{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6SJPEBIOCAPXTAUGANOPM6INBG","short_pith_number":"pith:6SJPEBIO","schema_version":"1.0","canonical_sha256":"f492f2050e101f798286035cf6790d099ca85ac418040be7843d2151dbaf2dc8","source":{"kind":"arxiv","id":"1209.4034","version":1},"attestation_state":"computed","paper":{"title":"Competing contact processes on homogeneous networks with tunable clusterization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.soc-ph","authors_text":"Krzysztof Kulakowski, Marcin Rybak","submitted_at":"2012-09-18T16:57:04Z","abstract_excerpt":"We investigate two homogeneous networks: the Watts-Strogatz network and the random Erdos-Renyi network, the latter with tunable clustering coefficient $C$. The network is an area of two competing contact processes, where nodes can be in two states, S or D. A node S becomes D with probability 1 if at least two its mutually linked neighbours are D. A node D becomes S with a given probability $p$ if at least one of its neighbours is S. The competition between the processes is described by a phase diagram, where the critical probability $p_c$ depends on the clustering coefficient $C$. For $p>p_c$ "},"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":"1209.4034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-18T16:57:04Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"88f906e9413abd81753a6126275af8723ccce7c1736d8f497542eaffd7aacb2f","abstract_canon_sha256":"4bfa55262c67454c7f96bda1565734168d8415c6c7543da6e61df56a1cb0493c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:26.754272Z","signature_b64":"6S9lzwsz4u4EZAmWwERRoSh6zsktKIySmiw8/09+J5boh3p21yUYjYwZJEgKGivqjAnhLfZytEX8WoqUtkn0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f492f2050e101f798286035cf6790d099ca85ac418040be7843d2151dbaf2dc8","last_reissued_at":"2026-05-18T01:54:26.753687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:26.753687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Competing contact processes on homogeneous networks with tunable clusterization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.soc-ph","authors_text":"Krzysztof Kulakowski, Marcin Rybak","submitted_at":"2012-09-18T16:57:04Z","abstract_excerpt":"We investigate two homogeneous networks: the Watts-Strogatz network and the random Erdos-Renyi network, the latter with tunable clustering coefficient $C$. The network is an area of two competing contact processes, where nodes can be in two states, S or D. A node S becomes D with probability 1 if at least two its mutually linked neighbours are D. A node D becomes S with a given probability $p$ if at least one of its neighbours is S. The competition between the processes is described by a phase diagram, where the critical probability $p_c$ depends on the clustering coefficient $C$. For $p>p_c$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4034","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.4034","created_at":"2026-05-18T01:54:26.753767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4034v1","created_at":"2026-05-18T01:54:26.753767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4034","created_at":"2026-05-18T01:54:26.753767+00:00"},{"alias_kind":"pith_short_12","alias_value":"6SJPEBIOCAPX","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6SJPEBIOCAPXTAUG","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6SJPEBIO","created_at":"2026-05-18T12:26:56.085431+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/6SJPEBIOCAPXTAUGANOPM6INBG","json":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG.json","graph_json":"https://pith.science/api/pith-number/6SJPEBIOCAPXTAUGANOPM6INBG/graph.json","events_json":"https://pith.science/api/pith-number/6SJPEBIOCAPXTAUGANOPM6INBG/events.json","paper":"https://pith.science/paper/6SJPEBIO"},"agent_actions":{"view_html":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG","download_json":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG.json","view_paper":"https://pith.science/paper/6SJPEBIO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4034&json=true","fetch_graph":"https://pith.science/api/pith-number/6SJPEBIOCAPXTAUGANOPM6INBG/graph.json","fetch_events":"https://pith.science/api/pith-number/6SJPEBIOCAPXTAUGANOPM6INBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG/action/storage_attestation","attest_author":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG/action/author_attestation","sign_citation":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG/action/citation_signature","submit_replication":"https://pith.science/pith/6SJPEBIOCAPXTAUGANOPM6INBG/action/replication_record"}},"created_at":"2026-05-18T01:54:26.753767+00:00","updated_at":"2026-05-18T01:54:26.753767+00:00"}