{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E35FDNS4FNX46JKSTME5AI6EGG","short_pith_number":"pith:E35FDNS4","canonical_record":{"source":{"id":"1704.06856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-04-22T23:26:57Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"b7235592c1369d197cb100324c8ef57b5f65664790b410bf4e7f18cac59db42b","abstract_canon_sha256":"0c72a7b1e259a37b80560856e84eb24710184f9faf9a78002090bff8f4e9cf7d"},"schema_version":"1.0"},"canonical_sha256":"26fa51b65c2b6fcf25529b09d023c431abfd8636e96324bbc2eb7ca0c063a110","source":{"kind":"arxiv","id":"1704.06856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06856","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06856v1","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06856","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"E35FDNS4FNX4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E35FDNS4FNX46JKS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E35FDNS4","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E35FDNS4FNX46JKSTME5AI6EGG","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-04-22T23:26:57Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"b7235592c1369d197cb100324c8ef57b5f65664790b410bf4e7f18cac59db42b","abstract_canon_sha256":"0c72a7b1e259a37b80560856e84eb24710184f9faf9a78002090bff8f4e9cf7d"},"schema_version":"1.0"},"canonical_sha256":"26fa51b65c2b6fcf25529b09d023c431abfd8636e96324bbc2eb7ca0c063a110","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:55.575123Z","signature_b64":"8cjgQx6ZSfbrZMuW9/iz0MszLFtWzWGNCj0aH5r3ntpjKdN2B2hzCpyRkulz/BGgPHyQrVTgQXWpuLId4SqfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26fa51b65c2b6fcf25529b09d023c431abfd8636e96324bbc2eb7ca0c063a110","last_reissued_at":"2026-05-18T00:45:55.574667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:55.574667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06856","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":"2026-05-18T00:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+BL6UJsTmNAySTqCiaC6qJEPRZKLL8jKBoyDBmMF7u42JF6FK0g+fDFDRSRQpD+uNKKlkncv9JfSGIF6MkZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:33:20.957152Z"},"content_sha256":"a19492c929698862fbce1aa9819762ca091feaf571a641d3fb8f1ed8532bf2e2","schema_version":"1.0","event_id":"sha256:a19492c929698862fbce1aa9819762ca091feaf571a641d3fb8f1ed8532bf2e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E35FDNS4FNX46JKSTME5AI6EGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"CAD Adjacency Computation Using Validated Numerics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.SC","authors_text":"Adam Strzebonski","submitted_at":"2017-04-22T23:26:57Z","abstract_excerpt":"We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and topological properties e.g. homology groups. Other applications include visualization and path planning. Our algorithm determines cell adjacency information using validated numerical methods similar to those used in CAD construction, thus computing CAD with adjacency information in time comparable to that of computing CAD without adjacency information. We report "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06856","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":"2026-05-18T00:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QBOSuOjpaXFSr1375llzgvN+7JIOKUYKs1lBl0LTvwYOZ9HkJduLrvy++xDWtBQEcQcch0JTfubh/avs4KqpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:33:20.957888Z"},"content_sha256":"a532b0f76faeacd5baec0a0b4868efeba89fa384482db40eee0c4a6148b44d71","schema_version":"1.0","event_id":"sha256:a532b0f76faeacd5baec0a0b4868efeba89fa384482db40eee0c4a6148b44d71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E35FDNS4FNX46JKSTME5AI6EGG/bundle.json","state_url":"https://pith.science/pith/E35FDNS4FNX46JKSTME5AI6EGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E35FDNS4FNX46JKSTME5AI6EGG/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":"2026-06-09T08:33:20Z","links":{"resolver":"https://pith.science/pith/E35FDNS4FNX46JKSTME5AI6EGG","bundle":"https://pith.science/pith/E35FDNS4FNX46JKSTME5AI6EGG/bundle.json","state":"https://pith.science/pith/E35FDNS4FNX46JKSTME5AI6EGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E35FDNS4FNX46JKSTME5AI6EGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E35FDNS4FNX46JKSTME5AI6EGG","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":"0c72a7b1e259a37b80560856e84eb24710184f9faf9a78002090bff8f4e9cf7d","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-04-22T23:26:57Z","title_canon_sha256":"b7235592c1369d197cb100324c8ef57b5f65664790b410bf4e7f18cac59db42b"},"schema_version":"1.0","source":{"id":"1704.06856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06856","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06856v1","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06856","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"E35FDNS4FNX4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E35FDNS4FNX46JKS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E35FDNS4","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:a532b0f76faeacd5baec0a0b4868efeba89fa384482db40eee0c4a6148b44d71","target":"graph","created_at":"2026-05-18T00:45:55Z","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":"We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and topological properties e.g. homology groups. Other applications include visualization and path planning. Our algorithm determines cell adjacency information using validated numerical methods similar to those used in CAD construction, thus computing CAD with adjacency information in time comparable to that of computing CAD without adjacency information. We report ","authors_text":"Adam Strzebonski","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-04-22T23:26:57Z","title":"CAD Adjacency Computation Using Validated Numerics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06856","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:a19492c929698862fbce1aa9819762ca091feaf571a641d3fb8f1ed8532bf2e2","target":"record","created_at":"2026-05-18T00:45:55Z","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":"0c72a7b1e259a37b80560856e84eb24710184f9faf9a78002090bff8f4e9cf7d","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-04-22T23:26:57Z","title_canon_sha256":"b7235592c1369d197cb100324c8ef57b5f65664790b410bf4e7f18cac59db42b"},"schema_version":"1.0","source":{"id":"1704.06856","kind":"arxiv","version":1}},"canonical_sha256":"26fa51b65c2b6fcf25529b09d023c431abfd8636e96324bbc2eb7ca0c063a110","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26fa51b65c2b6fcf25529b09d023c431abfd8636e96324bbc2eb7ca0c063a110","first_computed_at":"2026-05-18T00:45:55.574667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:55.574667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8cjgQx6ZSfbrZMuW9/iz0MszLFtWzWGNCj0aH5r3ntpjKdN2B2hzCpyRkulz/BGgPHyQrVTgQXWpuLId4SqfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:55.575123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a19492c929698862fbce1aa9819762ca091feaf571a641d3fb8f1ed8532bf2e2","sha256:a532b0f76faeacd5baec0a0b4868efeba89fa384482db40eee0c4a6148b44d71"],"state_sha256":"ef263ffb7175cfb48b7950f70a7b8c193441722bdb4bcaa994fc39e4509881d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2l5ItvNGnkE3QylPfJ5F0LYxg7svVtBZQsjn/ejuNid+C20nR7TDFIxmdH2NnnBYmLqfQ9Edtgq5uWxgWVMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:33:20.961858Z","bundle_sha256":"59a0232232e72ac1ae513178b1ba4ff733aec878d0e3d6c57412effdd32efc62"}}