{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RVAHLD7A2QEYHIQ4TL5IWA6AT3","short_pith_number":"pith:RVAHLD7A","canonical_record":{"source":{"id":"1705.07649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-22T10:26:52Z","cross_cats_sorted":[],"title_canon_sha256":"5cb5161df9f104572fa688434b5a74c62e585dc4a8380054a4f37573405391c9","abstract_canon_sha256":"55d5c90e06f3f2085987138497523de2b3f093a6d9f352320db93787a81f994e"},"schema_version":"1.0"},"canonical_sha256":"8d40758fe0d40983a21c9afa8b03c09ec7dfe067b6f622e77882c41ecc7cffae","source":{"kind":"arxiv","id":"1705.07649","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07649","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07649v2","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07649","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"RVAHLD7A2QEY","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RVAHLD7A2QEYHIQ4","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RVAHLD7A","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RVAHLD7A2QEYHIQ4TL5IWA6AT3","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-22T10:26:52Z","cross_cats_sorted":[],"title_canon_sha256":"5cb5161df9f104572fa688434b5a74c62e585dc4a8380054a4f37573405391c9","abstract_canon_sha256":"55d5c90e06f3f2085987138497523de2b3f093a6d9f352320db93787a81f994e"},"schema_version":"1.0"},"canonical_sha256":"8d40758fe0d40983a21c9afa8b03c09ec7dfe067b6f622e77882c41ecc7cffae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:30.759331Z","signature_b64":"zXdAMkye+DgA3RB1k+iWB8XAXao5IIQMQ7/yQxRW2to7gAesp/vpdFR95EVk6N1B72YbRmeMJOrXiGxjloTABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d40758fe0d40983a21c9afa8b03c09ec7dfe067b6f622e77882c41ecc7cffae","last_reissued_at":"2026-05-18T00:15:30.758815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:30.758815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07649","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":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"As5VCav8HnFzNTkrKaU8JFMavembwSrNShYpxnOGWWO1T8JokbelHQYTIxegUtAgpNUqs9T9t4Om3PYHQR/mAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:22:34.948696Z"},"content_sha256":"91b7d044dd0c024aff69b5e070f847d57e37b3e810d17f6874fc7217ab58a65c","schema_version":"1.0","event_id":"sha256:91b7d044dd0c024aff69b5e070f847d57e37b3e810d17f6874fc7217ab58a65c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RVAHLD7A2QEYHIQ4TL5IWA6AT3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Widom-Rowlinson Model on the Delaunay Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael Eyers, Stefan Adams","submitted_at":"2017-05-22T10:26:52Z","abstract_excerpt":"We establish phase transitions for continuum Delaunay multi-type particle systems (continuum Potts or Widom-Rowlinson models) with a repulsive interaction between particles of different types. Our interaction potential depends solely on the length of the Delaunay edges. We show that a phase transition occurs for sufficiently large activities and for sufficiently large potential parameter proving an old conjecture of Lebowitz and Lieb extended to the Delaunay structure. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07649","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":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lK2c0e38waORKHBytZzfoeyKsDKHIcyx02N+hD/mD1OSNKxQDRr9ilWvl+oTXprx8ItaUFACtN29cn7/X77Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:22:34.949335Z"},"content_sha256":"8b392a48c7d22e95419c205d210dd1271d376d12323a1978f53b49cae11f4752","schema_version":"1.0","event_id":"sha256:8b392a48c7d22e95419c205d210dd1271d376d12323a1978f53b49cae11f4752"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RVAHLD7A2QEYHIQ4TL5IWA6AT3/bundle.json","state_url":"https://pith.science/pith/RVAHLD7A2QEYHIQ4TL5IWA6AT3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RVAHLD7A2QEYHIQ4TL5IWA6AT3/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":"2026-05-31T03:22:34Z","links":{"resolver":"https://pith.science/pith/RVAHLD7A2QEYHIQ4TL5IWA6AT3","bundle":"https://pith.science/pith/RVAHLD7A2QEYHIQ4TL5IWA6AT3/bundle.json","state":"https://pith.science/pith/RVAHLD7A2QEYHIQ4TL5IWA6AT3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RVAHLD7A2QEYHIQ4TL5IWA6AT3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RVAHLD7A2QEYHIQ4TL5IWA6AT3","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":"55d5c90e06f3f2085987138497523de2b3f093a6d9f352320db93787a81f994e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-22T10:26:52Z","title_canon_sha256":"5cb5161df9f104572fa688434b5a74c62e585dc4a8380054a4f37573405391c9"},"schema_version":"1.0","source":{"id":"1705.07649","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07649","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07649v2","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07649","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"RVAHLD7A2QEY","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RVAHLD7A2QEYHIQ4","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RVAHLD7A","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:8b392a48c7d22e95419c205d210dd1271d376d12323a1978f53b49cae11f4752","target":"graph","created_at":"2026-05-18T00:15:30Z","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 establish phase transitions for continuum Delaunay multi-type particle systems (continuum Potts or Widom-Rowlinson models) with a repulsive interaction between particles of different types. Our interaction potential depends solely on the length of the Delaunay edges. We show that a phase transition occurs for sufficiently large activities and for sufficiently large potential parameter proving an old conjecture of Lebowitz and Lieb extended to the Delaunay structure. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts ","authors_text":"Michael Eyers, Stefan Adams","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-22T10:26:52Z","title":"The Widom-Rowlinson Model on the Delaunay Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07649","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":"sha256:91b7d044dd0c024aff69b5e070f847d57e37b3e810d17f6874fc7217ab58a65c","target":"record","created_at":"2026-05-18T00:15:30Z","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":"55d5c90e06f3f2085987138497523de2b3f093a6d9f352320db93787a81f994e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-22T10:26:52Z","title_canon_sha256":"5cb5161df9f104572fa688434b5a74c62e585dc4a8380054a4f37573405391c9"},"schema_version":"1.0","source":{"id":"1705.07649","kind":"arxiv","version":2}},"canonical_sha256":"8d40758fe0d40983a21c9afa8b03c09ec7dfe067b6f622e77882c41ecc7cffae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d40758fe0d40983a21c9afa8b03c09ec7dfe067b6f622e77882c41ecc7cffae","first_computed_at":"2026-05-18T00:15:30.758815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:30.758815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zXdAMkye+DgA3RB1k+iWB8XAXao5IIQMQ7/yQxRW2to7gAesp/vpdFR95EVk6N1B72YbRmeMJOrXiGxjloTABg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:30.759331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07649","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91b7d044dd0c024aff69b5e070f847d57e37b3e810d17f6874fc7217ab58a65c","sha256:8b392a48c7d22e95419c205d210dd1271d376d12323a1978f53b49cae11f4752"],"state_sha256":"59597ed8e3ec8e4ad64bf7de0cf3a226a68017094dbf4d21ad81026a3f7fe884"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wp7IbVVQ1HHTwwUsb3IzV7X/2oWAdQik3SNMnGVBuLUgAX4aWHC4s639ZUL/gqs98QXt0t/PsczY4m38WABGDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:22:34.952273Z","bundle_sha256":"59df3ba9cbd438d9697693f37733cea39f7b64cc9edd1c5f02cbd4e8667f6fbd"}}