{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UJ5BGA4XKSXEW6PKWLREVDSMLB","short_pith_number":"pith:UJ5BGA4X","canonical_record":{"source":{"id":"1202.2336","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-10T19:51:10Z","cross_cats_sorted":[],"title_canon_sha256":"0c283e8d09b569e7ef9f55bbd8495fd6bc6c0cdb63f447c4e2427bfd48289492","abstract_canon_sha256":"5ed29d9d8a9c533287d318c6d92a24b9784876602ab0e07423c3a45d07c9d7a3"},"schema_version":"1.0"},"canonical_sha256":"a27a13039754ae4b79eab2e24a8e4c58408b978ae87dc557c0448a0976d6feb3","source":{"kind":"arxiv","id":"1202.2336","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2336","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2336v3","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2336","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"UJ5BGA4XKSXE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UJ5BGA4XKSXEW6PK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UJ5BGA4X","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UJ5BGA4XKSXEW6PKWLREVDSMLB","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2336","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-10T19:51:10Z","cross_cats_sorted":[],"title_canon_sha256":"0c283e8d09b569e7ef9f55bbd8495fd6bc6c0cdb63f447c4e2427bfd48289492","abstract_canon_sha256":"5ed29d9d8a9c533287d318c6d92a24b9784876602ab0e07423c3a45d07c9d7a3"},"schema_version":"1.0"},"canonical_sha256":"a27a13039754ae4b79eab2e24a8e4c58408b978ae87dc557c0448a0976d6feb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:15.417828Z","signature_b64":"d6MzrNW/cI2F7aSB4d0q//bRFSH6HFxxU1e8XlD7/g1D+WuiKkBYjPiXijLcFjz4fEcX3XcJ1QJDkRF5r+YDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a27a13039754ae4b79eab2e24a8e4c58408b978ae87dc557c0448a0976d6feb3","last_reissued_at":"2026-05-18T03:44:15.417413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:15.417413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2336","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oMYtegg61HXgXjRrqH26n+X3+HmBlzXwl9fIyvaetRfZAjeJ2DumKTLZpqjDvSOTl994eHcbL1havmuNHgmuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:32:23.415099Z"},"content_sha256":"4e14d05e9fb9ebb44897d39586f8492640008b59f8c699ae169acf9976c23cdf","schema_version":"1.0","event_id":"sha256:4e14d05e9fb9ebb44897d39586f8492640008b59f8c699ae169acf9976c23cdf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UJ5BGA4XKSXEW6PKWLREVDSMLB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Distance Oracles with Improved Query Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Christian Wulff-Nilsen","submitted_at":"2012-02-10T19:51:10Z","abstract_excerpt":"Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\\geq 2$, we show that a $(2k-1)$-approximate distance oracle for $G$ of size $O(kn^{1 + 1/k})$ and with $O(\\log k)$ query time can be constructed in $O(\\min\\{kmn^{1/k},\\sqrt km + kn^{1 + c/\\sqrt k}\\})$ time for some constant $c$. This improves the $O(k)$ query time of Thorup and Zwick. Furthermore, for any $0 < \\epsilon \\leq 1$, we give an oracle of size $O(kn^{1 + 1/k})$ that answers $((2 + \\epsilon)k)$-approximate distance queries in $O(1/\\epsilon)$ time. At the cost of a $k$-fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2336","kind":"arxiv","version":3},"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":"2026-05-18T03:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ocv2Ks+S8sln9Pl2d0S9AyjugbXJC29xWKTlCbZwkQcYEorCriWSAqaA7l8BuqTo2tDHkIyWy9Zd06lezBqdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:32:23.415468Z"},"content_sha256":"ff3639cfc0dd23aab5c9eaf9fb82244106522185de323637cd8afc54cf4a7641","schema_version":"1.0","event_id":"sha256:ff3639cfc0dd23aab5c9eaf9fb82244106522185de323637cd8afc54cf4a7641"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJ5BGA4XKSXEW6PKWLREVDSMLB/bundle.json","state_url":"https://pith.science/pith/UJ5BGA4XKSXEW6PKWLREVDSMLB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJ5BGA4XKSXEW6PKWLREVDSMLB/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":"2026-06-05T12:32:23Z","links":{"resolver":"https://pith.science/pith/UJ5BGA4XKSXEW6PKWLREVDSMLB","bundle":"https://pith.science/pith/UJ5BGA4XKSXEW6PKWLREVDSMLB/bundle.json","state":"https://pith.science/pith/UJ5BGA4XKSXEW6PKWLREVDSMLB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJ5BGA4XKSXEW6PKWLREVDSMLB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UJ5BGA4XKSXEW6PKWLREVDSMLB","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":"5ed29d9d8a9c533287d318c6d92a24b9784876602ab0e07423c3a45d07c9d7a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-10T19:51:10Z","title_canon_sha256":"0c283e8d09b569e7ef9f55bbd8495fd6bc6c0cdb63f447c4e2427bfd48289492"},"schema_version":"1.0","source":{"id":"1202.2336","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2336","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2336v3","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2336","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"UJ5BGA4XKSXE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UJ5BGA4XKSXEW6PK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UJ5BGA4X","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:ff3639cfc0dd23aab5c9eaf9fb82244106522185de323637cd8afc54cf4a7641","target":"graph","created_at":"2026-05-18T03:44:15Z","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":"Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\\geq 2$, we show that a $(2k-1)$-approximate distance oracle for $G$ of size $O(kn^{1 + 1/k})$ and with $O(\\log k)$ query time can be constructed in $O(\\min\\{kmn^{1/k},\\sqrt km + kn^{1 + c/\\sqrt k}\\})$ time for some constant $c$. This improves the $O(k)$ query time of Thorup and Zwick. Furthermore, for any $0 < \\epsilon \\leq 1$, we give an oracle of size $O(kn^{1 + 1/k})$ that answers $((2 + \\epsilon)k)$-approximate distance queries in $O(1/\\epsilon)$ time. At the cost of a $k$-fac","authors_text":"Christian Wulff-Nilsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-10T19:51:10Z","title":"Approximate Distance Oracles with Improved Query Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2336","kind":"arxiv","version":3},"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":"sha256:4e14d05e9fb9ebb44897d39586f8492640008b59f8c699ae169acf9976c23cdf","target":"record","created_at":"2026-05-18T03:44:15Z","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":"5ed29d9d8a9c533287d318c6d92a24b9784876602ab0e07423c3a45d07c9d7a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-10T19:51:10Z","title_canon_sha256":"0c283e8d09b569e7ef9f55bbd8495fd6bc6c0cdb63f447c4e2427bfd48289492"},"schema_version":"1.0","source":{"id":"1202.2336","kind":"arxiv","version":3}},"canonical_sha256":"a27a13039754ae4b79eab2e24a8e4c58408b978ae87dc557c0448a0976d6feb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a27a13039754ae4b79eab2e24a8e4c58408b978ae87dc557c0448a0976d6feb3","first_computed_at":"2026-05-18T03:44:15.417413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:15.417413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d6MzrNW/cI2F7aSB4d0q//bRFSH6HFxxU1e8XlD7/g1D+WuiKkBYjPiXijLcFjz4fEcX3XcJ1QJDkRF5r+YDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:15.417828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2336","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e14d05e9fb9ebb44897d39586f8492640008b59f8c699ae169acf9976c23cdf","sha256:ff3639cfc0dd23aab5c9eaf9fb82244106522185de323637cd8afc54cf4a7641"],"state_sha256":"d6134f809c592b378c58981a0ba397dc368c42ab8b818ccc7bd6e7cc300a93ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kiTr+kH3pqZOoeSlZm00gEWkI93VNgY1flKTLG7meyhxl49hMYPTuO6iJNfAX6qWlpmoaO8n63olwTkW4F7yBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:32:23.417489Z","bundle_sha256":"68329dd84b2cd1adebedfca562fedc585dcbb09bfca2d0f05920c074013b6317"}}