{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PVGOALLSKEFMTNRY2CIQPPUNNV","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":"61273292ceecfabeb24bc547f15c9708d0c0089aad2cc406e10d5f3a664738a7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-07-29T14:40:35Z","title_canon_sha256":"35ef22322feaaffc12e421a0ef10b04addf8b3d84b0abaf269629b14c40853e0"},"schema_version":"1.0","source":{"id":"1507.08164","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08164","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08164v2","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08164","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"PVGOALLSKEFM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVGOALLSKEFMTNRY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVGOALLS","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:7e53226e9837371e6dfc3f96eec06282b6cddd25b9c373ec68572701b03b2506","target":"graph","created_at":"2026-05-18T00:40:19Z","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 consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a \\emph{solution} set, using which all vertices of the graph are distinguished. The identification can be done by considering the neighborhood within the solution set, or by employing the distances to the solution vertices. Normally the goal is to minimize the size of the solution set then. Here we study the case of interval graphs, unit interval graphs, (bipartite) perm","authors_text":"Aline Parreau, Florent Foucaud, George B. Mertzios, Petru Valicov, Reza Naserasr","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-07-29T14:40:35Z","title":"Identification, location-domination and metric dimension on interval and permutation graphs. I. Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08164","kind":"arxiv","version":2},"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":"sha256:9051b7421bbd2eaa501699d81cb146c1415beecfd7bb4b91414c3a17fa8d4d6e","target":"record","created_at":"2026-05-18T00:40:19Z","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":"61273292ceecfabeb24bc547f15c9708d0c0089aad2cc406e10d5f3a664738a7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-07-29T14:40:35Z","title_canon_sha256":"35ef22322feaaffc12e421a0ef10b04addf8b3d84b0abaf269629b14c40853e0"},"schema_version":"1.0","source":{"id":"1507.08164","kind":"arxiv","version":2}},"canonical_sha256":"7d4ce02d72510ac9b638d09107be8d6d6f4b295b1751cce37fcc25bd3bdc5f1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d4ce02d72510ac9b638d09107be8d6d6f4b295b1751cce37fcc25bd3bdc5f1d","first_computed_at":"2026-05-18T00:40:19.835449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:19.835449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sgqFXT6ZdsElZ8k6EwK0iWWWlNYyWq1kgyOUQXuTTozHRQ+a4ORccLiSFOt8Mq+Gf/PgAuDlF7O9/iNtyUwyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:19.836128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08164","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9051b7421bbd2eaa501699d81cb146c1415beecfd7bb4b91414c3a17fa8d4d6e","sha256:7e53226e9837371e6dfc3f96eec06282b6cddd25b9c373ec68572701b03b2506"],"state_sha256":"4f90aa3e25d89232a50da43f291d6ebdfe8b548c75926682f5032a0f13db9f07"}