{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WG6LX3HZRHYG6LOZ55UML4IQP2","short_pith_number":"pith:WG6LX3HZ","canonical_record":{"source":{"id":"1804.08237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-23T03:46:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"247a253a7d959398b02c06ad6cf43d1c19c5e5b32aef9585fda6d5f9572c78a1","abstract_canon_sha256":"2a5f37291c55343e8ec049ca5313a53f1d50915c8c8c2cdc36d8c939c540a30d"},"schema_version":"1.0"},"canonical_sha256":"b1bcbbecf989f06f2dd9ef68c5f1107eaf302d4b39dc5c36dca92367627ad6e5","source":{"kind":"arxiv","id":"1804.08237","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08237","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08237v1","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08237","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"WG6LX3HZRHYG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WG6LX3HZRHYG6LOZ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WG6LX3HZ","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WG6LX3HZRHYG6LOZ55UML4IQP2","target":"record","payload":{"canonical_record":{"source":{"id":"1804.08237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-23T03:46:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"247a253a7d959398b02c06ad6cf43d1c19c5e5b32aef9585fda6d5f9572c78a1","abstract_canon_sha256":"2a5f37291c55343e8ec049ca5313a53f1d50915c8c8c2cdc36d8c939c540a30d"},"schema_version":"1.0"},"canonical_sha256":"b1bcbbecf989f06f2dd9ef68c5f1107eaf302d4b39dc5c36dca92367627ad6e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:49.101030Z","signature_b64":"1rBEH6ZX0YsFRebRR2u3ypmpcJD3p3p9FLp0tPK1YC75bLMBglJ5P4dT8BZjfZR3kMivxEqsB8JKDakRrR5TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1bcbbecf989f06f2dd9ef68c5f1107eaf302d4b39dc5c36dca92367627ad6e5","last_reissued_at":"2026-05-18T00:17:49.100549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:49.100549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.08237","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":"2026-05-18T00:17:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/e6Hsha47HFe18Dr4PXKvfPelqS/r6Ur0BaZepW+Wt4PWIEPb5EIMutbYakuMcjHtYezorCTiroPXYa1oENdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:15:03.145292Z"},"content_sha256":"4a8170358585efc48fc830e330db978af3ee60983acea84a2c08a167d8ba77cc","schema_version":"1.0","event_id":"sha256:4a8170358585efc48fc830e330db978af3ee60983acea84a2c08a167d8ba77cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WG6LX3HZRHYG6LOZ55UML4IQP2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized comparison trees for point-location problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Daniel M Kane, Shachar Lovett, Shay Moran","submitted_at":"2018-04-23T03:46:20Z","abstract_excerpt":"Let $H$ be an arbitrary family of hyper-planes in $d$-dimensions. We show that the point-location problem for $H$ can be solved by a linear decision tree that only uses a special type of queries called \\emph{generalized comparison queries}. These queries correspond to hyperplanes that can be written as a linear combination of two hyperplanes from $H$; in particular, if all hyperplanes in $H$ are $k$-sparse then generalized comparisons are $2k$-sparse. The depth of the obtained linear decision tree is polynomial in $d$ and logarithmic in $|H|$, which is comparable to previous results in the lit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08237","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":"2026-05-18T00:17:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWpYL3/sIv77AElCGlcMTY82LRimM3WGpp13A/rxVOWkvhsCVGC1rBJp8mKE4TLhzFB6wFmtwao1zJTNiPtjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:15:03.145689Z"},"content_sha256":"2f6d6c3fdae4e61b315eefb705dad65dc602f5908adaccc50243a9d00c75bd4f","schema_version":"1.0","event_id":"sha256:2f6d6c3fdae4e61b315eefb705dad65dc602f5908adaccc50243a9d00c75bd4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WG6LX3HZRHYG6LOZ55UML4IQP2/bundle.json","state_url":"https://pith.science/pith/WG6LX3HZRHYG6LOZ55UML4IQP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WG6LX3HZRHYG6LOZ55UML4IQP2/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":"2026-06-07T06:15:03Z","links":{"resolver":"https://pith.science/pith/WG6LX3HZRHYG6LOZ55UML4IQP2","bundle":"https://pith.science/pith/WG6LX3HZRHYG6LOZ55UML4IQP2/bundle.json","state":"https://pith.science/pith/WG6LX3HZRHYG6LOZ55UML4IQP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WG6LX3HZRHYG6LOZ55UML4IQP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WG6LX3HZRHYG6LOZ55UML4IQP2","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":"2a5f37291c55343e8ec049ca5313a53f1d50915c8c8c2cdc36d8c939c540a30d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-23T03:46:20Z","title_canon_sha256":"247a253a7d959398b02c06ad6cf43d1c19c5e5b32aef9585fda6d5f9572c78a1"},"schema_version":"1.0","source":{"id":"1804.08237","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08237","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08237v1","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08237","created_at":"2026-05-18T00:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"WG6LX3HZRHYG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WG6LX3HZRHYG6LOZ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WG6LX3HZ","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:2f6d6c3fdae4e61b315eefb705dad65dc602f5908adaccc50243a9d00c75bd4f","target":"graph","created_at":"2026-05-18T00:17:49Z","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 $H$ be an arbitrary family of hyper-planes in $d$-dimensions. We show that the point-location problem for $H$ can be solved by a linear decision tree that only uses a special type of queries called \\emph{generalized comparison queries}. These queries correspond to hyperplanes that can be written as a linear combination of two hyperplanes from $H$; in particular, if all hyperplanes in $H$ are $k$-sparse then generalized comparisons are $2k$-sparse. The depth of the obtained linear decision tree is polynomial in $d$ and logarithmic in $|H|$, which is comparable to previous results in the lit","authors_text":"Daniel M Kane, Shachar Lovett, Shay Moran","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-23T03:46:20Z","title":"Generalized comparison trees for point-location problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08237","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":"sha256:4a8170358585efc48fc830e330db978af3ee60983acea84a2c08a167d8ba77cc","target":"record","created_at":"2026-05-18T00:17:49Z","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":"2a5f37291c55343e8ec049ca5313a53f1d50915c8c8c2cdc36d8c939c540a30d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-23T03:46:20Z","title_canon_sha256":"247a253a7d959398b02c06ad6cf43d1c19c5e5b32aef9585fda6d5f9572c78a1"},"schema_version":"1.0","source":{"id":"1804.08237","kind":"arxiv","version":1}},"canonical_sha256":"b1bcbbecf989f06f2dd9ef68c5f1107eaf302d4b39dc5c36dca92367627ad6e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1bcbbecf989f06f2dd9ef68c5f1107eaf302d4b39dc5c36dca92367627ad6e5","first_computed_at":"2026-05-18T00:17:49.100549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:49.100549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1rBEH6ZX0YsFRebRR2u3ypmpcJD3p3p9FLp0tPK1YC75bLMBglJ5P4dT8BZjfZR3kMivxEqsB8JKDakRrR5TAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:49.101030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08237","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a8170358585efc48fc830e330db978af3ee60983acea84a2c08a167d8ba77cc","sha256:2f6d6c3fdae4e61b315eefb705dad65dc602f5908adaccc50243a9d00c75bd4f"],"state_sha256":"1ea748201ced8dd600285759db23e16422b8c6757d079812008d9398d382712d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gDkfhjtacfpNNcaFL0f02rDAcHIQ4JmAJrOPsdxEop5S462LF7CwHiNGIe9DICDV0uB2ejckU7d0bhBTP7JxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:15:03.148055Z","bundle_sha256":"cedd32bd7210b34ac628db34448bbd78cbcf543e0773f6adc1f0c7e3d5579ca6"}}