{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X4BUBDNRN4UK6BDTT5RIIAGCPF","short_pith_number":"pith:X4BUBDNR","canonical_record":{"source":{"id":"1412.2300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-07T00:43:36Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"cf1293e93f85edc9834cf8961563d07ad510383f33aac6d1ff8250ce6545d2f4","abstract_canon_sha256":"24d10b55263d6636829e4bc21873f0659f041fd28d84f315db36b5f7795098b2"},"schema_version":"1.0"},"canonical_sha256":"bf03408db16f28af04739f628400c2794cdae3a00ab4e6f23d22139dfef662ea","source":{"kind":"arxiv","id":"1412.2300","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2300","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2300v1","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2300","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"X4BUBDNRN4UK","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"X4BUBDNRN4UK6BDT","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"X4BUBDNR","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X4BUBDNRN4UK6BDTT5RIIAGCPF","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-07T00:43:36Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"cf1293e93f85edc9834cf8961563d07ad510383f33aac6d1ff8250ce6545d2f4","abstract_canon_sha256":"24d10b55263d6636829e4bc21873f0659f041fd28d84f315db36b5f7795098b2"},"schema_version":"1.0"},"canonical_sha256":"bf03408db16f28af04739f628400c2794cdae3a00ab4e6f23d22139dfef662ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:58.392705Z","signature_b64":"DuDuK/EsA9cIWu8E7rf1JEK70AvNxwQ/15meGcT5jmpAap5mrrs8BnXhxABb74YL4LPTZuZu01/ewAxu3dLwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf03408db16f28af04739f628400c2794cdae3a00ab4e6f23d22139dfef662ea","last_reissued_at":"2026-05-18T02:31:58.392156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:58.392156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2300","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":"2026-05-18T02:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mvPhRF+K7icWtovoYS0p7tRfc6PQlec2tPe82Yly1FQs6jcbLWnCnqxfRiP1pX6dX+kKCCv8+zWMW61wri4eCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:30:43.490068Z"},"content_sha256":"824bb6dd0b1baf4da3ffe8a32596bba475183a4e76ed1e6578ce297c6fe65bdc","schema_version":"1.0","event_id":"sha256:824bb6dd0b1baf4da3ffe8a32596bba475183a4e76ed1e6578ce297c6fe65bdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X4BUBDNRN4UK6BDTT5RIIAGCPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimizing the Aggregate Movements for Interval Coverage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Aaron M. Andrews, Haitao Wang","submitted_at":"2014-12-07T00:43:36Z","abstract_excerpt":"We consider an interval coverage problem. Given $n$ intervals of the same length on a line $L$ and a line segment $B$ on $L$, we want to move the intervals along $L$ such that every point of $B$ is covered by at least one interval and the sum of the moving distances of all intervals is minimized. As a basic geometry problem, it has applications in mobile sensor barrier coverage in wireless sensor networks. The previous work solved the problem in $O(n^2)$ time. In this paper, by discovering many interesting observations and developing new algorithmic techniques, we present an $O(n\\log n)$ time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2300","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":"2026-05-18T02:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LHoNbqeD/o1tM5OM5jGCpZMuEZqaD7l+Sp36mKSU5ubH9t3Rjk3DNJT6/l2hpFgZNJI7c9pWEKFct4vAtNK4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:30:43.490743Z"},"content_sha256":"e89121d4a74b9f7455cdf56ca133ca786fb189a0a351be0e00e13da562bcd1b9","schema_version":"1.0","event_id":"sha256:e89121d4a74b9f7455cdf56ca133ca786fb189a0a351be0e00e13da562bcd1b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X4BUBDNRN4UK6BDTT5RIIAGCPF/bundle.json","state_url":"https://pith.science/pith/X4BUBDNRN4UK6BDTT5RIIAGCPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X4BUBDNRN4UK6BDTT5RIIAGCPF/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":"2026-05-25T18:30:43Z","links":{"resolver":"https://pith.science/pith/X4BUBDNRN4UK6BDTT5RIIAGCPF","bundle":"https://pith.science/pith/X4BUBDNRN4UK6BDTT5RIIAGCPF/bundle.json","state":"https://pith.science/pith/X4BUBDNRN4UK6BDTT5RIIAGCPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X4BUBDNRN4UK6BDTT5RIIAGCPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X4BUBDNRN4UK6BDTT5RIIAGCPF","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":"24d10b55263d6636829e4bc21873f0659f041fd28d84f315db36b5f7795098b2","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-07T00:43:36Z","title_canon_sha256":"cf1293e93f85edc9834cf8961563d07ad510383f33aac6d1ff8250ce6545d2f4"},"schema_version":"1.0","source":{"id":"1412.2300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2300","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2300v1","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2300","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"X4BUBDNRN4UK","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"X4BUBDNRN4UK6BDT","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"X4BUBDNR","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:e89121d4a74b9f7455cdf56ca133ca786fb189a0a351be0e00e13da562bcd1b9","target":"graph","created_at":"2026-05-18T02:31:58Z","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 an interval coverage problem. Given $n$ intervals of the same length on a line $L$ and a line segment $B$ on $L$, we want to move the intervals along $L$ such that every point of $B$ is covered by at least one interval and the sum of the moving distances of all intervals is minimized. As a basic geometry problem, it has applications in mobile sensor barrier coverage in wireless sensor networks. The previous work solved the problem in $O(n^2)$ time. In this paper, by discovering many interesting observations and developing new algorithmic techniques, we present an $O(n\\log n)$ time ","authors_text":"Aaron M. Andrews, Haitao Wang","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-07T00:43:36Z","title":"Minimizing the Aggregate Movements for Interval Coverage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2300","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":"sha256:824bb6dd0b1baf4da3ffe8a32596bba475183a4e76ed1e6578ce297c6fe65bdc","target":"record","created_at":"2026-05-18T02:31:58Z","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":"24d10b55263d6636829e4bc21873f0659f041fd28d84f315db36b5f7795098b2","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-07T00:43:36Z","title_canon_sha256":"cf1293e93f85edc9834cf8961563d07ad510383f33aac6d1ff8250ce6545d2f4"},"schema_version":"1.0","source":{"id":"1412.2300","kind":"arxiv","version":1}},"canonical_sha256":"bf03408db16f28af04739f628400c2794cdae3a00ab4e6f23d22139dfef662ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf03408db16f28af04739f628400c2794cdae3a00ab4e6f23d22139dfef662ea","first_computed_at":"2026-05-18T02:31:58.392156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:58.392156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DuDuK/EsA9cIWu8E7rf1JEK70AvNxwQ/15meGcT5jmpAap5mrrs8BnXhxABb74YL4LPTZuZu01/ewAxu3dLwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:58.392705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:824bb6dd0b1baf4da3ffe8a32596bba475183a4e76ed1e6578ce297c6fe65bdc","sha256:e89121d4a74b9f7455cdf56ca133ca786fb189a0a351be0e00e13da562bcd1b9"],"state_sha256":"b306cc668f36a46345b4fec8e2d78442bde49cf0bc6e391cf23f46765c34bddf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lI20qdcgJOd8HNzgv+erj2maHABK9NFeXdAL6NMnsQFhXk5E23Nh9YctR9E4y7vVa3tFQBJEAGPVkZHl+VIQDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:30:43.494454Z","bundle_sha256":"7f61e663edba9cee7c609fca00a1eb0811c7032b081e9657e20deb567b40f726"}}