{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MFXT2H4XCIGEEWZYKUTPHJGBA7","short_pith_number":"pith:MFXT2H4X","canonical_record":{"source":{"id":"1208.3801","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T02:20:57Z","cross_cats_sorted":[],"title_canon_sha256":"d81cdf9abfe8f6a3f0b92d4b148453640419394fd18899c746ac7da8adf11144","abstract_canon_sha256":"e0e2792c7ecc406a456ce2411f55f52dbf0bb9c3f61b54e6f23a775328492f1b"},"schema_version":"1.0"},"canonical_sha256":"616f3d1f97120c425b385526f3a4c107d17a29b4ebaf49a2be50dd7f8d7b8195","source":{"kind":"arxiv","id":"1208.3801","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3801","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3801v3","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3801","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"MFXT2H4XCIGE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MFXT2H4XCIGEEWZY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MFXT2H4X","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MFXT2H4XCIGEEWZYKUTPHJGBA7","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3801","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T02:20:57Z","cross_cats_sorted":[],"title_canon_sha256":"d81cdf9abfe8f6a3f0b92d4b148453640419394fd18899c746ac7da8adf11144","abstract_canon_sha256":"e0e2792c7ecc406a456ce2411f55f52dbf0bb9c3f61b54e6f23a775328492f1b"},"schema_version":"1.0"},"canonical_sha256":"616f3d1f97120c425b385526f3a4c107d17a29b4ebaf49a2be50dd7f8d7b8195","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:01.044551Z","signature_b64":"v5YQPqVhPjsvFnHonqCz1D4BSZjt3ZeYEhwhYZ2R9nrqj2suYkTWkw+bHRp3cre6CQcg5CMgF+O59x/VbDNiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"616f3d1f97120c425b385526f3a4c107d17a29b4ebaf49a2be50dd7f8d7b8195","last_reissued_at":"2026-05-18T02:50:01.044032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:01.044032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3801","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":"2026-05-18T02:50:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"URdPMHmnKIDIqYtsjexWfSAKUozcFCoKY0rY9d5MyQLQupONCfpyxy2Gf20DnUOc8OmN4qPHOjdD8fGXtBUwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:08:18.383041Z"},"content_sha256":"ba788ac38d2a1d80e8e5eb1fdb9af8aa529316859b6b3fe9e84d189d0c0805ca","schema_version":"1.0","event_id":"sha256:ba788ac38d2a1d80e8e5eb1fdb9af8aa529316859b6b3fe9e84d189d0c0805ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MFXT2H4XCIGEEWZYKUTPHJGBA7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metric dimension for random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B. Bollobas, D. Mitsche, P. Pralat","submitted_at":"2012-08-19T02:20:57Z","abstract_excerpt":"The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the metric dimension of the random graph $G(n,p)$ for a wide range of probabilities $p=p(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3801","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":"2026-05-18T02:50:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CQLCHf1EsjJFXGWTAsHsi8M3inhioPWMBnk/EUmsG99/xKvQRUa/PhiwvoZlgIn7iAH9G0zJ0sElBssWaNf7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:08:18.383403Z"},"content_sha256":"86f310ba246c8fd2ba6b14ac8ff9d4de46621011c7599f9e05657cc13e8eb724","schema_version":"1.0","event_id":"sha256:86f310ba246c8fd2ba6b14ac8ff9d4de46621011c7599f9e05657cc13e8eb724"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFXT2H4XCIGEEWZYKUTPHJGBA7/bundle.json","state_url":"https://pith.science/pith/MFXT2H4XCIGEEWZYKUTPHJGBA7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFXT2H4XCIGEEWZYKUTPHJGBA7/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":"2026-07-01T16:08:18Z","links":{"resolver":"https://pith.science/pith/MFXT2H4XCIGEEWZYKUTPHJGBA7","bundle":"https://pith.science/pith/MFXT2H4XCIGEEWZYKUTPHJGBA7/bundle.json","state":"https://pith.science/pith/MFXT2H4XCIGEEWZYKUTPHJGBA7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFXT2H4XCIGEEWZYKUTPHJGBA7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MFXT2H4XCIGEEWZYKUTPHJGBA7","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":"e0e2792c7ecc406a456ce2411f55f52dbf0bb9c3f61b54e6f23a775328492f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T02:20:57Z","title_canon_sha256":"d81cdf9abfe8f6a3f0b92d4b148453640419394fd18899c746ac7da8adf11144"},"schema_version":"1.0","source":{"id":"1208.3801","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3801","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3801v3","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3801","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"MFXT2H4XCIGE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MFXT2H4XCIGEEWZY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MFXT2H4X","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:86f310ba246c8fd2ba6b14ac8ff9d4de46621011c7599f9e05657cc13e8eb724","target":"graph","created_at":"2026-05-18T02:50:01Z","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":"The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the metric dimension of the random graph $G(n,p)$ for a wide range of probabilities $p=p(n)$.","authors_text":"B. Bollobas, D. Mitsche, P. Pralat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T02:20:57Z","title":"Metric dimension for random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3801","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:ba788ac38d2a1d80e8e5eb1fdb9af8aa529316859b6b3fe9e84d189d0c0805ca","target":"record","created_at":"2026-05-18T02:50:01Z","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":"e0e2792c7ecc406a456ce2411f55f52dbf0bb9c3f61b54e6f23a775328492f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-19T02:20:57Z","title_canon_sha256":"d81cdf9abfe8f6a3f0b92d4b148453640419394fd18899c746ac7da8adf11144"},"schema_version":"1.0","source":{"id":"1208.3801","kind":"arxiv","version":3}},"canonical_sha256":"616f3d1f97120c425b385526f3a4c107d17a29b4ebaf49a2be50dd7f8d7b8195","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"616f3d1f97120c425b385526f3a4c107d17a29b4ebaf49a2be50dd7f8d7b8195","first_computed_at":"2026-05-18T02:50:01.044032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:01.044032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5YQPqVhPjsvFnHonqCz1D4BSZjt3ZeYEhwhYZ2R9nrqj2suYkTWkw+bHRp3cre6CQcg5CMgF+O59x/VbDNiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:01.044551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3801","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba788ac38d2a1d80e8e5eb1fdb9af8aa529316859b6b3fe9e84d189d0c0805ca","sha256:86f310ba246c8fd2ba6b14ac8ff9d4de46621011c7599f9e05657cc13e8eb724"],"state_sha256":"3d537829871ad0f22cf901a02ed9db9bca258d311570ab680cecfda28b9d282c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AwSoCCG7molBW1mVPgltnSKCBtVjMJCZsSIPtMMgquFvi/SxzKRjtubwjMRWU4P44eacIt1buunFsXHHOJrVBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T16:08:18.385336Z","bundle_sha256":"8190f3780d0253f1184c33b274c3aab88388b658797e9ddb1b1fc48104dc1114"}}