{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q3U2XVDPLIJCOWOEOYROPJPHFK","short_pith_number":"pith:Q3U2XVDP","canonical_record":{"source":{"id":"1803.07974","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-21T15:48:12Z","cross_cats_sorted":["cs.SC","math.NA"],"title_canon_sha256":"04535db3965030d537c30b26534b5c8e4cf4f45264a1edf38cdb248b35d0e70e","abstract_canon_sha256":"0039a15bbd2c2d991809e6be0f55b77f1885b609b42e50270a13c66c2e4e2425"},"schema_version":"1.0"},"canonical_sha256":"86e9abd46f5a122759c47622e7a5e72aa05d14dfe466bea7d2177d84e4b29064","source":{"kind":"arxiv","id":"1803.07974","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07974","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07974v3","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07974","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"pith_short_12","alias_value":"Q3U2XVDPLIJC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q3U2XVDPLIJCOWOE","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q3U2XVDP","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q3U2XVDPLIJCOWOEOYROPJPHFK","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07974","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-21T15:48:12Z","cross_cats_sorted":["cs.SC","math.NA"],"title_canon_sha256":"04535db3965030d537c30b26534b5c8e4cf4f45264a1edf38cdb248b35d0e70e","abstract_canon_sha256":"0039a15bbd2c2d991809e6be0f55b77f1885b609b42e50270a13c66c2e4e2425"},"schema_version":"1.0"},"canonical_sha256":"86e9abd46f5a122759c47622e7a5e72aa05d14dfe466bea7d2177d84e4b29064","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:52.887174Z","signature_b64":"QRhe8hxDw00xE5+COAoMcf9J/CfyllYSCuhhvW913MOkcYIUWscWxHH2CC+g1X3o2KmG59epFHZKm67CQ/ndAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86e9abd46f5a122759c47622e7a5e72aa05d14dfe466bea7d2177d84e4b29064","last_reissued_at":"2026-05-17T23:58:52.886739Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:52.886739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07974","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1WpiC6KjWq9Ib9FY50Di3LjGq0VenDhic3bNlksN6Nx7V098M4SKFRyDxirBKUJYmw9TnhpCit8P0lbvGu9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T22:26:26.109109Z"},"content_sha256":"f20b20981bd564007fa59064ff890f63fd1e7a69f8e78e08f53b368f22413a8e","schema_version":"1.0","event_id":"sha256:f20b20981bd564007fa59064ff890f63fd1e7a69f8e78e08f53b368f22413a8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q3U2XVDPLIJCOWOEOYROPJPHFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NA"],"primary_cat":"math.AG","authors_text":"Bernard Mourrain (AROMATH), Marc Van Barel, Simon Telen","submitted_at":"2018-03-21T15:48:12Z","abstract_excerpt":"We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem. The framework presented in Telen et al. (2018) uses truncated normal forms (TNFs) to compute the algebra structure of R/I and the solutions of I. This framework allows for the use of much more general bases than the standard monomials for R/I. This is exploited in this paper to introduce the use of two special (nonmonomial) types of basis functions with nic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07974","kind":"arxiv","version":3},"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":"2026-05-17T23:58:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5vLcwYesdm1fO5b8intygEBkzcJuklWs/WhvlYhphW4Z6Yo7w0utgTn6/uS1wwVjSqNIcEOG5ygGA6X6EEjTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T22:26:26.109707Z"},"content_sha256":"52503147ab0bd51c71ba54d0b55a9935d47832b44679746ab9464d129d82f863","schema_version":"1.0","event_id":"sha256:52503147ab0bd51c71ba54d0b55a9935d47832b44679746ab9464d129d82f863"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3U2XVDPLIJCOWOEOYROPJPHFK/bundle.json","state_url":"https://pith.science/pith/Q3U2XVDPLIJCOWOEOYROPJPHFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3U2XVDPLIJCOWOEOYROPJPHFK/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":"2026-05-21T22:26:26Z","links":{"resolver":"https://pith.science/pith/Q3U2XVDPLIJCOWOEOYROPJPHFK","bundle":"https://pith.science/pith/Q3U2XVDPLIJCOWOEOYROPJPHFK/bundle.json","state":"https://pith.science/pith/Q3U2XVDPLIJCOWOEOYROPJPHFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3U2XVDPLIJCOWOEOYROPJPHFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q3U2XVDPLIJCOWOEOYROPJPHFK","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":"0039a15bbd2c2d991809e6be0f55b77f1885b609b42e50270a13c66c2e4e2425","cross_cats_sorted":["cs.SC","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-21T15:48:12Z","title_canon_sha256":"04535db3965030d537c30b26534b5c8e4cf4f45264a1edf38cdb248b35d0e70e"},"schema_version":"1.0","source":{"id":"1803.07974","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07974","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07974v3","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07974","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"pith_short_12","alias_value":"Q3U2XVDPLIJC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q3U2XVDPLIJCOWOE","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q3U2XVDP","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:52503147ab0bd51c71ba54d0b55a9935d47832b44679746ab9464d129d82f863","target":"graph","created_at":"2026-05-17T23:58:52Z","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 the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem. The framework presented in Telen et al. (2018) uses truncated normal forms (TNFs) to compute the algebra structure of R/I and the solutions of I. This framework allows for the use of much more general bases than the standard monomials for R/I. This is exploited in this paper to introduce the use of two special (nonmonomial) types of basis functions with nic","authors_text":"Bernard Mourrain (AROMATH), Marc Van Barel, Simon Telen","cross_cats":["cs.SC","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-21T15:48:12Z","title":"Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07974","kind":"arxiv","version":3},"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:f20b20981bd564007fa59064ff890f63fd1e7a69f8e78e08f53b368f22413a8e","target":"record","created_at":"2026-05-17T23:58:52Z","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":"0039a15bbd2c2d991809e6be0f55b77f1885b609b42e50270a13c66c2e4e2425","cross_cats_sorted":["cs.SC","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-21T15:48:12Z","title_canon_sha256":"04535db3965030d537c30b26534b5c8e4cf4f45264a1edf38cdb248b35d0e70e"},"schema_version":"1.0","source":{"id":"1803.07974","kind":"arxiv","version":3}},"canonical_sha256":"86e9abd46f5a122759c47622e7a5e72aa05d14dfe466bea7d2177d84e4b29064","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86e9abd46f5a122759c47622e7a5e72aa05d14dfe466bea7d2177d84e4b29064","first_computed_at":"2026-05-17T23:58:52.886739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:52.886739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QRhe8hxDw00xE5+COAoMcf9J/CfyllYSCuhhvW913MOkcYIUWscWxHH2CC+g1X3o2KmG59epFHZKm67CQ/ndAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:52.887174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07974","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f20b20981bd564007fa59064ff890f63fd1e7a69f8e78e08f53b368f22413a8e","sha256:52503147ab0bd51c71ba54d0b55a9935d47832b44679746ab9464d129d82f863"],"state_sha256":"f91f648b0052a4fede41ef1b940a7a2e0c74189806c4748d7e6f2da616953c4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WK7QaUoZJK/qfQrgcRIx+YeHTnS0kZLNtlTys0LeE0oAQupFwqyerdCKMkyYh+XN9JA3l0PsOGPe+lWbCyKlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T22:26:26.113473Z","bundle_sha256":"7165f797cc588cf37ff0592a6e8be67e81a06fd2ffd5b670ccf279cd2e92cfc1"}}