{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WUSGRGN3KEZCEYL5N5DSPLVUVM","short_pith_number":"pith:WUSGRGN3","canonical_record":{"source":{"id":"1202.1136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-06T13:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"26d88e52ab3789b5c66c5a6758db9b29e1811618b285efacab6e048eb8a833ee","abstract_canon_sha256":"bc18ea30aafbf7f24c7e163c29b6851d9fd2e19808ccc92223a5146689813bf3"},"schema_version":"1.0"},"canonical_sha256":"b5246899bb513222617d6f4727aeb4ab33b6701eadf1c3938c435267c7e4c161","source":{"kind":"arxiv","id":"1202.1136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1136","created_at":"2026-05-18T04:03:04Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1136v1","created_at":"2026-05-18T04:03:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1136","created_at":"2026-05-18T04:03:04Z"},{"alias_kind":"pith_short_12","alias_value":"WUSGRGN3KEZC","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WUSGRGN3KEZCEYL5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WUSGRGN3","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WUSGRGN3KEZCEYL5N5DSPLVUVM","target":"record","payload":{"canonical_record":{"source":{"id":"1202.1136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-06T13:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"26d88e52ab3789b5c66c5a6758db9b29e1811618b285efacab6e048eb8a833ee","abstract_canon_sha256":"bc18ea30aafbf7f24c7e163c29b6851d9fd2e19808ccc92223a5146689813bf3"},"schema_version":"1.0"},"canonical_sha256":"b5246899bb513222617d6f4727aeb4ab33b6701eadf1c3938c435267c7e4c161","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:04.904599Z","signature_b64":"UKIUtciQIvz8m8CEvqOGtUXnEyV/U37315hrwuHBLqJ3+AvFvQVaOy0sO0Foz6M/t4hRfW17hvqWBZbrtFiMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5246899bb513222617d6f4727aeb4ab33b6701eadf1c3938c435267c7e4c161","last_reissued_at":"2026-05-18T04:03:04.903882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:04.903882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.1136","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LP4aCxd8miliAYh5RTJp3R4O4ojdmTLHGs/ZWrV1A25KtAHxla00mdI78iNkzatbEYamu4RDjdXAN7Sa2J9MCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:16:28.778791Z"},"content_sha256":"378e549556356ce0d6a7cab9f173b6fdfef2d4d9ce3d7fda9e64d8d9051dc3ff","schema_version":"1.0","event_id":"sha256:378e549556356ce0d6a7cab9f173b6fdfef2d4d9ce3d7fda9e64d8d9051dc3ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WUSGRGN3KEZCEYL5N5DSPLVUVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bipartite stable Poisson graphs on R","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Lopes, Maria Deijfen","submitted_at":"2012-02-06T13:39:36Z","abstract_excerpt":"Let red and blue points be distributed on $\\mathbb{R}$ according to two independent Poisson processes $\\mathcal{R}$ and $\\mathcal{B}$ and let each red (blue) point independently be equipped with a random number of half-edges according to a probability distribution $\\nu$ ($\\mu$). We consider translation-invariant bipartite random graphs with vertex classes defined by the point sets of $\\mathcal{R}$ and $\\mathcal{B}$, respectively, generated by a scheme based on the Gale-Shapley stable marriage for perfectly matching the half-edges. Our main result is that, when all vertices have degree 2 almost"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1136","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P2UkTO2hf6Ediu0u559kmnCQkFHYJmYFajU4WDnXNqhsapLO3WjEiiVSNN9NqdzZY9N1jyNLuuEAHDHCaA09Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:16:28.779139Z"},"content_sha256":"f824c78be6cd94139730f09af0fc9cf5a68922a76b834e41cd21d23056d748ed","schema_version":"1.0","event_id":"sha256:f824c78be6cd94139730f09af0fc9cf5a68922a76b834e41cd21d23056d748ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUSGRGN3KEZCEYL5N5DSPLVUVM/bundle.json","state_url":"https://pith.science/pith/WUSGRGN3KEZCEYL5N5DSPLVUVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUSGRGN3KEZCEYL5N5DSPLVUVM/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":"2026-06-20T12:16:28Z","links":{"resolver":"https://pith.science/pith/WUSGRGN3KEZCEYL5N5DSPLVUVM","bundle":"https://pith.science/pith/WUSGRGN3KEZCEYL5N5DSPLVUVM/bundle.json","state":"https://pith.science/pith/WUSGRGN3KEZCEYL5N5DSPLVUVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUSGRGN3KEZCEYL5N5DSPLVUVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WUSGRGN3KEZCEYL5N5DSPLVUVM","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":"bc18ea30aafbf7f24c7e163c29b6851d9fd2e19808ccc92223a5146689813bf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-06T13:39:36Z","title_canon_sha256":"26d88e52ab3789b5c66c5a6758db9b29e1811618b285efacab6e048eb8a833ee"},"schema_version":"1.0","source":{"id":"1202.1136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1136","created_at":"2026-05-18T04:03:04Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1136v1","created_at":"2026-05-18T04:03:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1136","created_at":"2026-05-18T04:03:04Z"},{"alias_kind":"pith_short_12","alias_value":"WUSGRGN3KEZC","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WUSGRGN3KEZCEYL5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WUSGRGN3","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:f824c78be6cd94139730f09af0fc9cf5a68922a76b834e41cd21d23056d748ed","target":"graph","created_at":"2026-05-18T04:03:04Z","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":"Let red and blue points be distributed on $\\mathbb{R}$ according to two independent Poisson processes $\\mathcal{R}$ and $\\mathcal{B}$ and let each red (blue) point independently be equipped with a random number of half-edges according to a probability distribution $\\nu$ ($\\mu$). We consider translation-invariant bipartite random graphs with vertex classes defined by the point sets of $\\mathcal{R}$ and $\\mathcal{B}$, respectively, generated by a scheme based on the Gale-Shapley stable marriage for perfectly matching the half-edges. Our main result is that, when all vertices have degree 2 almost","authors_text":"Fabio Lopes, Maria Deijfen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-06T13:39:36Z","title":"Bipartite stable Poisson graphs on R"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1136","kind":"arxiv","version":1},"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":"sha256:378e549556356ce0d6a7cab9f173b6fdfef2d4d9ce3d7fda9e64d8d9051dc3ff","target":"record","created_at":"2026-05-18T04:03:04Z","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":"bc18ea30aafbf7f24c7e163c29b6851d9fd2e19808ccc92223a5146689813bf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-06T13:39:36Z","title_canon_sha256":"26d88e52ab3789b5c66c5a6758db9b29e1811618b285efacab6e048eb8a833ee"},"schema_version":"1.0","source":{"id":"1202.1136","kind":"arxiv","version":1}},"canonical_sha256":"b5246899bb513222617d6f4727aeb4ab33b6701eadf1c3938c435267c7e4c161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5246899bb513222617d6f4727aeb4ab33b6701eadf1c3938c435267c7e4c161","first_computed_at":"2026-05-18T04:03:04.903882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:04.903882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UKIUtciQIvz8m8CEvqOGtUXnEyV/U37315hrwuHBLqJ3+AvFvQVaOy0sO0Foz6M/t4hRfW17hvqWBZbrtFiMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:04.904599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:378e549556356ce0d6a7cab9f173b6fdfef2d4d9ce3d7fda9e64d8d9051dc3ff","sha256:f824c78be6cd94139730f09af0fc9cf5a68922a76b834e41cd21d23056d748ed"],"state_sha256":"8cba6d8c37c0e7c16dc5ae354579e9268fc27231026995d79a92d5f6913fdded"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iz/kkgL20J47WM3wI7oIZeIyoCiKuN2unFKQ8iJxODjU7ixzExHBn/zOqxuGDJbFbQTaL/EMgE9fBsp8zbBBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T12:16:28.781165Z","bundle_sha256":"1a943613fdd031b12639995e21506c4aece729ad1a770685d13dc11526606722"}}