{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:XVB3SVMWZLZ545WKCVH4L2KOBD","short_pith_number":"pith:XVB3SVMW","canonical_record":{"source":{"id":"math/9809060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-09-11T00:50:40Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fd5f08658890d88bc8be4902d2bfc9738959f1dfcd52de7df2aecd13eaf42604","abstract_canon_sha256":"fd748e19b884955b8d006cca8267edf9d598274d3255fd6add33cd507daa82a1"},"schema_version":"1.0"},"canonical_sha256":"bd43b95596caf3de76ca154fc5e94e08ecac3f56d8fefbecb3b9a44e171ec06f","source":{"kind":"arxiv","id":"math/9809060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9809060","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/9809060v1","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9809060","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"XVB3SVMWZLZ5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"XVB3SVMWZLZ545WK","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"XVB3SVMW","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:XVB3SVMWZLZ545WKCVH4L2KOBD","target":"record","payload":{"canonical_record":{"source":{"id":"math/9809060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-09-11T00:50:40Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fd5f08658890d88bc8be4902d2bfc9738959f1dfcd52de7df2aecd13eaf42604","abstract_canon_sha256":"fd748e19b884955b8d006cca8267edf9d598274d3255fd6add33cd507daa82a1"},"schema_version":"1.0"},"canonical_sha256":"bd43b95596caf3de76ca154fc5e94e08ecac3f56d8fefbecb3b9a44e171ec06f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:15.437272Z","signature_b64":"3rVmgcd3q15/YB3SOprmlWhqPI19co9dif0VmqTDS7vvLH1JGVDu/vXYoFzrnrPSKDGlvjM7lWBXF85QmZPKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd43b95596caf3de76ca154fc5e94e08ecac3f56d8fefbecb3b9a44e171ec06f","last_reissued_at":"2026-05-18T04:02:15.436587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:15.436587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9809060","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":"2026-05-18T04:02:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrbOVeWwbv0r3MaflEMdaO5sji9VZoPpFwR90dYHbikTHepUOcWcEE0qcDHajpgA+nmGSbIWURckgRWZG/avAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:47:23.616467Z"},"content_sha256":"0eb51086bf65311f8c9bfa620ab117563bcc6a2b6df2461e708be4591c00efda","schema_version":"1.0","event_id":"sha256:0eb51086bf65311f8c9bfa620ab117563bcc6a2b6df2461e708be4591c00efda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:XVB3SVMWZLZ545WKCVH4L2KOBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of real algebraic sets of dimension 4: necessary conditions","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Adam Parusinski, Clint McCrory","submitted_at":"1998-09-11T00:50:40Z","abstract_excerpt":"Operators on the ring of algebraically constructible functions are used to compute local obstructions for a four-dimensional semialgebraic set to be homeomorphic to a real algebraic set. The link operator and arithmetic operators yield $2^{43}-43$ independent characteristic numbers mod 2, which generalize the Akbulut-King numbers in dimension three."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9809060","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":"2026-05-18T04:02:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMDvTzSkp/qNZzHcE2ABAPyxtcqg4yWN5DnKk8waqlGkHq2/Blz9wqNQrKVvQ8d90Vyq6uYMlgHwgce7JqkrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:47:23.616811Z"},"content_sha256":"62d07140a41de96458fc4c26728a779e6df6b247afb7bb45a4ce8a392bed9c0d","schema_version":"1.0","event_id":"sha256:62d07140a41de96458fc4c26728a779e6df6b247afb7bb45a4ce8a392bed9c0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVB3SVMWZLZ545WKCVH4L2KOBD/bundle.json","state_url":"https://pith.science/pith/XVB3SVMWZLZ545WKCVH4L2KOBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVB3SVMWZLZ545WKCVH4L2KOBD/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":"2026-06-09T13:47:23Z","links":{"resolver":"https://pith.science/pith/XVB3SVMWZLZ545WKCVH4L2KOBD","bundle":"https://pith.science/pith/XVB3SVMWZLZ545WKCVH4L2KOBD/bundle.json","state":"https://pith.science/pith/XVB3SVMWZLZ545WKCVH4L2KOBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVB3SVMWZLZ545WKCVH4L2KOBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:XVB3SVMWZLZ545WKCVH4L2KOBD","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":"fd748e19b884955b8d006cca8267edf9d598274d3255fd6add33cd507daa82a1","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AG","submitted_at":"1998-09-11T00:50:40Z","title_canon_sha256":"fd5f08658890d88bc8be4902d2bfc9738959f1dfcd52de7df2aecd13eaf42604"},"schema_version":"1.0","source":{"id":"math/9809060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9809060","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/9809060v1","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9809060","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"XVB3SVMWZLZ5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"XVB3SVMWZLZ545WK","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"XVB3SVMW","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:62d07140a41de96458fc4c26728a779e6df6b247afb7bb45a4ce8a392bed9c0d","target":"graph","created_at":"2026-05-18T04:02:15Z","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":"Operators on the ring of algebraically constructible functions are used to compute local obstructions for a four-dimensional semialgebraic set to be homeomorphic to a real algebraic set. The link operator and arithmetic operators yield $2^{43}-43$ independent characteristic numbers mod 2, which generalize the Akbulut-King numbers in dimension three.","authors_text":"Adam Parusinski, Clint McCrory","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1998-09-11T00:50:40Z","title":"Topology of real algebraic sets of dimension 4: necessary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9809060","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":"sha256:0eb51086bf65311f8c9bfa620ab117563bcc6a2b6df2461e708be4591c00efda","target":"record","created_at":"2026-05-18T04:02:15Z","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":"fd748e19b884955b8d006cca8267edf9d598274d3255fd6add33cd507daa82a1","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AG","submitted_at":"1998-09-11T00:50:40Z","title_canon_sha256":"fd5f08658890d88bc8be4902d2bfc9738959f1dfcd52de7df2aecd13eaf42604"},"schema_version":"1.0","source":{"id":"math/9809060","kind":"arxiv","version":1}},"canonical_sha256":"bd43b95596caf3de76ca154fc5e94e08ecac3f56d8fefbecb3b9a44e171ec06f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd43b95596caf3de76ca154fc5e94e08ecac3f56d8fefbecb3b9a44e171ec06f","first_computed_at":"2026-05-18T04:02:15.436587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:15.436587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rVmgcd3q15/YB3SOprmlWhqPI19co9dif0VmqTDS7vvLH1JGVDu/vXYoFzrnrPSKDGlvjM7lWBXF85QmZPKBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:15.437272Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9809060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eb51086bf65311f8c9bfa620ab117563bcc6a2b6df2461e708be4591c00efda","sha256:62d07140a41de96458fc4c26728a779e6df6b247afb7bb45a4ce8a392bed9c0d"],"state_sha256":"8b298eb180ae89dc0fbd52a2ebac7be091ca69063f36f193653db0ca2baadf05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LtZjV7aoXHnI7IB0jcKOFqGZwIfGoAaXozR1ZYI+CrshqNuUAdRBmbQGfqtduYDSQHFOFONPmGWMCQtJC+UdDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:47:23.618875Z","bundle_sha256":"3f9f70fa480ecbc3363963e716f58c994f2ea9154b4594b86e69963a264912ca"}}