{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YL7MLO3TOVLQ3MDJX2EV3ZROBZ","short_pith_number":"pith:YL7MLO3T","canonical_record":{"source":{"id":"1109.2641","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-12T22:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"9262a6d51c4e8aef5de5f15a332341bab9e2737fef3879e603f34e9f6cd7223e","abstract_canon_sha256":"31f61a4962ce64d6590317a79ff7d62322fa3fece2e6adce7a15a62fb59f10aa"},"schema_version":"1.0"},"canonical_sha256":"c2fec5bb7375570db069be895de62e0e556274968448e1c5c56c844da5831141","source":{"kind":"arxiv","id":"1109.2641","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2641","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2641v2","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2641","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"YL7MLO3TOVLQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YL7MLO3TOVLQ3MDJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YL7MLO3T","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YL7MLO3TOVLQ3MDJX2EV3ZROBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2641","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-12T22:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"9262a6d51c4e8aef5de5f15a332341bab9e2737fef3879e603f34e9f6cd7223e","abstract_canon_sha256":"31f61a4962ce64d6590317a79ff7d62322fa3fece2e6adce7a15a62fb59f10aa"},"schema_version":"1.0"},"canonical_sha256":"c2fec5bb7375570db069be895de62e0e556274968448e1c5c56c844da5831141","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:55.972830Z","signature_b64":"mDiQ7R/MBExX4D220CTyYIVQCl1nBGxdEezM+3otjqC/K9VA32vwXCT5JU6th1f5s7L7+ePVHsxGgY1bOf/NAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2fec5bb7375570db069be895de62e0e556274968448e1c5c56c844da5831141","last_reissued_at":"2026-05-18T04:09:55.972010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:55.972010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2641","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":"2026-05-18T04:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9N3YRN+Sla75W1bSMPVbaWfFilgF5fPtvUanC4+SkYTAdlGAlZFc3y9ASkC33GGisC5cX5NIImADWrdQHdaYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:34:51.828599Z"},"content_sha256":"cf3b7795bef6fdd94a9f042f0a55ccd0f9cfc19e702663fb3a8be31bc31302cb","schema_version":"1.0","event_id":"sha256:cf3b7795bef6fdd94a9f042f0a55ccd0f9cfc19e702663fb3a8be31bc31302cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YL7MLO3TOVLQ3MDJX2EV3ZROBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More Compact Oracles for Approximate Distances in Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Sommer","submitted_at":"2011-09-12T22:17:33Z","abstract_excerpt":"Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper.\n  In FOCS'01, Thorup introduced approximate distance oracles for planar graphs. He proved that, for any eps>0 and for any planar graph on n nodes, there exists a (1+eps)-approximate distance oracle using space O(n eps^{-1} log n) such that approximate distance queries can be answered in time O(1/eps).\n  Ten years later, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2641","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":"2026-05-18T04:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mom7lsZl1yp4del/MpQGYr3rkXsYS1ni5yfWo3RKSQ3VAIqORubET9jQqjhdQ5HGYQNHVCvkU3M93Segc7oIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:34:51.828943Z"},"content_sha256":"e026a5d2fd72b238e1871bdf326f53c71a2ea0abb2c8c27a411c3b18974f192b","schema_version":"1.0","event_id":"sha256:e026a5d2fd72b238e1871bdf326f53c71a2ea0abb2c8c27a411c3b18974f192b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YL7MLO3TOVLQ3MDJX2EV3ZROBZ/bundle.json","state_url":"https://pith.science/pith/YL7MLO3TOVLQ3MDJX2EV3ZROBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YL7MLO3TOVLQ3MDJX2EV3ZROBZ/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":"2026-06-03T17:34:51Z","links":{"resolver":"https://pith.science/pith/YL7MLO3TOVLQ3MDJX2EV3ZROBZ","bundle":"https://pith.science/pith/YL7MLO3TOVLQ3MDJX2EV3ZROBZ/bundle.json","state":"https://pith.science/pith/YL7MLO3TOVLQ3MDJX2EV3ZROBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YL7MLO3TOVLQ3MDJX2EV3ZROBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YL7MLO3TOVLQ3MDJX2EV3ZROBZ","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":"31f61a4962ce64d6590317a79ff7d62322fa3fece2e6adce7a15a62fb59f10aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-12T22:17:33Z","title_canon_sha256":"9262a6d51c4e8aef5de5f15a332341bab9e2737fef3879e603f34e9f6cd7223e"},"schema_version":"1.0","source":{"id":"1109.2641","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2641","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2641v2","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2641","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"YL7MLO3TOVLQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YL7MLO3TOVLQ3MDJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YL7MLO3T","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:e026a5d2fd72b238e1871bdf326f53c71a2ea0abb2c8c27a411c3b18974f192b","target":"graph","created_at":"2026-05-18T04:09:55Z","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":"Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper.\n  In FOCS'01, Thorup introduced approximate distance oracles for planar graphs. He proved that, for any eps>0 and for any planar graph on n nodes, there exists a (1+eps)-approximate distance oracle using space O(n eps^{-1} log n) such that approximate distance queries can be answered in time O(1/eps).\n  Ten years later, ","authors_text":"Christian Sommer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-12T22:17:33Z","title":"More Compact Oracles for Approximate Distances in Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2641","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:cf3b7795bef6fdd94a9f042f0a55ccd0f9cfc19e702663fb3a8be31bc31302cb","target":"record","created_at":"2026-05-18T04:09:55Z","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":"31f61a4962ce64d6590317a79ff7d62322fa3fece2e6adce7a15a62fb59f10aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-12T22:17:33Z","title_canon_sha256":"9262a6d51c4e8aef5de5f15a332341bab9e2737fef3879e603f34e9f6cd7223e"},"schema_version":"1.0","source":{"id":"1109.2641","kind":"arxiv","version":2}},"canonical_sha256":"c2fec5bb7375570db069be895de62e0e556274968448e1c5c56c844da5831141","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2fec5bb7375570db069be895de62e0e556274968448e1c5c56c844da5831141","first_computed_at":"2026-05-18T04:09:55.972010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:55.972010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mDiQ7R/MBExX4D220CTyYIVQCl1nBGxdEezM+3otjqC/K9VA32vwXCT5JU6th1f5s7L7+ePVHsxGgY1bOf/NAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:55.972830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2641","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf3b7795bef6fdd94a9f042f0a55ccd0f9cfc19e702663fb3a8be31bc31302cb","sha256:e026a5d2fd72b238e1871bdf326f53c71a2ea0abb2c8c27a411c3b18974f192b"],"state_sha256":"0f13f460cdccf6f45cddee11569f447cf097bd956e26e9eec86ddca5e350ffca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h9nbAuI4EaD5TlcnCX0yOMe6nG49ETNzZcJ6jWYp1pnr1+MdJHOJHvN0ntY8dkBmDyAxSrFtjDLdz+hSNzz5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:34:51.831147Z","bundle_sha256":"739b6fe66f8ea008b8f3737e2b3d42c859ffa405e6a570270739bdd7a53b1393"}}