{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XLOIFPSCJUBB25SRF3IFCOOKR5","short_pith_number":"pith:XLOIFPSC","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"},"canonical_sha256":"badc82be424d021d76512ed05139ca8f74c77223185bf4e90934e20b76e6c475","source":{"kind":"arxiv","id":"1805.10071","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10071","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10071v2","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10071","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"XLOIFPSCJUBB","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XLOIFPSCJUBB25SR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XLOIFPSC","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XLOIFPSCJUBB25SRF3IFCOOKR5","target":"record","payload":{"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"},"canonical_sha256":"badc82be424d021d76512ed05139ca8f74c77223185bf4e90934e20b76e6c475","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"},"source_kind":"arxiv","source_id":"1805.10071","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":"2026-05-17T23:44:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8rVJfX485vNTVQulA3TrbGyUnWk07tWcCW4jvLtcuAZJuwxnGJ/9NPv2t8CNTwxkkY3mWPsv6MozHgIBx7cPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:48:05.014590Z"},"content_sha256":"fff672549ae72fef0083635efa809eec689950a35ff899929dd84d4a26baad68","schema_version":"1.0","event_id":"sha256:fff672549ae72fef0083635efa809eec689950a35ff899929dd84d4a26baad68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XLOIFPSCJUBB25SRF3IFCOOKR5","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5NbRkkxvSVfqr7i7h9FpQYGTq6nmk1426MqZoWAOJT5rQpUpGP1QKeYcu5zqMQy3JS51E8LY9t5nEWN00kSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:48:05.014934Z"},"content_sha256":"e2163f9d573f61fa72fe5f4da5bbf05c84cc0e0e544e2961b237f4cc8b57c2d0","schema_version":"1.0","event_id":"sha256:e2163f9d573f61fa72fe5f4da5bbf05c84cc0e0e544e2961b237f4cc8b57c2d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/bundle.json","state_url":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/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":"2026-06-23T16:48:05Z","links":{"resolver":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5","bundle":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/bundle.json","state":"https://pith.science/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLOIFPSCJUBB25SRF3IFCOOKR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XLOIFPSCJUBB25SRF3IFCOOKR5","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":"24efd6d9219d573aced7e0564637406849276f2cf7ec2cc8e377001e76c8308d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-25T10:28:52Z","title_canon_sha256":"7a5a1e3c1209bc1c97e942e9e9c1e66a87093ed28d2eb4db92a7ef6e3fb13164"},"schema_version":"1.0","source":{"id":"1805.10071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10071","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10071v2","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10071","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"XLOIFPSCJUBB","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XLOIFPSCJUBB25SR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XLOIFPSC","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:e2163f9d573f61fa72fe5f4da5bbf05c84cc0e0e544e2961b237f4cc8b57c2d0","target":"graph","created_at":"2026-05-17T23:44:32Z","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":"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.","authors_text":"John Haslegrave, Jonathan Jordan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-25T10:28:52Z","title":"Non-convergence of proportions of types in a preferential attachment graph with three co-existing types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10071","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:fff672549ae72fef0083635efa809eec689950a35ff899929dd84d4a26baad68","target":"record","created_at":"2026-05-17T23:44:32Z","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":"24efd6d9219d573aced7e0564637406849276f2cf7ec2cc8e377001e76c8308d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-25T10:28:52Z","title_canon_sha256":"7a5a1e3c1209bc1c97e942e9e9c1e66a87093ed28d2eb4db92a7ef6e3fb13164"},"schema_version":"1.0","source":{"id":"1805.10071","kind":"arxiv","version":2}},"canonical_sha256":"badc82be424d021d76512ed05139ca8f74c77223185bf4e90934e20b76e6c475","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"badc82be424d021d76512ed05139ca8f74c77223185bf4e90934e20b76e6c475","first_computed_at":"2026-05-17T23:44:32.494510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:32.494510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T+gGabP0KehoK0Yz2MX8SRLq5+9LdbLl9nZ7h5CCUkF9qtYmdQHlQ1PoQtf3HkObvH2gv50wrTHetkkPkgQqBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:32.495075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fff672549ae72fef0083635efa809eec689950a35ff899929dd84d4a26baad68","sha256:e2163f9d573f61fa72fe5f4da5bbf05c84cc0e0e544e2961b237f4cc8b57c2d0"],"state_sha256":"197da8bacc7ca8ed4d5b44558e7e02942ede6d4338126475634bba42f36a6061"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJDwTetohmqYgO1+typxwFk2ILptBeOVtZnbFA7kIY6LHChWxmngxhrR+vYncyTGkZ+GakdJp8I/cf4qs34CDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:48:05.016908Z","bundle_sha256":"15aaf898b9fd2e1cbd7e2fa0d3bd21a30d10f73ef9d568a3af0b6c1a7d139643"}}