{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HRHEEL7QWFYYBYWJLQZYWDWQWI","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":"1342b7233f33b188d4f8b8300484ef87922227addb8708f0cc686400e2ea2769","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-04T07:41:08Z","title_canon_sha256":"391b50b192f66092ace7a1a5b419ae4360033b4ceb2e105ef8c0a02eec7a87f4"},"schema_version":"1.0","source":{"id":"2506.03646","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.03646","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"arxiv_version","alias_value":"2506.03646v3","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03646","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_12","alias_value":"HRHEEL7QWFYY","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_16","alias_value":"HRHEEL7QWFYYBYWJ","created_at":"2026-06-08T01:03:45Z"},{"alias_kind":"pith_short_8","alias_value":"HRHEEL7Q","created_at":"2026-06-08T01:03:45Z"}],"graph_snapshots":[{"event_id":"sha256:9ae3f40e29c1e98aaf61335af43bbe99143ad92e039eade3497203462d2d28c3","target":"graph","created_at":"2026-06-08T01:03:45Z","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/2506.03646/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this short paper, we establish relations between the domination number $\\gamma$, the total domination number $\\gamma_t$, and the connected domination number $\\gamma_c$ of a graph. In particular, we prove upper and lower bounds for $\\gamma_t$ in terms of $\\gamma$ and $\\gamma_c$.","authors_text":"Dickson Y. B. Annor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-04T07:41:08Z","title":"A Note on Inequalities for Three Domination Parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03646","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":"sha256:50b3da5812e09ba53259e5c7bf2ee710569ab6f68c397e461fb55dcf477e39c3","target":"record","created_at":"2026-06-08T01:03:45Z","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":"1342b7233f33b188d4f8b8300484ef87922227addb8708f0cc686400e2ea2769","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-04T07:41:08Z","title_canon_sha256":"391b50b192f66092ace7a1a5b419ae4360033b4ceb2e105ef8c0a02eec7a87f4"},"schema_version":"1.0","source":{"id":"2506.03646","kind":"arxiv","version":3}},"canonical_sha256":"3c4e422ff0b17180e2c95c338b0ed0b20031c66c405bb03d4322041b5dc3c433","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c4e422ff0b17180e2c95c338b0ed0b20031c66c405bb03d4322041b5dc3c433","first_computed_at":"2026-06-08T01:03:45.432780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:03:45.432780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F7HP46q7Y7no8xxqBqQilHwoKTpzrxmx/aI9H/s8HugiIwWMxCnBxXRjKqBbXdzi7pdH5PfcJDPh6AO6oKDkBg==","signature_status":"signed_v1","signed_at":"2026-06-08T01:03:45.433654Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.03646","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50b3da5812e09ba53259e5c7bf2ee710569ab6f68c397e461fb55dcf477e39c3","sha256:9ae3f40e29c1e98aaf61335af43bbe99143ad92e039eade3497203462d2d28c3"],"state_sha256":"f820a4e743d33f20dac863dd317cb224b55506a1bdb88b31718fc136c191cadd"}