{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XLOIFPSCJUBB25SRF3IFCOOKR5","short_pith_number":"pith:XLOIFPSC","schema_version":"1.0","canonical_sha256":"badc82be424d021d76512ed05139ca8f74c77223185bf4e90934e20b76e6c475","source":{"kind":"arxiv","id":"1805.10071","version":2},"attestation_state":"computed","paper":{"title":"Non-convergence of proportions of types in a preferential attachment graph with three co-existing types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"John Haslegrave, Jonathan Jordan","submitted_at":"2018-05-25T10:28:52Z","abstract_excerpt":"We consider the preferential attachment model with multiple vertex types introduced by Antunovi\\'c, Mossel and R\\'acz. We give an example with three types, based on the game of rock-paper-scissors, where the proportions of vertices of the different types almost surely do not converge to a limit, giving a counterexample to a conjecture of Antunovi\\'c, Mossel and R\\'acz. We also consider another family of examples where we show that the conjecture does hold."},"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":"1805.10071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-25T10:28:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7a5a1e3c1209bc1c97e942e9e9c1e66a87093ed28d2eb4db92a7ef6e3fb13164","abstract_canon_sha256":"24efd6d9219d573aced7e0564637406849276f2cf7ec2cc8e377001e76c8308d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:32.495075Z","signature_b64":"T+gGabP0KehoK0Yz2MX8SRLq5+9LdbLl9nZ7h5CCUkF9qtYmdQHlQ1PoQtf3HkObvH2gv50wrTHetkkPkgQqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"badc82be424d021d76512ed05139ca8f74c77223185bf4e90934e20b76e6c475","last_reissued_at":"2026-05-17T23:44:32.494510Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:32.494510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-convergence of proportions of types in a preferential attachment graph with three co-existing types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"John Haslegrave, Jonathan Jordan","submitted_at":"2018-05-25T10:28:52Z","abstract_excerpt":"We consider the preferential attachment model with multiple vertex types introduced by Antunovi\\'c, Mossel and R\\'acz. We give an example with three types, based on the game of rock-paper-scissors, where the proportions of vertices of the different types almost surely do not converge to a limit, giving a counterexample to a conjecture of Antunovi\\'c, Mossel and R\\'acz. We also consider another family of examples where we show that the conjecture does hold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10071","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":"1805.10071","created_at":"2026-05-17T23:44:32.494591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.10071v2","created_at":"2026-05-17T23:44:32.494591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10071","created_at":"2026-05-17T23:44:32.494591+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLOIFPSCJUBB","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLOIFPSCJUBB25SR","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLOIFPSC","created_at":"2026-05-18T12:33:01.666342+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/XLOIFPSCJUBB25SRF3IFCOOKR5","json":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5.json","graph_json":"https://pith.science/api/pith-number/XLOIFPSCJUBB25SRF3IFCOOKR5/graph.json","events_json":"https://pith.science/api/pith-number/XLOIFPSCJUBB25SRF3IFCOOKR5/events.json","paper":"https://pith.science/paper/XLOIFPSC"},"agent_actions":{"view_html":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5","download_json":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5.json","view_paper":"https://pith.science/paper/XLOIFPSC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.10071&json=true","fetch_graph":"https://pith.science/api/pith-number/XLOIFPSCJUBB25SRF3IFCOOKR5/graph.json","fetch_events":"https://pith.science/api/pith-number/XLOIFPSCJUBB25SRF3IFCOOKR5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/action/storage_attestation","attest_author":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/action/author_attestation","sign_citation":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/action/citation_signature","submit_replication":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/action/replication_record"}},"created_at":"2026-05-17T23:44:32.494591+00:00","updated_at":"2026-05-17T23:44:32.494591+00:00"}