{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VV3NZZD2INDZGOI4SOJOYNINTA","short_pith_number":"pith:VV3NZZD2","canonical_record":{"source":{"id":"1501.06563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-26T20:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"63fe01bc9b917cf79bc7ee92df5db49cfbbed6cb6db9e32b2275bae78053e182","abstract_canon_sha256":"b397c3f0bd9cc0ddd2a9b725a60c608c4e0893eeb36838dffc38f9f61851b83f"},"schema_version":"1.0"},"canonical_sha256":"ad76dce47a434793391c9392ec350d983db4fe42c5addc5fd2517c802b22b486","source":{"kind":"arxiv","id":"1501.06563","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06563","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06563v2","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06563","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"VV3NZZD2INDZ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VV3NZZD2INDZGOI4","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VV3NZZD2","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VV3NZZD2INDZGOI4SOJOYNINTA","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-26T20:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"63fe01bc9b917cf79bc7ee92df5db49cfbbed6cb6db9e32b2275bae78053e182","abstract_canon_sha256":"b397c3f0bd9cc0ddd2a9b725a60c608c4e0893eeb36838dffc38f9f61851b83f"},"schema_version":"1.0"},"canonical_sha256":"ad76dce47a434793391c9392ec350d983db4fe42c5addc5fd2517c802b22b486","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:31.539017Z","signature_b64":"jhz6AZb/F2s8XyzuJywzk1VKldeivq/xfyZWr95EjuoTRV1Q37m6qMR8/ElkdlQIlVLDjawqdve+XrDrPkuJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad76dce47a434793391c9392ec350d983db4fe42c5addc5fd2517c802b22b486","last_reissued_at":"2026-05-18T02:27:31.538337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:31.538337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06563","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":"2026-05-18T02:27:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3xm86v35pOEc9YcC8KlrRNjRbmVKntSP6xBs4PVbMsEdJoQihrpj+pgsuUIZ6llEEkV8co7gWpt6VoOlC2INAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T08:15:08.389797Z"},"content_sha256":"3c6e1922906b3007d5a6b6d1889ee9ee8e60d30272f7763ceade7674aa9f3028","schema_version":"1.0","event_id":"sha256:3c6e1922906b3007d5a6b6d1889ee9ee8e60d30272f7763ceade7674aa9f3028"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VV3NZZD2INDZGOI4SOJOYNINTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Lazard's Valuation and CAD Construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hoon Hong, Scott McCallum","submitted_at":"2015-01-26T20:57:00Z","abstract_excerpt":"In 1990 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results for the improved projection was subsequently noticed. In this report we study a more limited but rigorous concept of Lazard's valuation: namely, we study Lazard's valuation of a multivariate polynomial at a point. We prove some basic properties of the limited Lazard valuation and identify some relationships between valuation-invariance and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06563","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":"2026-05-18T02:27:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R9jzvupws/OxHFbZYqwQ4Ax7WNGZgeLS5cvj6D1ByROTDzfFPp/yNx5+lJqB7LvNuRYxq77cB7DO+vQL+0xfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T08:15:08.390621Z"},"content_sha256":"561e08c80a2b41873a58965c033886a59665351a446b2931ccc29393ec557008","schema_version":"1.0","event_id":"sha256:561e08c80a2b41873a58965c033886a59665351a446b2931ccc29393ec557008"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VV3NZZD2INDZGOI4SOJOYNINTA/bundle.json","state_url":"https://pith.science/pith/VV3NZZD2INDZGOI4SOJOYNINTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VV3NZZD2INDZGOI4SOJOYNINTA/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":"2026-05-19T08:15:08Z","links":{"resolver":"https://pith.science/pith/VV3NZZD2INDZGOI4SOJOYNINTA","bundle":"https://pith.science/pith/VV3NZZD2INDZGOI4SOJOYNINTA/bundle.json","state":"https://pith.science/pith/VV3NZZD2INDZGOI4SOJOYNINTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VV3NZZD2INDZGOI4SOJOYNINTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VV3NZZD2INDZGOI4SOJOYNINTA","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":"b397c3f0bd9cc0ddd2a9b725a60c608c4e0893eeb36838dffc38f9f61851b83f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-26T20:57:00Z","title_canon_sha256":"63fe01bc9b917cf79bc7ee92df5db49cfbbed6cb6db9e32b2275bae78053e182"},"schema_version":"1.0","source":{"id":"1501.06563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06563","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06563v2","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06563","created_at":"2026-05-18T02:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"VV3NZZD2INDZ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VV3NZZD2INDZGOI4","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VV3NZZD2","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:561e08c80a2b41873a58965c033886a59665351a446b2931ccc29393ec557008","target":"graph","created_at":"2026-05-18T02:27:31Z","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":"In 1990 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results for the improved projection was subsequently noticed. In this report we study a more limited but rigorous concept of Lazard's valuation: namely, we study Lazard's valuation of a multivariate polynomial at a point. We prove some basic properties of the limited Lazard valuation and identify some relationships between valuation-invariance and ","authors_text":"Hoon Hong, Scott McCallum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-26T20:57:00Z","title":"On Lazard's Valuation and CAD Construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06563","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":"sha256:3c6e1922906b3007d5a6b6d1889ee9ee8e60d30272f7763ceade7674aa9f3028","target":"record","created_at":"2026-05-18T02:27:31Z","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":"b397c3f0bd9cc0ddd2a9b725a60c608c4e0893eeb36838dffc38f9f61851b83f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-26T20:57:00Z","title_canon_sha256":"63fe01bc9b917cf79bc7ee92df5db49cfbbed6cb6db9e32b2275bae78053e182"},"schema_version":"1.0","source":{"id":"1501.06563","kind":"arxiv","version":2}},"canonical_sha256":"ad76dce47a434793391c9392ec350d983db4fe42c5addc5fd2517c802b22b486","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad76dce47a434793391c9392ec350d983db4fe42c5addc5fd2517c802b22b486","first_computed_at":"2026-05-18T02:27:31.538337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:31.538337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jhz6AZb/F2s8XyzuJywzk1VKldeivq/xfyZWr95EjuoTRV1Q37m6qMR8/ElkdlQIlVLDjawqdve+XrDrPkuJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:31.539017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c6e1922906b3007d5a6b6d1889ee9ee8e60d30272f7763ceade7674aa9f3028","sha256:561e08c80a2b41873a58965c033886a59665351a446b2931ccc29393ec557008"],"state_sha256":"090f398d758b622d3c4deb2030d243a794169a97018d7ffddb4405e5b11c5474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7JrkpRfawFclqmDnu8lHRPGcyhD0kGtdGkehWOer2qfECdMpUb6Y75oRPnLQ5IAnceRSg0HvzgIaKvcFzjgTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T08:15:08.393687Z","bundle_sha256":"3c29b1caa5f140d5fa2f80c6b602afdb62c2ff425c92c6e73d82ae9380d79ea1"}}