{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HTCYWPCXACSQR5W3PT3CWFRCME","short_pith_number":"pith:HTCYWPCX","canonical_record":{"source":{"id":"1407.6132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-23T08:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"67587524c56561f856905d333dd073e26d248215094d31f7578f9199b014e50a","abstract_canon_sha256":"9c58ab8cba25d44962ce3f5bc41bbeb727b32ea8e0eb199aac734f2f47ac0a0d"},"schema_version":"1.0"},"canonical_sha256":"3cc58b3c5700a508f6db7cf62b162261085df2c99da92e216e158dc711013d76","source":{"kind":"arxiv","id":"1407.6132","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6132","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6132v2","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6132","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"HTCYWPCXACSQ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HTCYWPCXACSQR5W3","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HTCYWPCX","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HTCYWPCXACSQR5W3PT3CWFRCME","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-23T08:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"67587524c56561f856905d333dd073e26d248215094d31f7578f9199b014e50a","abstract_canon_sha256":"9c58ab8cba25d44962ce3f5bc41bbeb727b32ea8e0eb199aac734f2f47ac0a0d"},"schema_version":"1.0"},"canonical_sha256":"3cc58b3c5700a508f6db7cf62b162261085df2c99da92e216e158dc711013d76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:53.937055Z","signature_b64":"t+DV+SCaCYBltQ/ECeg3jGRdkHD6EmYnuYhHQi9eWq/VDYt53cyWo79ThZ27bTGtxdEGnloOfEA9LEKV1eI/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cc58b3c5700a508f6db7cf62b162261085df2c99da92e216e158dc711013d76","last_reissued_at":"2026-05-18T02:28:53.936713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:53.936713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6132","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":"2026-05-18T02:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSrLHEt3s3bnNPo7wa+ahargjPRbrBo8JEkFKNZxH1PidVeoBjfrg8EiRp6zE/KXHxVg+O0Uv8OBUvdQ1SruAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:53:17.708109Z"},"content_sha256":"b313ea51adc0b79e1f55a31f59dadeb0af7e4c69e5fa80e37099129b177b1caa","schema_version":"1.0","event_id":"sha256:b313ea51adc0b79e1f55a31f59dadeb0af7e4c69e5fa80e37099129b177b1caa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HTCYWPCXACSQR5W3PT3CWFRCME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Offset Filtration of Convex Objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Dan Halperin, Doron Shaharabani, Michael Kerber","submitted_at":"2014-07-23T08:30:02Z","abstract_excerpt":"We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based on the Voronoi partition with respect to the given convex objects. We prove that, in two and three dimensions, the size of the filtration is proportional to the size of the Voronoi diagram. Our algorithm runs in $\\Theta(n \\log{n})$ in the $2$-dimensional case and in expected time $O(n^{3 + \\epsilon})$, for any $\\epsilon > 0$, in the $3$-dimensional case. Our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6132","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":"2026-05-18T02:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+lEvvQ9zTOK6KU6rdMXS8L1vEL6w2vDUQa/yf/OngwkR6fP0nGpIHMAslVQ32XMbOzGF7st6nD6xMQQtwQUUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:53:17.708478Z"},"content_sha256":"4a1c06cd7e20f190ded1548dd449d198988197c6e4da9ba1f83df93ca355ea5f","schema_version":"1.0","event_id":"sha256:4a1c06cd7e20f190ded1548dd449d198988197c6e4da9ba1f83df93ca355ea5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTCYWPCXACSQR5W3PT3CWFRCME/bundle.json","state_url":"https://pith.science/pith/HTCYWPCXACSQR5W3PT3CWFRCME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTCYWPCXACSQR5W3PT3CWFRCME/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":"2026-06-04T03:53:17Z","links":{"resolver":"https://pith.science/pith/HTCYWPCXACSQR5W3PT3CWFRCME","bundle":"https://pith.science/pith/HTCYWPCXACSQR5W3PT3CWFRCME/bundle.json","state":"https://pith.science/pith/HTCYWPCXACSQR5W3PT3CWFRCME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTCYWPCXACSQR5W3PT3CWFRCME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HTCYWPCXACSQR5W3PT3CWFRCME","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":"9c58ab8cba25d44962ce3f5bc41bbeb727b32ea8e0eb199aac734f2f47ac0a0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-23T08:30:02Z","title_canon_sha256":"67587524c56561f856905d333dd073e26d248215094d31f7578f9199b014e50a"},"schema_version":"1.0","source":{"id":"1407.6132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6132","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6132v2","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6132","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"HTCYWPCXACSQ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HTCYWPCXACSQR5W3","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HTCYWPCX","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:4a1c06cd7e20f190ded1548dd449d198988197c6e4da9ba1f83df93ca355ea5f","target":"graph","created_at":"2026-05-18T02:28:53Z","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 consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based on the Voronoi partition with respect to the given convex objects. We prove that, in two and three dimensions, the size of the filtration is proportional to the size of the Voronoi diagram. Our algorithm runs in $\\Theta(n \\log{n})$ in the $2$-dimensional case and in expected time $O(n^{3 + \\epsilon})$, for any $\\epsilon > 0$, in the $3$-dimensional case. Our ","authors_text":"Dan Halperin, Doron Shaharabani, Michael Kerber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-23T08:30:02Z","title":"The Offset Filtration of Convex Objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6132","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:b313ea51adc0b79e1f55a31f59dadeb0af7e4c69e5fa80e37099129b177b1caa","target":"record","created_at":"2026-05-18T02:28:53Z","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":"9c58ab8cba25d44962ce3f5bc41bbeb727b32ea8e0eb199aac734f2f47ac0a0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-23T08:30:02Z","title_canon_sha256":"67587524c56561f856905d333dd073e26d248215094d31f7578f9199b014e50a"},"schema_version":"1.0","source":{"id":"1407.6132","kind":"arxiv","version":2}},"canonical_sha256":"3cc58b3c5700a508f6db7cf62b162261085df2c99da92e216e158dc711013d76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cc58b3c5700a508f6db7cf62b162261085df2c99da92e216e158dc711013d76","first_computed_at":"2026-05-18T02:28:53.936713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:53.936713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+DV+SCaCYBltQ/ECeg3jGRdkHD6EmYnuYhHQi9eWq/VDYt53cyWo79ThZ27bTGtxdEGnloOfEA9LEKV1eI/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:53.937055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b313ea51adc0b79e1f55a31f59dadeb0af7e4c69e5fa80e37099129b177b1caa","sha256:4a1c06cd7e20f190ded1548dd449d198988197c6e4da9ba1f83df93ca355ea5f"],"state_sha256":"52cbdf20b71015d7aed893f47b507f649f8a961efcd7226d7a0525aef1b59e1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dHiGucrdEtJ9NRuPms3nsjB0oZJMHOGz/+ZySIwovPwZ34jx5xv3CFlm2LV0y348idJX2V93jYytwoOwTyFLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:53:17.710479Z","bundle_sha256":"78f649e30a77b3866d142e8aa951b9a71c58949118021c355f92b0c1de6a856c"}}