{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:466B4QC2OIUW3E2ZSTGIPN6OBX","short_pith_number":"pith:466B4QC2","canonical_record":{"source":{"id":"1712.04595","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-13T03:01:56Z","cross_cats_sorted":[],"title_canon_sha256":"d8cac4e245e014fb62d6f2439bb9e176d84d9d1596e704e5ad0f6999e1fc089e","abstract_canon_sha256":"7fcb4b9e3a400ee22fb9ec874d7bb76d04398d728bcc8b27e69297647cb4c299"},"schema_version":"1.0"},"canonical_sha256":"e7bc1e405a72296d935994cc87b7ce0dd81f64142b2a24182d3b1971d03ab4ee","source":{"kind":"arxiv","id":"1712.04595","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04595","created_at":"2026-05-18T00:28:04Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04595v1","created_at":"2026-05-18T00:28:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04595","created_at":"2026-05-18T00:28:04Z"},{"alias_kind":"pith_short_12","alias_value":"466B4QC2OIUW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"466B4QC2OIUW3E2Z","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"466B4QC2","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:466B4QC2OIUW3E2ZSTGIPN6OBX","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04595","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-13T03:01:56Z","cross_cats_sorted":[],"title_canon_sha256":"d8cac4e245e014fb62d6f2439bb9e176d84d9d1596e704e5ad0f6999e1fc089e","abstract_canon_sha256":"7fcb4b9e3a400ee22fb9ec874d7bb76d04398d728bcc8b27e69297647cb4c299"},"schema_version":"1.0"},"canonical_sha256":"e7bc1e405a72296d935994cc87b7ce0dd81f64142b2a24182d3b1971d03ab4ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:04.129428Z","signature_b64":"lfNNY2bRw1arjZsPotHECjxEj9qBpe0u4niKWyjr6TTvBicZViuqdTWr44OiAcjP6lhAhS9hWXJVAlkMeo2+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7bc1e405a72296d935994cc87b7ce0dd81f64142b2a24182d3b1971d03ab4ee","last_reissued_at":"2026-05-18T00:28:04.128888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:04.128888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04595","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":"2026-05-18T00:28:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cTX8kxdc57jscpMpB0jMsvl5RQ9z6tpLGPg5uw7PvmkCHiU7sJaDMXIW35yogQhUzMzCxnhHLt4akUPmu/ZFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:09:28.622156Z"},"content_sha256":"2e1e4e4b8fdde08f37bca05a6f1e7d4c6bb8678df117d248a2b407ccac658c4e","schema_version":"1.0","event_id":"sha256:2e1e4e4b8fdde08f37bca05a6f1e7d4c6bb8678df117d248a2b407ccac658c4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:466B4QC2OIUW3E2ZSTGIPN6OBX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractal dimension and lower bounds for geometric problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anastasios Sidiropoulos, Kritika Singhal, Vijay Sridhar","submitted_at":"2017-12-13T03:01:56Z","abstract_excerpt":"We study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space with fractal dimension smaller than the ambient dimension. In this paper we prove nearly-matching lower bounds, thus establishing nearly-optimal bounds for various problems as a function of the fractal dimension.\n  More specifically, we show that for any set of $n$ points in $d$-dimensional Euclidean space, of fractal dimension $\\delta\\in (1,d)$, for any $\\eps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04595","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":"2026-05-18T00:28:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tE8hKzf/fY8g1G0c72sVv1b6KQX3pPaEBsE4LemnWt8TX18un/dxSHzUXv+2i7i+iNUhGcLiAZiA61EidaACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:09:28.622877Z"},"content_sha256":"e9708f5403c14befe089bdce7b13e3fd624034d1cc3cb720eb4b490814440276","schema_version":"1.0","event_id":"sha256:e9708f5403c14befe089bdce7b13e3fd624034d1cc3cb720eb4b490814440276"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/466B4QC2OIUW3E2ZSTGIPN6OBX/bundle.json","state_url":"https://pith.science/pith/466B4QC2OIUW3E2ZSTGIPN6OBX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/466B4QC2OIUW3E2ZSTGIPN6OBX/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":"2026-06-09T18:09:28Z","links":{"resolver":"https://pith.science/pith/466B4QC2OIUW3E2ZSTGIPN6OBX","bundle":"https://pith.science/pith/466B4QC2OIUW3E2ZSTGIPN6OBX/bundle.json","state":"https://pith.science/pith/466B4QC2OIUW3E2ZSTGIPN6OBX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/466B4QC2OIUW3E2ZSTGIPN6OBX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:466B4QC2OIUW3E2ZSTGIPN6OBX","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":"7fcb4b9e3a400ee22fb9ec874d7bb76d04398d728bcc8b27e69297647cb4c299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-13T03:01:56Z","title_canon_sha256":"d8cac4e245e014fb62d6f2439bb9e176d84d9d1596e704e5ad0f6999e1fc089e"},"schema_version":"1.0","source":{"id":"1712.04595","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04595","created_at":"2026-05-18T00:28:04Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04595v1","created_at":"2026-05-18T00:28:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04595","created_at":"2026-05-18T00:28:04Z"},{"alias_kind":"pith_short_12","alias_value":"466B4QC2OIUW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"466B4QC2OIUW3E2Z","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"466B4QC2","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:e9708f5403c14befe089bdce7b13e3fd624034d1cc3cb720eb4b490814440276","target":"graph","created_at":"2026-05-18T00:28:04Z","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 study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space with fractal dimension smaller than the ambient dimension. In this paper we prove nearly-matching lower bounds, thus establishing nearly-optimal bounds for various problems as a function of the fractal dimension.\n  More specifically, we show that for any set of $n$ points in $d$-dimensional Euclidean space, of fractal dimension $\\delta\\in (1,d)$, for any $\\eps","authors_text":"Anastasios Sidiropoulos, Kritika Singhal, Vijay Sridhar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-13T03:01:56Z","title":"Fractal dimension and lower bounds for geometric problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04595","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":"sha256:2e1e4e4b8fdde08f37bca05a6f1e7d4c6bb8678df117d248a2b407ccac658c4e","target":"record","created_at":"2026-05-18T00:28:04Z","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":"7fcb4b9e3a400ee22fb9ec874d7bb76d04398d728bcc8b27e69297647cb4c299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-13T03:01:56Z","title_canon_sha256":"d8cac4e245e014fb62d6f2439bb9e176d84d9d1596e704e5ad0f6999e1fc089e"},"schema_version":"1.0","source":{"id":"1712.04595","kind":"arxiv","version":1}},"canonical_sha256":"e7bc1e405a72296d935994cc87b7ce0dd81f64142b2a24182d3b1971d03ab4ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7bc1e405a72296d935994cc87b7ce0dd81f64142b2a24182d3b1971d03ab4ee","first_computed_at":"2026-05-18T00:28:04.128888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:04.128888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lfNNY2bRw1arjZsPotHECjxEj9qBpe0u4niKWyjr6TTvBicZViuqdTWr44OiAcjP6lhAhS9hWXJVAlkMeo2+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:04.129428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04595","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e1e4e4b8fdde08f37bca05a6f1e7d4c6bb8678df117d248a2b407ccac658c4e","sha256:e9708f5403c14befe089bdce7b13e3fd624034d1cc3cb720eb4b490814440276"],"state_sha256":"ae32ee8485842b0cd7e741ca5a8af8178eb795c1ac145672c77fa926015e82ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X/9ZP1AB+zMCECfNnF1jUH0VmLxwQp+Bn8wgef4y1+LujfiWLoU6SnjfRkrMXohMORa4frP5DASDSxPuNXLkDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T18:09:28.627117Z","bundle_sha256":"02fabd3659529d6e051a89dadbd2ce50926d1cf774460049f5405e82961bc124"}}