{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:74ZJR7CNWN66MVSCVZQVQ2FXPN","short_pith_number":"pith:74ZJR7CN","canonical_record":{"source":{"id":"1407.2053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"e8dc3e5081bf06f422f4d91fe3ebefb6f75261110a01dffaa8d263720476c077","abstract_canon_sha256":"1f345dfb5c300c9b493dea0677b78a41add88d72ddd75dc725b136ca1a1ffd5b"},"schema_version":"1.0"},"canonical_sha256":"ff3298fc4db37de65642ae615868b77b7903e0d0e2de76d1248de834cf0585c1","source":{"kind":"arxiv","id":"1407.2053","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2053","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2053v1","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2053","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"74ZJR7CNWN66","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"74ZJR7CNWN66MVSC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"74ZJR7CN","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:74ZJR7CNWN66MVSCVZQVQ2FXPN","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"e8dc3e5081bf06f422f4d91fe3ebefb6f75261110a01dffaa8d263720476c077","abstract_canon_sha256":"1f345dfb5c300c9b493dea0677b78a41add88d72ddd75dc725b136ca1a1ffd5b"},"schema_version":"1.0"},"canonical_sha256":"ff3298fc4db37de65642ae615868b77b7903e0d0e2de76d1248de834cf0585c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:08.563377Z","signature_b64":"q5FwM/1eJYLaSvGqaWWs/mKFC1CchCq5n5zD7cxoDbWoqWn3sXyTMoPDfuF6pIbd7XIwWzhUYd6hBn0jgBmNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff3298fc4db37de65642ae615868b77b7903e0d0e2de76d1248de834cf0585c1","last_reissued_at":"2026-05-18T02:48:08.562850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:08.562850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2053","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":"2026-05-18T02:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4FDYUqUC7xBKV8RsO/hR8JrAQbcNAWcJs0fB+Pe/WpnGxx8i5hGjjlb6/KqXr0/GTjazha2ep7kmdwdorM2MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:52:29.049458Z"},"content_sha256":"13238c70bc289922fcc01e372cf3d0710c9b9c41ab1769eb325f7b6650eb274e","schema_version":"1.0","event_id":"sha256:13238c70bc289922fcc01e372cf3d0710c9b9c41ab1769eb325f7b6650eb274e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:74ZJR7CNWN66MVSCVZQVQ2FXPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Enumeration of Minimal Dominating Sets and Related Notions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Arnaud Mary, Lhouari Nourine, Mamadou Moustapha Kant\\'e, Vincent Limouzy","submitted_at":"2014-07-08T12:03:01Z","abstract_excerpt":"A dominating set $D$ in a graph is a subset of its vertex set such that each vertex is either in $D$ or has a neighbour in $D$. In this paper, we are interested in the enumeration of (inclusion-wise) minimal dominating sets in graphs, called the Dom-Enum problem. It is well known that this problem can be polynomially reduced to the Trans-Enum problem in hypergraphs, i.e., the problem of enumerating all minimal transversals in a hypergraph. Firstly we show that the Trans-Enum problem can be polynomially reduced to the Dom-Enum problem. As a consequence there exists an output-polynomial time alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2053","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":"2026-05-18T02:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HtHCtlRlpycMsllD1nW2efWR4i1aAQHYJovre/ttn2mBzrbjOD/3v1IthaO/b4c98xjzfrtSEmz8HjVwfxYtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:52:29.049881Z"},"content_sha256":"4c11549fe80bbed81f5c0551c0ddd82ba8319f24c1728c316746a9e3f89f9537","schema_version":"1.0","event_id":"sha256:4c11549fe80bbed81f5c0551c0ddd82ba8319f24c1728c316746a9e3f89f9537"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74ZJR7CNWN66MVSCVZQVQ2FXPN/bundle.json","state_url":"https://pith.science/pith/74ZJR7CNWN66MVSCVZQVQ2FXPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74ZJR7CNWN66MVSCVZQVQ2FXPN/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":"2026-05-27T20:52:29Z","links":{"resolver":"https://pith.science/pith/74ZJR7CNWN66MVSCVZQVQ2FXPN","bundle":"https://pith.science/pith/74ZJR7CNWN66MVSCVZQVQ2FXPN/bundle.json","state":"https://pith.science/pith/74ZJR7CNWN66MVSCVZQVQ2FXPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74ZJR7CNWN66MVSCVZQVQ2FXPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:74ZJR7CNWN66MVSCVZQVQ2FXPN","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":"1f345dfb5c300c9b493dea0677b78a41add88d72ddd75dc725b136ca1a1ffd5b","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","title_canon_sha256":"e8dc3e5081bf06f422f4d91fe3ebefb6f75261110a01dffaa8d263720476c077"},"schema_version":"1.0","source":{"id":"1407.2053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2053","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2053v1","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2053","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"74ZJR7CNWN66","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"74ZJR7CNWN66MVSC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"74ZJR7CN","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:4c11549fe80bbed81f5c0551c0ddd82ba8319f24c1728c316746a9e3f89f9537","target":"graph","created_at":"2026-05-18T02:48:08Z","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 $D$ in a graph is a subset of its vertex set such that each vertex is either in $D$ or has a neighbour in $D$. In this paper, we are interested in the enumeration of (inclusion-wise) minimal dominating sets in graphs, called the Dom-Enum problem. It is well known that this problem can be polynomially reduced to the Trans-Enum problem in hypergraphs, i.e., the problem of enumerating all minimal transversals in a hypergraph. Firstly we show that the Trans-Enum problem can be polynomially reduced to the Dom-Enum problem. As a consequence there exists an output-polynomial time alg","authors_text":"Arnaud Mary, Lhouari Nourine, Mamadou Moustapha Kant\\'e, Vincent Limouzy","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","title":"On the Enumeration of Minimal Dominating Sets and Related Notions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2053","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":"sha256:13238c70bc289922fcc01e372cf3d0710c9b9c41ab1769eb325f7b6650eb274e","target":"record","created_at":"2026-05-18T02:48:08Z","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":"1f345dfb5c300c9b493dea0677b78a41add88d72ddd75dc725b136ca1a1ffd5b","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","title_canon_sha256":"e8dc3e5081bf06f422f4d91fe3ebefb6f75261110a01dffaa8d263720476c077"},"schema_version":"1.0","source":{"id":"1407.2053","kind":"arxiv","version":1}},"canonical_sha256":"ff3298fc4db37de65642ae615868b77b7903e0d0e2de76d1248de834cf0585c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff3298fc4db37de65642ae615868b77b7903e0d0e2de76d1248de834cf0585c1","first_computed_at":"2026-05-18T02:48:08.562850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:08.562850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q5FwM/1eJYLaSvGqaWWs/mKFC1CchCq5n5zD7cxoDbWoqWn3sXyTMoPDfuF6pIbd7XIwWzhUYd6hBn0jgBmNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:08.563377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13238c70bc289922fcc01e372cf3d0710c9b9c41ab1769eb325f7b6650eb274e","sha256:4c11549fe80bbed81f5c0551c0ddd82ba8319f24c1728c316746a9e3f89f9537"],"state_sha256":"c72f47651e3b6792e5fcf2c3ab08747c63570074b203df3ab43c48a89d1ebfd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r0UGfCMiJxZCtIcN2WvvdyycjqCJuOLPf5MiWm/3rTHJu3S1BYTqB3D0fCWk3tSOx3GRhfis8hjF93Axqs+8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:52:29.052264Z","bundle_sha256":"33dc6365bb8ccab45494e9ad2e0dd713b48c19c4b43e910a26a76199a7883f08"}}