith-number/GJACHHSSBMXKHAUADWQ7KHQSZK/graph.json","fetch_events":"https://pith.science/api/pith-number/GJACHHSSBMXKHAUADWQ7KHQSZK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK/action/storage_attestation","attest_author":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK/action/author_attestation","sign_citation":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK/action/citation_signature","submit_replication":"https://pith.science/pith/GJACHHSSBMXKHAUADWQ7KHQSZK/action/replication_record"}},"created_at":"2026-05-18T01:11:55.550888+00:00","updated_at":"2026-05-18T01:11:55.550888+00:00"}