{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H6FWVHDAJKGWWZMFMLOTII6VFX","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":"676c51dfe515f1ee49a09b2d55dc9bb3da3189231f058bcb011adbeb6b0f68a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-14T16:36:22Z","title_canon_sha256":"8e4908e948c5a7be9d9b260311155c63f8bbfce001d95a77e82da4646dd05536"},"schema_version":"1.0","source":{"id":"1704.04473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.04473","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1704.04473v1","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04473","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"H6FWVHDAJKGW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H6FWVHDAJKGWWZMF","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H6FWVHDA","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:39665d873d783f3d89e9afe3a503728e1abde87a90ecb647cd2414510c9f1e8b","target":"graph","created_at":"2026-05-18T00:46:21Z","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":"Let $G$ be an unweighted, undirected graph. An additive $k$-spanner of $G$ is a subgraph $H$ that approximates all distances between pairs of nodes up to an additive error of $+k$, that is, it satisfies $d_H(u,v) \\le d_G(u,v)+k$ for all nodes $u,v$, where $d$ is the shortest path distance. We give a deterministic algorithm that constructs an additive $O\\!\\left(1\\right)$-spanner with $O\\!\\left(n^{4/3}\\right)$ edges in $O\\!\\left(n^2\\right)$ time. This should be compared with the randomized Monte Carlo algorithm by Woodruff [ICALP 2010] giving an additive $6$-spanner with $O\\!\\left(n^{4/3}\\log^3 ","authors_text":"Mathias B{\\ae}k Tejs Knudsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-14T16:36:22Z","title":"Additive Spanners and Distance Oracles in Quadratic Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04473","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":"sha256:53f715957773f74d74190dd53a9de2220bcf4c192db7862db756546612ce781b","target":"record","created_at":"2026-05-18T00:46:21Z","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":"676c51dfe515f1ee49a09b2d55dc9bb3da3189231f058bcb011adbeb6b0f68a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-14T16:36:22Z","title_canon_sha256":"8e4908e948c5a7be9d9b260311155c63f8bbfce001d95a77e82da4646dd05536"},"schema_version":"1.0","source":{"id":"1704.04473","kind":"arxiv","version":1}},"canonical_sha256":"3f8b6a9c604a8d6b658562dd3423d52dee5ddc9c2febfefe0173ba6c9cd47c51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f8b6a9c604a8d6b658562dd3423d52dee5ddc9c2febfefe0173ba6c9cd47c51","first_computed_at":"2026-05-18T00:46:21.610204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:21.610204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LRcew1ihVCiQT9swGkr0SkdZAYH5NxWlk8T4DTccWvuMq7FE4Fk5fZSah/wFrYvsvZfAs1rT/+emuY6L8UlyCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:21.610630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.04473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53f715957773f74d74190dd53a9de2220bcf4c192db7862db756546612ce781b","sha256:39665d873d783f3d89e9afe3a503728e1abde87a90ecb647cd2414510c9f1e8b"],"state_sha256":"1cda34ed2d470ecde2c065ff03b7384e1b3c28ee8cbe1a998159a9059efb0aff"}