{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:HR5BBVJBMUJ27AMKFWYBVOTCO2","short_pith_number":"pith:HR5BBVJB","canonical_record":{"source":{"id":"alg-geom/9609004","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1996-09-06T01:27:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"13f1854cea4083bcc7c50e62c1335a974ff02dea6988a5323f8fa1032957a913","abstract_canon_sha256":"46925997b3a29ea654975465e80d2aa42a60c513c9c30244404c07e932f726c6"},"schema_version":"1.0"},"canonical_sha256":"3c7a10d5216513af818a2db01aba62768ce1f61065345da0c0e5c934e1d055f0","source":{"kind":"arxiv","id":"alg-geom/9609004","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9609004","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9609004v1","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9609004","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"pith_short_12","alias_value":"HR5BBVJBMUJ2","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"pith_short_16","alias_value":"HR5BBVJBMUJ27AMK","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"pith_short_8","alias_value":"HR5BBVJB","created_at":"2026-07-04T15:08:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:HR5BBVJBMUJ27AMKFWYBVOTCO2","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9609004","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1996-09-06T01:27:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"13f1854cea4083bcc7c50e62c1335a974ff02dea6988a5323f8fa1032957a913","abstract_canon_sha256":"46925997b3a29ea654975465e80d2aa42a60c513c9c30244404c07e932f726c6"},"schema_version":"1.0"},"canonical_sha256":"3c7a10d5216513af818a2db01aba62768ce1f61065345da0c0e5c934e1d055f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:06.895854Z","signature_b64":"Gqbh5gY5JVuAMFXdPL44SanmjXDGqoPghUh3pv/APegZLk41WbYUqNJP5F2NLMMg3+nb8plnlI3WzhqXYeeYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c7a10d5216513af818a2db01aba62768ce1f61065345da0c0e5c934e1d055f0","last_reissued_at":"2026-07-04T15:08:06.895465Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:06.895465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9609004","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":"2026-07-04T15:08:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CqlGAVXokX6Ou5K+iDNsZkwVhrPYY4Zdp30AvOBHulZRVBZ4zSe/cHtxA1IZLJKRkJ6bZOTGcSRRR2SGpVQ/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:43:42.969016Z"},"content_sha256":"12d499fa4b8f1c624ed6d67f38a1a7ed1abe1ebcf8d5ff8d25d162c7039fffa7","schema_version":"1.0","event_id":"sha256:12d499fa4b8f1c624ed6d67f38a1a7ed1abe1ebcf8d5ff8d25d162c7039fffa7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:HR5BBVJBMUJ27AMKFWYBVOTCO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"B. Bank, G.M. Mbakop, J. Heintz, M. Giusti","submitted_at":"1996-09-06T01:27:49Z","abstract_excerpt":"In this paper we apply for the first time a new method for multivariate equation solving which was developed in \\cite{gh1}, \\cite{gh2}, \\cite{gh3} for complex root determination to the {\\em real} case. Our main result concerns the problem of finding at least one representative point for each connected component of a real compact and smooth hypersurface. The basic algorithm of \\cite{gh1}, \\cite{gh2}, \\cite{gh3} yields a new method for symbolically solving zero-dimensional polynomial equation systems over the complex numbers. One feature of central importance of this algorithm is the use of a pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9609004","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/alg-geom/9609004/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:08:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f7yIZia3t7jDJ1tpN7YFFd3q4lHqGBkEXaSw/0ck6RFEomKznnC7woNIbnJ9HqFnqL9yRIJr9Fd8TqoqlAxsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:43:42.969514Z"},"content_sha256":"d811675a02dbfc56351d96202f6eba3a8d83e5272220d50d245b7b752894ca1d","schema_version":"1.0","event_id":"sha256:d811675a02dbfc56351d96202f6eba3a8d83e5272220d50d245b7b752894ca1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HR5BBVJBMUJ27AMKFWYBVOTCO2/bundle.json","state_url":"https://pith.science/pith/HR5BBVJBMUJ27AMKFWYBVOTCO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HR5BBVJBMUJ27AMKFWYBVOTCO2/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":"2026-08-06T06:43:42Z","links":{"resolver":"https://pith.science/pith/HR5BBVJBMUJ27AMKFWYBVOTCO2","bundle":"https://pith.science/pith/HR5BBVJBMUJ27AMKFWYBVOTCO2/bundle.json","state":"https://pith.science/pith/HR5BBVJBMUJ27AMKFWYBVOTCO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HR5BBVJBMUJ27AMKFWYBVOTCO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:HR5BBVJBMUJ27AMKFWYBVOTCO2","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":"46925997b3a29ea654975465e80d2aa42a60c513c9c30244404c07e932f726c6","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-09-06T01:27:49Z","title_canon_sha256":"13f1854cea4083bcc7c50e62c1335a974ff02dea6988a5323f8fa1032957a913"},"schema_version":"1.0","source":{"id":"alg-geom/9609004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9609004","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9609004v1","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9609004","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"pith_short_12","alias_value":"HR5BBVJBMUJ2","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"pith_short_16","alias_value":"HR5BBVJBMUJ27AMK","created_at":"2026-07-04T15:08:06Z"},{"alias_kind":"pith_short_8","alias_value":"HR5BBVJB","created_at":"2026-07-04T15:08:06Z"}],"graph_snapshots":[{"event_id":"sha256:d811675a02dbfc56351d96202f6eba3a8d83e5272220d50d245b7b752894ca1d","target":"graph","created_at":"2026-07-04T15:08:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/alg-geom/9609004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we apply for the first time a new method for multivariate equation solving which was developed in \\cite{gh1}, \\cite{gh2}, \\cite{gh3} for complex root determination to the {\\em real} case. Our main result concerns the problem of finding at least one representative point for each connected component of a real compact and smooth hypersurface. The basic algorithm of \\cite{gh1}, \\cite{gh2}, \\cite{gh3} yields a new method for symbolically solving zero-dimensional polynomial equation systems over the complex numbers. One feature of central importance of this algorithm is the use of a pr","authors_text":"B. Bank, G.M. Mbakop, J. Heintz, M. Giusti","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1996-09-06T01:27:49Z","title":"Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9609004","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":"sha256:12d499fa4b8f1c624ed6d67f38a1a7ed1abe1ebcf8d5ff8d25d162c7039fffa7","target":"record","created_at":"2026-07-04T15:08:06Z","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":"46925997b3a29ea654975465e80d2aa42a60c513c9c30244404c07e932f726c6","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-09-06T01:27:49Z","title_canon_sha256":"13f1854cea4083bcc7c50e62c1335a974ff02dea6988a5323f8fa1032957a913"},"schema_version":"1.0","source":{"id":"alg-geom/9609004","kind":"arxiv","version":1}},"canonical_sha256":"3c7a10d5216513af818a2db01aba62768ce1f61065345da0c0e5c934e1d055f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c7a10d5216513af818a2db01aba62768ce1f61065345da0c0e5c934e1d055f0","first_computed_at":"2026-07-04T15:08:06.895465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:06.895465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gqbh5gY5JVuAMFXdPL44SanmjXDGqoPghUh3pv/APegZLk41WbYUqNJP5F2NLMMg3+nb8plnlI3WzhqXYeeYBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:06.895854Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9609004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12d499fa4b8f1c624ed6d67f38a1a7ed1abe1ebcf8d5ff8d25d162c7039fffa7","sha256:d811675a02dbfc56351d96202f6eba3a8d83e5272220d50d245b7b752894ca1d"],"state_sha256":"89f3876a936d9e1b0f498d03b72ee6a0197685e09311d7d228403eeca1f19928"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WnuPH+T6LcyOo7hsHXGvvp0G0n3mrr2U2mXUPRqkNbPH2PLPi3nhRmGMvfxhQBEjJgTwK72UYogOYd0aZ+MTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T06:43:42.972807Z","bundle_sha256":"f90a97472d676afa827991cdccaef96f4ad21ab4982917af161949f30199a6c9"}}