{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KHSF2OGHY5QSUNPSBBLAYPXR4T","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":"ff7514fde90d6632d67f6cc2045f5d219150c56cd94a29195f0402d57741cc9f","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-18T15:18:44Z","title_canon_sha256":"3f8160906c0cec39f72d57b1d3a5497a80fa2d2acfb06334cc72d6288627577b"},"schema_version":"1.0","source":{"id":"0908.2590","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2590","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2590v1","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2590","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"KHSF2OGHY5QS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KHSF2OGHY5QSUNPS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KHSF2OGH","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:616ef632db3666a057c57274069349cf6cce807ca054879792e6603f299c5169","target":"graph","created_at":"2026-05-18T03:47:09Z","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 introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given threshold. If the vertex set is a countable dense set in R^n equipped with the metric derived from the L_{\\infty}-norm, then it is shown that with probability 1 such infinite random geometric graphs have a unique isomorphism type. The isomorphism type, which we call GR_n, is characterized by a geometric analogue of the existentially closed adjacency property, a","authors_text":"Anthony Bonato, Jeannette Janssen","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-18T15:18:44Z","title":"Infinite random geometric graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2590","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":"sha256:12b558e320bc3d26c91e4464164dc26a95ead0498f3cc786a0e704f5b908166f","target":"record","created_at":"2026-05-18T03:47:09Z","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":"ff7514fde90d6632d67f6cc2045f5d219150c56cd94a29195f0402d57741cc9f","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-18T15:18:44Z","title_canon_sha256":"3f8160906c0cec39f72d57b1d3a5497a80fa2d2acfb06334cc72d6288627577b"},"schema_version":"1.0","source":{"id":"0908.2590","kind":"arxiv","version":1}},"canonical_sha256":"51e45d38c7c7612a35f208560c3ef1e4e995ac708efb6b6a68bf104799d0c2dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51e45d38c7c7612a35f208560c3ef1e4e995ac708efb6b6a68bf104799d0c2dc","first_computed_at":"2026-05-18T03:47:09.093632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:09.093632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R+Lyi2zhkqPMryLymc0RrkcMgTmlK92HUSVUiREXbg/NlBAeKkQ8Oka4TNdC5u5S3W9Yx90xK5x+sj6mnqk1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:09.094170Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.2590","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12b558e320bc3d26c91e4464164dc26a95ead0498f3cc786a0e704f5b908166f","sha256:616ef632db3666a057c57274069349cf6cce807ca054879792e6603f299c5169"],"state_sha256":"08b555d46dc013d79664950deaa2b9749894f3ac3000bb0f0dfc87f8167e4cdb"}