{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3UVSFXNUPNPRBRXRUFOPDLWZH3","short_pith_number":"pith:3UVSFXNU","canonical_record":{"source":{"id":"1406.4851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-06-18T19:35:06Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"56247bfbf10343433f00dee2740248f3176f266a16f51748016ed6ded8eafdd6","abstract_canon_sha256":"21dca6f13d74e8692d08241759833a069f5b50c60cbfccd47beb660af7536c1f"},"schema_version":"1.0"},"canonical_sha256":"dd2b22ddb47b5f10c6f1a15cf1aed93ef41fa849a0720411135bf3d32a1b0556","source":{"kind":"arxiv","id":"1406.4851","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4851","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4851v1","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4851","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"3UVSFXNUPNPR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3UVSFXNUPNPRBRXR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3UVSFXNU","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3UVSFXNUPNPRBRXRUFOPDLWZH3","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-06-18T19:35:06Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"56247bfbf10343433f00dee2740248f3176f266a16f51748016ed6ded8eafdd6","abstract_canon_sha256":"21dca6f13d74e8692d08241759833a069f5b50c60cbfccd47beb660af7536c1f"},"schema_version":"1.0"},"canonical_sha256":"dd2b22ddb47b5f10c6f1a15cf1aed93ef41fa849a0720411135bf3d32a1b0556","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:14.370649Z","signature_b64":"KITLbKssmi9gwYeMt4lLUWvgHybikd7PFlPq0bw8jiqsfHWL8VFiFkdGtJH/bSvtQqnmmuDefZPfkT9IUrZ9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd2b22ddb47b5f10c6f1a15cf1aed93ef41fa849a0720411135bf3d32a1b0556","last_reissued_at":"2026-05-18T02:42:14.370241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:14.370241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4851","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":"2026-05-18T02:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9UY3L5cfe/ze604hnUEp8Zs2TkiXl5HsCM5QU6gdAdqWQvXSRjpZg7aqWi22QUSoKQO/jKv169kEDEHFLs7uBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:19:35.569400Z"},"content_sha256":"20d39fb93108c8bb3a51b38a8089d0a0e9bc2aac029db4e56a0ea042f359c159","schema_version":"1.0","event_id":"sha256:20d39fb93108c8bb3a51b38a8089d0a0e9bc2aac029db4e56a0ea042f359c159"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3UVSFXNUPNPRBRXRUFOPDLWZH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dominating Scale-Free Networks Using Generalized Probabilistic Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"B. K. Szymanski, \\'E. Czabarka, F. Moln\\'ar Jr., G. Korniss, L. Sz\\'ekely, N. Derzsy","submitted_at":"2014-06-18T19:35:06Z","abstract_excerpt":"We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for applications. We propose two novel probabilistic dominating set selection strategies that are applicable to heterogeneous networks. One of them obtains the smallest probabilistic dominating set and also outperforms the deterministic degree-ranked method. We show that a degree-dependent probabilistic selection method becomes optimal in its deterministic limit. In addi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4851","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":"2026-05-18T02:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCd4IWZJEMJd/FRjsVoR7h4wmP7H0n5LRrPQC2orziyjd9xCHQb0JiHxVdY6xQ0+kksz6PqiJLh6dJR8EqaiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:19:35.570013Z"},"content_sha256":"9dc20cef3572823a969c2f8f1916932a08f7185625035f293b15b8a3785703e2","schema_version":"1.0","event_id":"sha256:9dc20cef3572823a969c2f8f1916932a08f7185625035f293b15b8a3785703e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UVSFXNUPNPRBRXRUFOPDLWZH3/bundle.json","state_url":"https://pith.science/pith/3UVSFXNUPNPRBRXRUFOPDLWZH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UVSFXNUPNPRBRXRUFOPDLWZH3/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":"2026-05-26T13:19:35Z","links":{"resolver":"https://pith.science/pith/3UVSFXNUPNPRBRXRUFOPDLWZH3","bundle":"https://pith.science/pith/3UVSFXNUPNPRBRXRUFOPDLWZH3/bundle.json","state":"https://pith.science/pith/3UVSFXNUPNPRBRXRUFOPDLWZH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UVSFXNUPNPRBRXRUFOPDLWZH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3UVSFXNUPNPRBRXRUFOPDLWZH3","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":"21dca6f13d74e8692d08241759833a069f5b50c60cbfccd47beb660af7536c1f","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-06-18T19:35:06Z","title_canon_sha256":"56247bfbf10343433f00dee2740248f3176f266a16f51748016ed6ded8eafdd6"},"schema_version":"1.0","source":{"id":"1406.4851","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4851","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4851v1","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4851","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"3UVSFXNUPNPR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3UVSFXNUPNPRBRXR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3UVSFXNU","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:9dc20cef3572823a969c2f8f1916932a08f7185625035f293b15b8a3785703e2","target":"graph","created_at":"2026-05-18T02:42:14Z","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 study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for applications. We propose two novel probabilistic dominating set selection strategies that are applicable to heterogeneous networks. One of them obtains the smallest probabilistic dominating set and also outperforms the deterministic degree-ranked method. We show that a degree-dependent probabilistic selection method becomes optimal in its deterministic limit. In addi","authors_text":"B. K. Szymanski, \\'E. Czabarka, F. Moln\\'ar Jr., G. Korniss, L. Sz\\'ekely, N. Derzsy","cross_cats":["cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-06-18T19:35:06Z","title":"Dominating Scale-Free Networks Using Generalized Probabilistic Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4851","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":"sha256:20d39fb93108c8bb3a51b38a8089d0a0e9bc2aac029db4e56a0ea042f359c159","target":"record","created_at":"2026-05-18T02:42:14Z","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":"21dca6f13d74e8692d08241759833a069f5b50c60cbfccd47beb660af7536c1f","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-06-18T19:35:06Z","title_canon_sha256":"56247bfbf10343433f00dee2740248f3176f266a16f51748016ed6ded8eafdd6"},"schema_version":"1.0","source":{"id":"1406.4851","kind":"arxiv","version":1}},"canonical_sha256":"dd2b22ddb47b5f10c6f1a15cf1aed93ef41fa849a0720411135bf3d32a1b0556","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd2b22ddb47b5f10c6f1a15cf1aed93ef41fa849a0720411135bf3d32a1b0556","first_computed_at":"2026-05-18T02:42:14.370241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:14.370241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KITLbKssmi9gwYeMt4lLUWvgHybikd7PFlPq0bw8jiqsfHWL8VFiFkdGtJH/bSvtQqnmmuDefZPfkT9IUrZ9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:14.370649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4851","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20d39fb93108c8bb3a51b38a8089d0a0e9bc2aac029db4e56a0ea042f359c159","sha256:9dc20cef3572823a969c2f8f1916932a08f7185625035f293b15b8a3785703e2"],"state_sha256":"bac2d8e6808e9a4eadcf3c12649a589a7810131006994494ae2768c3f571fb87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YL7EfqSRm0GyKcl/71dByU1S9YBiZX/JQ9FoprCvhz5gerLZD96FEbLG6/BlMxPyZarSVB6WEzLo6TNHff4SCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:19:35.573136Z","bundle_sha256":"c0936cad162088edd349f75576ebc3e3d13fadbac3653efd59ce90b77451c8dd"}}