{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:F35662OVPQCQLMEE6MPDVOGRF6","short_pith_number":"pith:F35662OV","canonical_record":{"source":{"id":"1805.07135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-18T10:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"9a5bd35f1bce5b9e868e21b1d86bf7c50d3a528f8258cff8f767240f148bf5d5","abstract_canon_sha256":"2793f491c0ab235c276fb5b0f2af33f6e9b7f4bbb24e23c5e2e5e43f2c91f9bc"},"schema_version":"1.0"},"canonical_sha256":"2efbef69d57c0505b084f31e3ab8d12f8947f0a65ce8a5a56bf377abe51a0bb7","source":{"kind":"arxiv","id":"1805.07135","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07135","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07135v1","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07135","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"F35662OVPQCQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F35662OVPQCQLMEE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F35662OV","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:F35662OVPQCQLMEE6MPDVOGRF6","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-18T10:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"9a5bd35f1bce5b9e868e21b1d86bf7c50d3a528f8258cff8f767240f148bf5d5","abstract_canon_sha256":"2793f491c0ab235c276fb5b0f2af33f6e9b7f4bbb24e23c5e2e5e43f2c91f9bc"},"schema_version":"1.0"},"canonical_sha256":"2efbef69d57c0505b084f31e3ab8d12f8947f0a65ce8a5a56bf377abe51a0bb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:41.033373Z","signature_b64":"wH2jJWGGmLeNVAGwUZXXvW0AYCscmwqsskqr38BXThvJOywDJikyv1gU8dV0uHbnLAGKSY/v1FKLlxeJVIDgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2efbef69d57c0505b084f31e3ab8d12f8947f0a65ce8a5a56bf377abe51a0bb7","last_reissued_at":"2026-05-18T00:15:41.032756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:41.032756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07135","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":"2026-05-18T00:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKzBTlGoz4XdIBRNBiTUMuWMMbxpIxMSLX3DMl2YG5TRngWs8epOvUiQH+G27QOgb4xsoHzbGKVT2q9pkQVvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:50:02.909831Z"},"content_sha256":"53cb904dfb8232e4cce856225833680a41c5d6145918f4849e0dd2967658c2a3","schema_version":"1.0","event_id":"sha256:53cb904dfb8232e4cce856225833680a41c5d6145918f4849e0dd2967658c2a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:F35662OVPQCQLMEE6MPDVOGRF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Karl Bringmann, M{\\aa}ns Magnusson, Thore Husfeldt","submitted_at":"2018-05-18T10:47:16Z","abstract_excerpt":"We show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\\cdot \\binom{k+\\lceil\\log n\\rceil}{k} \\cdot 2^k k^2 \\log n)$, where $k$ is the treewidth of the graph. For every $\\epsilon>0$, this bound is $n^{1+\\epsilon}\\exp O(k)$, which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an algorithm of Cabello and Knauer (Comp. Geom., 2009) i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07135","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":"2026-05-18T00:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FWJc55d7/vih9TU2e3D8bSisjDjUGZ4RzLMBwad/J6r7b2DxEeIC7KnvOD0xpNn+0N2AP4fHj8Zm2Uh35VYcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:50:02.910180Z"},"content_sha256":"66c6e0acda225f6acb07aa24860bdd2de3d3c74ffdedf78a4bbf3f86f7cb8333","schema_version":"1.0","event_id":"sha256:66c6e0acda225f6acb07aa24860bdd2de3d3c74ffdedf78a4bbf3f86f7cb8333"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F35662OVPQCQLMEE6MPDVOGRF6/bundle.json","state_url":"https://pith.science/pith/F35662OVPQCQLMEE6MPDVOGRF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F35662OVPQCQLMEE6MPDVOGRF6/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":"2026-06-03T16:50:02Z","links":{"resolver":"https://pith.science/pith/F35662OVPQCQLMEE6MPDVOGRF6","bundle":"https://pith.science/pith/F35662OVPQCQLMEE6MPDVOGRF6/bundle.json","state":"https://pith.science/pith/F35662OVPQCQLMEE6MPDVOGRF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F35662OVPQCQLMEE6MPDVOGRF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F35662OVPQCQLMEE6MPDVOGRF6","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":"2793f491c0ab235c276fb5b0f2af33f6e9b7f4bbb24e23c5e2e5e43f2c91f9bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-18T10:47:16Z","title_canon_sha256":"9a5bd35f1bce5b9e868e21b1d86bf7c50d3a528f8258cff8f767240f148bf5d5"},"schema_version":"1.0","source":{"id":"1805.07135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07135","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07135v1","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07135","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"F35662OVPQCQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F35662OVPQCQLMEE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F35662OV","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:66c6e0acda225f6acb07aa24860bdd2de3d3c74ffdedf78a4bbf3f86f7cb8333","target":"graph","created_at":"2026-05-18T00:15:41Z","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 show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\\cdot \\binom{k+\\lceil\\log n\\rceil}{k} \\cdot 2^k k^2 \\log n)$, where $k$ is the treewidth of the graph. For every $\\epsilon>0$, this bound is $n^{1+\\epsilon}\\exp O(k)$, which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an algorithm of Cabello and Knauer (Comp. Geom., 2009) i","authors_text":"Karl Bringmann, M{\\aa}ns Magnusson, Thore Husfeldt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-18T10:47:16Z","title":"Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07135","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":"sha256:53cb904dfb8232e4cce856225833680a41c5d6145918f4849e0dd2967658c2a3","target":"record","created_at":"2026-05-18T00:15:41Z","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":"2793f491c0ab235c276fb5b0f2af33f6e9b7f4bbb24e23c5e2e5e43f2c91f9bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-18T10:47:16Z","title_canon_sha256":"9a5bd35f1bce5b9e868e21b1d86bf7c50d3a528f8258cff8f767240f148bf5d5"},"schema_version":"1.0","source":{"id":"1805.07135","kind":"arxiv","version":1}},"canonical_sha256":"2efbef69d57c0505b084f31e3ab8d12f8947f0a65ce8a5a56bf377abe51a0bb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2efbef69d57c0505b084f31e3ab8d12f8947f0a65ce8a5a56bf377abe51a0bb7","first_computed_at":"2026-05-18T00:15:41.032756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:41.032756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wH2jJWGGmLeNVAGwUZXXvW0AYCscmwqsskqr38BXThvJOywDJikyv1gU8dV0uHbnLAGKSY/v1FKLlxeJVIDgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:41.033373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53cb904dfb8232e4cce856225833680a41c5d6145918f4849e0dd2967658c2a3","sha256:66c6e0acda225f6acb07aa24860bdd2de3d3c74ffdedf78a4bbf3f86f7cb8333"],"state_sha256":"dc702a6f4d935e1eceaa3f4a8ae234c1a79088b98989f42f7df1cce2ad871c73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iApl9QuvREFYLX6oPTP4/W0t82cG9zgpClsyvpuxzLWtxM/yUoNR/37d1wx+yjj3WLrKdKEnK5UsiVYORqH8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:50:02.912124Z","bundle_sha256":"caf3f97c35c141ee0ee3fcc4c84501ebd147e27b1a46745a490205f59f396367"}}