{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QINBRCTWHDGOIRZQKQE2D3SCVS","short_pith_number":"pith:QINBRCTW","canonical_record":{"source":{"id":"1004.2839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-16T13:30:47Z","cross_cats_sorted":[],"title_canon_sha256":"0fa97be72e803c02c59cfd68a8e9018a408eba398ff6f4adb41c7c2afbdfd1e3","abstract_canon_sha256":"9daff27fa21cc8bf7f04122dea3572e628ea2941104cc13ff4b3e82eb46b85e3"},"schema_version":"1.0"},"canonical_sha256":"821a188a7638cce447305409a1ee42ac8c9528a4f6babcca24dd72e80be57660","source":{"kind":"arxiv","id":"1004.2839","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2839","created_at":"2026-05-18T02:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2839v2","created_at":"2026-05-18T02:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2839","created_at":"2026-05-18T02:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"QINBRCTWHDGO","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QINBRCTWHDGOIRZQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QINBRCTW","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QINBRCTWHDGOIRZQKQE2D3SCVS","target":"record","payload":{"canonical_record":{"source":{"id":"1004.2839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-16T13:30:47Z","cross_cats_sorted":[],"title_canon_sha256":"0fa97be72e803c02c59cfd68a8e9018a408eba398ff6f4adb41c7c2afbdfd1e3","abstract_canon_sha256":"9daff27fa21cc8bf7f04122dea3572e628ea2941104cc13ff4b3e82eb46b85e3"},"schema_version":"1.0"},"canonical_sha256":"821a188a7638cce447305409a1ee42ac8c9528a4f6babcca24dd72e80be57660","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:04.664848Z","signature_b64":"fnIYY+DzHZ+NgIsYV616Vox3jDJTssV1+JrC5z3+e8zv9apdKMl15YH5hWbtoe5fArlhtBwsy9CmkB+/RFC4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"821a188a7638cce447305409a1ee42ac8c9528a4f6babcca24dd72e80be57660","last_reissued_at":"2026-05-18T02:08:04.664174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:04.664174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.2839","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rGfd+VBHJoYHvu5dY9vjH5FqOJ+w9MiSg/gnkACN1Sw01o3bTd5bZBZ69jAkfg2AT41ZqrD9iT5+9PCz6rlNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:13:01.847622Z"},"content_sha256":"ceefedfa66f60f2b24c425263437f0cad36641d55915a9f26c858cffec286701","schema_version":"1.0","event_id":"sha256:ceefedfa66f60f2b24c425263437f0cad36641d55915a9f26c858cffec286701"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QINBRCTWHDGOIRZQKQE2D3SCVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation Algorithms for the Capacitated Domination Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Han-Lin Chen, Mong-Jen Kao","submitted_at":"2010-04-16T13:30:47Z","abstract_excerpt":"We consider the {\\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\\em Dominating Set} problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service. In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2839","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":""},"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":"2026-05-18T02:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rmjLCemXeoL3RJjkuSaGT0S9tupS9/HUN0M1XsKkMqh2ISBPfG8gqJN0jG1cYnMrWKrrHgwS8di/mAAPntHEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:13:01.847974Z"},"content_sha256":"8f3fe36a4d83d0cf465eab4d9594f5266ab5a6085a360bd617d9d425192284e0","schema_version":"1.0","event_id":"sha256:8f3fe36a4d83d0cf465eab4d9594f5266ab5a6085a360bd617d9d425192284e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QINBRCTWHDGOIRZQKQE2D3SCVS/bundle.json","state_url":"https://pith.science/pith/QINBRCTWHDGOIRZQKQE2D3SCVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QINBRCTWHDGOIRZQKQE2D3SCVS/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":"2026-06-03T15:13:01Z","links":{"resolver":"https://pith.science/pith/QINBRCTWHDGOIRZQKQE2D3SCVS","bundle":"https://pith.science/pith/QINBRCTWHDGOIRZQKQE2D3SCVS/bundle.json","state":"https://pith.science/pith/QINBRCTWHDGOIRZQKQE2D3SCVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QINBRCTWHDGOIRZQKQE2D3SCVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QINBRCTWHDGOIRZQKQE2D3SCVS","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":"9daff27fa21cc8bf7f04122dea3572e628ea2941104cc13ff4b3e82eb46b85e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-16T13:30:47Z","title_canon_sha256":"0fa97be72e803c02c59cfd68a8e9018a408eba398ff6f4adb41c7c2afbdfd1e3"},"schema_version":"1.0","source":{"id":"1004.2839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2839","created_at":"2026-05-18T02:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2839v2","created_at":"2026-05-18T02:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2839","created_at":"2026-05-18T02:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"QINBRCTWHDGO","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QINBRCTWHDGOIRZQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QINBRCTW","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:8f3fe36a4d83d0cf465eab4d9594f5266ab5a6085a360bd617d9d425192284e0","target":"graph","created_at":"2026-05-18T02:08:04Z","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 consider the {\\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\\em Dominating Set} problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service. In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to diffe","authors_text":"Han-Lin Chen, Mong-Jen Kao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-16T13:30:47Z","title":"Approximation Algorithms for the Capacitated Domination Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2839","kind":"arxiv","version":2},"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:ceefedfa66f60f2b24c425263437f0cad36641d55915a9f26c858cffec286701","target":"record","created_at":"2026-05-18T02:08:04Z","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":"9daff27fa21cc8bf7f04122dea3572e628ea2941104cc13ff4b3e82eb46b85e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-16T13:30:47Z","title_canon_sha256":"0fa97be72e803c02c59cfd68a8e9018a408eba398ff6f4adb41c7c2afbdfd1e3"},"schema_version":"1.0","source":{"id":"1004.2839","kind":"arxiv","version":2}},"canonical_sha256":"821a188a7638cce447305409a1ee42ac8c9528a4f6babcca24dd72e80be57660","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"821a188a7638cce447305409a1ee42ac8c9528a4f6babcca24dd72e80be57660","first_computed_at":"2026-05-18T02:08:04.664174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:04.664174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fnIYY+DzHZ+NgIsYV616Vox3jDJTssV1+JrC5z3+e8zv9apdKMl15YH5hWbtoe5fArlhtBwsy9CmkB+/RFC4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:04.664848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ceefedfa66f60f2b24c425263437f0cad36641d55915a9f26c858cffec286701","sha256:8f3fe36a4d83d0cf465eab4d9594f5266ab5a6085a360bd617d9d425192284e0"],"state_sha256":"0c9ef5461e5dd7999c2e47ec78870809bcfd3b8bea4b71ff20a74b018effd4b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TVEcy1aN0pwtv3SY+0VOhEyk2LVPM4cV3gY01nDMy+7I8xWRzrHsnWcWrAxx+xCOplzTf+M5jlwxBMEdpRGODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:13:01.850310Z","bundle_sha256":"5419066d67e8cc7f6664d6a2d76399f067090d7977bb4501e71da4c46518c9dc"}}