{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PMCZ3BNF6WBZ7WRW7TV5ZC5BR2","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":"1761d7d03305d8c58432107cec1c25776cab2416bfc73b6869f9c7d8f6bdd2b0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-05T16:49:14Z","title_canon_sha256":"bed833b8232fc534321c23bc16cececed40145b451257a030ca3e0ee05fed0b7"},"schema_version":"1.0","source":{"id":"2406.03451","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03451","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03451v1","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03451","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"PMCZ3BNF6WBZ","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_16","alias_value":"PMCZ3BNF6WBZ7WRW","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_8","alias_value":"PMCZ3BNF","created_at":"2026-07-05T08:27:56Z"}],"graph_snapshots":[{"event_id":"sha256:064a8c9a2aac0a5dc0f0e0f6ff8a15175b632f3018bd612becde563e20077d92","target":"graph","created_at":"2026-07-05T08:27:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.03451/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore the question asking for graphs $G$ for which the total distance decreases, possibly by a fixed constant $k$, upon the removal of any of its vertices. We obtain results leading to intuition and doubts for the \\v{S}olt\\'es' problem ($k=0$) and its conjectures.","authors_text":"Stijn Cambie","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-05T16:49:14Z","title":"Towards the essence of \\v{S}olt\\'es' problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03451","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":"sha256:96f59e25f1d70621700c7e8549fd96267e3b06e713b73bcd8b3dfdc855334761","target":"record","created_at":"2026-07-05T08:27:56Z","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":"1761d7d03305d8c58432107cec1c25776cab2416bfc73b6869f9c7d8f6bdd2b0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-05T16:49:14Z","title_canon_sha256":"bed833b8232fc534321c23bc16cececed40145b451257a030ca3e0ee05fed0b7"},"schema_version":"1.0","source":{"id":"2406.03451","kind":"arxiv","version":1}},"canonical_sha256":"7b059d85a5f5839fda36fcebdc8ba18e99b63c0e0fa30cefeacaadae7fb13977","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b059d85a5f5839fda36fcebdc8ba18e99b63c0e0fa30cefeacaadae7fb13977","first_computed_at":"2026-07-05T08:27:56.919911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:56.919911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5g2PrscnlSZ97XVJZtMHcJ2TzXoKOjd5nS9KSppIoYdWFc93px55WIcdYidqem6Hyg5CS24jHdjn9+mLqwPZBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:56.920371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.03451","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96f59e25f1d70621700c7e8549fd96267e3b06e713b73bcd8b3dfdc855334761","sha256:064a8c9a2aac0a5dc0f0e0f6ff8a15175b632f3018bd612becde563e20077d92"],"state_sha256":"986961c64d15f9e8e8cfe9011ad4edc3da264c3be206f1c92f523d48a4507746"}