{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UKEONPTOLSNZNDAXRNTYBCKBX4","short_pith_number":"pith:UKEONPTO","canonical_record":{"source":{"id":"1712.03311","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-08T23:09:06Z","cross_cats_sorted":[],"title_canon_sha256":"a93fb944f2f87538136c6a71e4128df04f5a35b2639e3669a97fa3887817b7c3","abstract_canon_sha256":"7fc41f136212c091a01934f7c028854ef6e770479864a28fa282032f2be3929f"},"schema_version":"1.0"},"canonical_sha256":"a288e6be6e5c9b968c178b67808941bf3af2ad55fa1ce28615b4e3204f2252a9","source":{"kind":"arxiv","id":"1712.03311","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03311","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03311v3","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03311","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"UKEONPTOLSNZ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UKEONPTOLSNZNDAX","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UKEONPTO","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UKEONPTOLSNZNDAXRNTYBCKBX4","target":"record","payload":{"canonical_record":{"source":{"id":"1712.03311","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-08T23:09:06Z","cross_cats_sorted":[],"title_canon_sha256":"a93fb944f2f87538136c6a71e4128df04f5a35b2639e3669a97fa3887817b7c3","abstract_canon_sha256":"7fc41f136212c091a01934f7c028854ef6e770479864a28fa282032f2be3929f"},"schema_version":"1.0"},"canonical_sha256":"a288e6be6e5c9b968c178b67808941bf3af2ad55fa1ce28615b4e3204f2252a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:11.263601Z","signature_b64":"PGIVgTObRz325caUOOqEAKCqW/5SPFv8jgwBfm5ROvdQyeKWfpKRHU9Tx2WNbAwjX43JE9yP2s0z4BcZG+e/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a288e6be6e5c9b968c178b67808941bf3af2ad55fa1ce28615b4e3204f2252a9","last_reissued_at":"2026-05-17T23:46:11.263262Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:11.263262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.03311","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRLEFuOoUZf1zAPCdNCIIPm6mWWzLnyXs286vgMHKjPEPF4kmIWfueJwAXDCdEWSRRdqTMUGMi4bpUTM3N+JBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:52.540534Z"},"content_sha256":"0c4ba7813a9b40cfe297f14b490e1f0d26769c6b8b41a595cdbcaac92d941879","schema_version":"1.0","event_id":"sha256:0c4ba7813a9b40cfe297f14b490e1f0d26769c6b8b41a595cdbcaac92d941879"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UKEONPTOLSNZNDAXRNTYBCKBX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the localization number of random graphs: diameter two case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Frieze, Andrzej Dudek, Wesley Pegden","submitted_at":"2017-12-08T23:09:06Z","abstract_excerpt":"We study the localization game on dense random graphs. In this game, a {\\em cop} $x$ tries to locate a {\\em robber} $y$ by asking for the graph distance of $y$ from every vertex in a sequence of sets $W_1,W_2,\\ldots,W_\\ell$. We prove high probability upper and lower bounds for the minimum size of each $W_i$ that will guarantee that $x$ will be able to locate $y$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03311","kind":"arxiv","version":3},"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":"2026-05-17T23:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkPZAztTN6RJ2MQQt4Ciladmb69dq6XBYp93OFg6aYQI5+xnl2624knjPQ+3O2uDhMo6Y4cchalAfx+c4oJ6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:52.541192Z"},"content_sha256":"23c7749e863c860e7c486aedc8bb59376e0caa4db6e58e450fe8f6862b1d2996","schema_version":"1.0","event_id":"sha256:23c7749e863c860e7c486aedc8bb59376e0caa4db6e58e450fe8f6862b1d2996"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKEONPTOLSNZNDAXRNTYBCKBX4/bundle.json","state_url":"https://pith.science/pith/UKEONPTOLSNZNDAXRNTYBCKBX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKEONPTOLSNZNDAXRNTYBCKBX4/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":"2026-06-11T23:02:52Z","links":{"resolver":"https://pith.science/pith/UKEONPTOLSNZNDAXRNTYBCKBX4","bundle":"https://pith.science/pith/UKEONPTOLSNZNDAXRNTYBCKBX4/bundle.json","state":"https://pith.science/pith/UKEONPTOLSNZNDAXRNTYBCKBX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKEONPTOLSNZNDAXRNTYBCKBX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UKEONPTOLSNZNDAXRNTYBCKBX4","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":"7fc41f136212c091a01934f7c028854ef6e770479864a28fa282032f2be3929f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-08T23:09:06Z","title_canon_sha256":"a93fb944f2f87538136c6a71e4128df04f5a35b2639e3669a97fa3887817b7c3"},"schema_version":"1.0","source":{"id":"1712.03311","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03311","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03311v3","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03311","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"UKEONPTOLSNZ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UKEONPTOLSNZNDAX","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UKEONPTO","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:23c7749e863c860e7c486aedc8bb59376e0caa4db6e58e450fe8f6862b1d2996","target":"graph","created_at":"2026-05-17T23:46:11Z","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 study the localization game on dense random graphs. In this game, a {\\em cop} $x$ tries to locate a {\\em robber} $y$ by asking for the graph distance of $y$ from every vertex in a sequence of sets $W_1,W_2,\\ldots,W_\\ell$. We prove high probability upper and lower bounds for the minimum size of each $W_i$ that will guarantee that $x$ will be able to locate $y$.","authors_text":"Alan Frieze, Andrzej Dudek, Wesley Pegden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-08T23:09:06Z","title":"A note on the localization number of random graphs: diameter two case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03311","kind":"arxiv","version":3},"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":"sha256:0c4ba7813a9b40cfe297f14b490e1f0d26769c6b8b41a595cdbcaac92d941879","target":"record","created_at":"2026-05-17T23:46:11Z","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":"7fc41f136212c091a01934f7c028854ef6e770479864a28fa282032f2be3929f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-08T23:09:06Z","title_canon_sha256":"a93fb944f2f87538136c6a71e4128df04f5a35b2639e3669a97fa3887817b7c3"},"schema_version":"1.0","source":{"id":"1712.03311","kind":"arxiv","version":3}},"canonical_sha256":"a288e6be6e5c9b968c178b67808941bf3af2ad55fa1ce28615b4e3204f2252a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a288e6be6e5c9b968c178b67808941bf3af2ad55fa1ce28615b4e3204f2252a9","first_computed_at":"2026-05-17T23:46:11.263262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:11.263262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PGIVgTObRz325caUOOqEAKCqW/5SPFv8jgwBfm5ROvdQyeKWfpKRHU9Tx2WNbAwjX43JE9yP2s0z4BcZG+e/DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:11.263601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03311","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c4ba7813a9b40cfe297f14b490e1f0d26769c6b8b41a595cdbcaac92d941879","sha256:23c7749e863c860e7c486aedc8bb59376e0caa4db6e58e450fe8f6862b1d2996"],"state_sha256":"4ee904ab540c6dcea09a940f9fe7ac5b9dfc1e828b500e082150e2a94f332dfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sO+hLmPstykLCXVPtispFG9/duMQi/zOLMm0aBOmiHK2RyoAYLQENtMq8jeDoiLv01fUbH4RKrXYgJncsgFrDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:02:52.544470Z","bundle_sha256":"4eb91117aac7f3804af348adebbf770b3277c52df31c0508e26657fb7c244c7b"}}