{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OLVUOIP4PZZM3RN2W6XKPVO5NX","short_pith_number":"pith:OLVUOIP4","canonical_record":{"source":{"id":"1312.0772","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T11:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"d31f6b10426b1537c21f21973d79b49fec36dcd3ead48151a4d9ad445518a647","abstract_canon_sha256":"c7040a0c7557302713c8c163020646f859383443232230a041e9ee08c90206f9"},"schema_version":"1.0"},"canonical_sha256":"72eb4721fc7e72cdc5bab7aea7d5dd6ddadd40cf518405b60096235ae495f556","source":{"kind":"arxiv","id":"1312.0772","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0772","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0772v1","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0772","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"OLVUOIP4PZZM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OLVUOIP4PZZM3RN2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OLVUOIP4","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OLVUOIP4PZZM3RN2W6XKPVO5NX","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0772","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T11:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"d31f6b10426b1537c21f21973d79b49fec36dcd3ead48151a4d9ad445518a647","abstract_canon_sha256":"c7040a0c7557302713c8c163020646f859383443232230a041e9ee08c90206f9"},"schema_version":"1.0"},"canonical_sha256":"72eb4721fc7e72cdc5bab7aea7d5dd6ddadd40cf518405b60096235ae495f556","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:36.738564Z","signature_b64":"NLSHK3NJlv1KUZWoIKoe4M8jwGw59V66O3lRg0u4iRO2tAbjNqLghuaZCpMqU0Xk8jzy/EX5q0tv8FHcLO1vAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72eb4721fc7e72cdc5bab7aea7d5dd6ddadd40cf518405b60096235ae495f556","last_reissued_at":"2026-05-18T03:05:36.737850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:36.737850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0772","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":"2026-05-18T03:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zI8rZrWVQMY2ujHcZ3IFbb9Ndik1BZKFAnWRwAaBIO5u6AGDJS4M+I+cJ2ig+ma77wlPudyHbgSw2zNPDlsdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:34:52.426259Z"},"content_sha256":"7339d5fbc9b8e4eeb6282ee01a50c38404a3aa0d3eb3a1f4e403608f9fd5ba43","schema_version":"1.0","event_id":"sha256:7339d5fbc9b8e4eeb6282ee01a50c38404a3aa0d3eb3a1f4e403608f9fd5ba43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OLVUOIP4PZZM3RN2W6XKPVO5NX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On global location-domination in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Hernando, I. M. Pelayo, M. Mora","submitted_at":"2013-12-03T11:23:46Z","abstract_excerpt":"A dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the location-domination number $\\lambda(G)$. An LD-set $S$ of a graph $G$ is global if it is an LD-set of both $G$ and its complement $\\overline{G}$. The global location-domination number $\\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$. In this work, we give some relations between loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0772","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":"2026-05-18T03:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNUtVqioBxquDSoYTqt7QE2466RvHYT+Tl3RXqig6GvmJgpbq1CMG3AtBQVbrQfl8hTzmGU+myU3KyEfRwdmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:34:52.426798Z"},"content_sha256":"9f4710cbf7b11df37fed729c8b5beff6aaf3747783d0a827626b970bef2ccc23","schema_version":"1.0","event_id":"sha256:9f4710cbf7b11df37fed729c8b5beff6aaf3747783d0a827626b970bef2ccc23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLVUOIP4PZZM3RN2W6XKPVO5NX/bundle.json","state_url":"https://pith.science/pith/OLVUOIP4PZZM3RN2W6XKPVO5NX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLVUOIP4PZZM3RN2W6XKPVO5NX/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":"2026-05-30T06:34:52Z","links":{"resolver":"https://pith.science/pith/OLVUOIP4PZZM3RN2W6XKPVO5NX","bundle":"https://pith.science/pith/OLVUOIP4PZZM3RN2W6XKPVO5NX/bundle.json","state":"https://pith.science/pith/OLVUOIP4PZZM3RN2W6XKPVO5NX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLVUOIP4PZZM3RN2W6XKPVO5NX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OLVUOIP4PZZM3RN2W6XKPVO5NX","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":"c7040a0c7557302713c8c163020646f859383443232230a041e9ee08c90206f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T11:23:46Z","title_canon_sha256":"d31f6b10426b1537c21f21973d79b49fec36dcd3ead48151a4d9ad445518a647"},"schema_version":"1.0","source":{"id":"1312.0772","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0772","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0772v1","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0772","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"OLVUOIP4PZZM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OLVUOIP4PZZM3RN2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OLVUOIP4","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:9f4710cbf7b11df37fed729c8b5beff6aaf3747783d0a827626b970bef2ccc23","target":"graph","created_at":"2026-05-18T03:05:36Z","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":"A dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the location-domination number $\\lambda(G)$. An LD-set $S$ of a graph $G$ is global if it is an LD-set of both $G$ and its complement $\\overline{G}$. The global location-domination number $\\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$. In this work, we give some relations between loc","authors_text":"C. Hernando, I. M. Pelayo, M. Mora","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T11:23:46Z","title":"On global location-domination in graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0772","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":"sha256:7339d5fbc9b8e4eeb6282ee01a50c38404a3aa0d3eb3a1f4e403608f9fd5ba43","target":"record","created_at":"2026-05-18T03:05:36Z","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":"c7040a0c7557302713c8c163020646f859383443232230a041e9ee08c90206f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T11:23:46Z","title_canon_sha256":"d31f6b10426b1537c21f21973d79b49fec36dcd3ead48151a4d9ad445518a647"},"schema_version":"1.0","source":{"id":"1312.0772","kind":"arxiv","version":1}},"canonical_sha256":"72eb4721fc7e72cdc5bab7aea7d5dd6ddadd40cf518405b60096235ae495f556","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72eb4721fc7e72cdc5bab7aea7d5dd6ddadd40cf518405b60096235ae495f556","first_computed_at":"2026-05-18T03:05:36.737850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:36.737850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NLSHK3NJlv1KUZWoIKoe4M8jwGw59V66O3lRg0u4iRO2tAbjNqLghuaZCpMqU0Xk8jzy/EX5q0tv8FHcLO1vAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:36.738564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0772","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7339d5fbc9b8e4eeb6282ee01a50c38404a3aa0d3eb3a1f4e403608f9fd5ba43","sha256:9f4710cbf7b11df37fed729c8b5beff6aaf3747783d0a827626b970bef2ccc23"],"state_sha256":"d8785f96a7479246ed0657f9eafba1a73af5c31e8b9bafc0a17b3e7e4d2b1f1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrYwVXmD1sBjeGIU3jBTCqwsNDTiH8xMADWcWsCbdahjPC3NLKkDhRHaMFEx81yeF3bcTaKz82VHwrtSoMRJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:34:52.430930Z","bundle_sha256":"fe62befaf30046b976197f0a46dc3eef1d80acf46d6ff1f1382ddbc01ee5b4e5"}}