{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7N533HNNTUZK5VT62ROPFJYVJL","short_pith_number":"pith:7N533HNN","schema_version":"1.0","canonical_sha256":"fb7bbd9dad9d32aed67ed45cf2a7154adf679165f690d7ed37a355458efb7adf","source":{"kind":"arxiv","id":"2603.14749","version":2},"attestation_state":"computed","paper":{"title":"The Counting General Dominating Set Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Boning Meng, Jiayi Zheng","submitted_at":"2026-03-16T02:36:02Z","abstract_excerpt":"We introduce a new framework of counting problems called #GDS that encompasses #$(\\sigma, \\rho)$-Set, a class of domination-type problems that includes counting dominating sets and counting total dominating sets. We explore the intricate relation between #GDS and the well-known Holant. We adapt the technique of gadget construction of Holant to the #GDS framework; using this technique, we prove the #P-completeness of counting dominating sets for 3-regular planar bipartite simple graphs. Through a generalization of a Holant dichotomy, and a special reduction method via symmetric bipartite graphs"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.14749","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2026-03-16T02:36:02Z","cross_cats_sorted":[],"title_canon_sha256":"8ad2182cb22d4461d197124c076616eab57ae2b8f75d4de544e089b98119cea9","abstract_canon_sha256":"b4e409b50f429645e2c884648d85a8985eaa1ab55d9feb57b3c00387abd38b4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:11.008270Z","signature_b64":"Wd4K4xtnwngdgXCNKS8KkP5fFDdFPf5TvOfiQV4ZD0TUKZ9RsDELWx3WhW5/aRxNgGB8X//eUvqOASFw4o9cAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb7bbd9dad9d32aed67ed45cf2a7154adf679165f690d7ed37a355458efb7adf","last_reissued_at":"2026-05-20T01:05:11.007382Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:11.007382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Counting General Dominating Set Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Boning Meng, Jiayi Zheng","submitted_at":"2026-03-16T02:36:02Z","abstract_excerpt":"We introduce a new framework of counting problems called #GDS that encompasses #$(\\sigma, \\rho)$-Set, a class of domination-type problems that includes counting dominating sets and counting total dominating sets. We explore the intricate relation between #GDS and the well-known Holant. We adapt the technique of gadget construction of Holant to the #GDS framework; using this technique, we prove the #P-completeness of counting dominating sets for 3-regular planar bipartite simple graphs. Through a generalization of a Holant dichotomy, and a special reduction method via symmetric bipartite graphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.14749","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.14749/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.14749","created_at":"2026-05-20T01:05:11.007502+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.14749v2","created_at":"2026-05-20T01:05:11.007502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.14749","created_at":"2026-05-20T01:05:11.007502+00:00"},{"alias_kind":"pith_short_12","alias_value":"7N533HNNTUZK","created_at":"2026-05-20T01:05:11.007502+00:00"},{"alias_kind":"pith_short_16","alias_value":"7N533HNNTUZK5VT6","created_at":"2026-05-20T01:05:11.007502+00:00"},{"alias_kind":"pith_short_8","alias_value":"7N533HNN","created_at":"2026-05-20T01:05:11.007502+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL","json":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL.json","graph_json":"https://pith.science/api/pith-number/7N533HNNTUZK5VT62ROPFJYVJL/graph.json","events_json":"https://pith.science/api/pith-number/7N533HNNTUZK5VT62ROPFJYVJL/events.json","paper":"https://pith.science/paper/7N533HNN"},"agent_actions":{"view_html":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL","download_json":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL.json","view_paper":"https://pith.science/paper/7N533HNN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.14749&json=true","fetch_graph":"https://pith.science/api/pith-number/7N533HNNTUZK5VT62ROPFJYVJL/graph.json","fetch_events":"https://pith.science/api/pith-number/7N533HNNTUZK5VT62ROPFJYVJL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL/action/storage_attestation","attest_author":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL/action/author_attestation","sign_citation":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL/action/citation_signature","submit_replication":"https://pith.science/pith/7N533HNNTUZK5VT62ROPFJYVJL/action/replication_record"}},"created_at":"2026-05-20T01:05:11.007502+00:00","updated_at":"2026-05-20T01:05:11.007502+00:00"}