{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:KQM7A4PP4IAQ4MAU4XUIPQCKPI","short_pith_number":"pith:KQM7A4PP","canonical_record":{"source":{"id":"2101.00243","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2021-01-01T14:27:45Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"aaced50acafa916c04a0ec31598fb4a589969a5af38176c240955cf61bb7abbd","abstract_canon_sha256":"b837d2cee393387a38991efba2fc9ab81033cc7f1ba4cbf6059bc99c93d592e1"},"schema_version":"1.0"},"canonical_sha256":"5419f071efe2010e3014e5e887c04a7a093cc893acc8be5f51e05c3f3abe13cc","source":{"kind":"arxiv","id":"2101.00243","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.00243","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"arxiv_version","alias_value":"2101.00243v6","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.00243","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"pith_short_12","alias_value":"KQM7A4PP4IAQ","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"pith_short_16","alias_value":"KQM7A4PP4IAQ4MAU","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"pith_short_8","alias_value":"KQM7A4PP","created_at":"2026-07-05T07:29:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:KQM7A4PP4IAQ4MAU4XUIPQCKPI","target":"record","payload":{"canonical_record":{"source":{"id":"2101.00243","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2021-01-01T14:27:45Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"aaced50acafa916c04a0ec31598fb4a589969a5af38176c240955cf61bb7abbd","abstract_canon_sha256":"b837d2cee393387a38991efba2fc9ab81033cc7f1ba4cbf6059bc99c93d592e1"},"schema_version":"1.0"},"canonical_sha256":"5419f071efe2010e3014e5e887c04a7a093cc893acc8be5f51e05c3f3abe13cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:29:08.069376Z","signature_b64":"6HRDGdbCPSzwI+aQ9KOrxJPWZGE83xRKvSDUnNvUBinmagTCZBzyExyKOaSEGyBy7c2D6UpDIH77ci45nu9TCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5419f071efe2010e3014e5e887c04a7a093cc893acc8be5f51e05c3f3abe13cc","last_reissued_at":"2026-07-05T07:29:08.068866Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:29:08.068866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.00243","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:29:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ylA4cgWtp2slgI+rdqxWeGujMwc4byElVUQoLceIT+QtBGIv6C6UgMkpO95UC9pi2Fg+Igm8taRroUsHEvXvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T01:05:23.018846Z"},"content_sha256":"af842180bdf82bc78b98a92c76b980c4f611548fb9df45828696aa3861e76cdc","schema_version":"1.0","event_id":"sha256:af842180bdf82bc78b98a92c76b980c4f611548fb9df45828696aa3861e76cdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:KQM7A4PP4IAQ4MAU4XUIPQCKPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monomial-agnostic computation of vanishing ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.SC","authors_text":"Hiroshi Kera, Yoshihiko Hasegawa","submitted_at":"2021-01-01T14:27:45Z","abstract_excerpt":"In the last decade, the approximate basis computation of vanishing ideals has been studied extensively in computational algebra and data-driven applications such as machine learning. However, symbolic computation and the dependency on term order remain essential gaps between the two fields. In this study, we present the first $\\textit{monomial-agnostic}$ basis computation, which works fully numerically with proper normalization and without term order. This is realized by gradient normalization, a newly proposed data-dependent normalization that normalizes a polynomial with the magnitude of gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.00243","kind":"arxiv","version":6},"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/2101.00243/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":"2026-07-05T07:29:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7OIBdMw7buKc8my4l75KO98burR/WIj9sTvRuqhZOv3DDxz+M0liScF30N9lw8Aj7vJvfJIAMLu891QIMivBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T01:05:23.019387Z"},"content_sha256":"ccb1836d14fe43b085325916f5e62a269e58cddbe73fc107d9be72ce08c61215","schema_version":"1.0","event_id":"sha256:ccb1836d14fe43b085325916f5e62a269e58cddbe73fc107d9be72ce08c61215"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQM7A4PP4IAQ4MAU4XUIPQCKPI/bundle.json","state_url":"https://pith.science/pith/KQM7A4PP4IAQ4MAU4XUIPQCKPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQM7A4PP4IAQ4MAU4XUIPQCKPI/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":"2026-08-07T01:05:23Z","links":{"resolver":"https://pith.science/pith/KQM7A4PP4IAQ4MAU4XUIPQCKPI","bundle":"https://pith.science/pith/KQM7A4PP4IAQ4MAU4XUIPQCKPI/bundle.json","state":"https://pith.science/pith/KQM7A4PP4IAQ4MAU4XUIPQCKPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQM7A4PP4IAQ4MAU4XUIPQCKPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KQM7A4PP4IAQ4MAU4XUIPQCKPI","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":"b837d2cee393387a38991efba2fc9ab81033cc7f1ba4cbf6059bc99c93d592e1","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2021-01-01T14:27:45Z","title_canon_sha256":"aaced50acafa916c04a0ec31598fb4a589969a5af38176c240955cf61bb7abbd"},"schema_version":"1.0","source":{"id":"2101.00243","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.00243","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"arxiv_version","alias_value":"2101.00243v6","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.00243","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"pith_short_12","alias_value":"KQM7A4PP4IAQ","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"pith_short_16","alias_value":"KQM7A4PP4IAQ4MAU","created_at":"2026-07-05T07:29:08Z"},{"alias_kind":"pith_short_8","alias_value":"KQM7A4PP","created_at":"2026-07-05T07:29:08Z"}],"graph_snapshots":[{"event_id":"sha256:ccb1836d14fe43b085325916f5e62a269e58cddbe73fc107d9be72ce08c61215","target":"graph","created_at":"2026-07-05T07:29:08Z","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/2101.00243/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the last decade, the approximate basis computation of vanishing ideals has been studied extensively in computational algebra and data-driven applications such as machine learning. However, symbolic computation and the dependency on term order remain essential gaps between the two fields. In this study, we present the first $\\textit{monomial-agnostic}$ basis computation, which works fully numerically with proper normalization and without term order. This is realized by gradient normalization, a newly proposed data-dependent normalization that normalizes a polynomial with the magnitude of gra","authors_text":"Hiroshi Kera, Yoshihiko Hasegawa","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2021-01-01T14:27:45Z","title":"Monomial-agnostic computation of vanishing ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.00243","kind":"arxiv","version":6},"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:af842180bdf82bc78b98a92c76b980c4f611548fb9df45828696aa3861e76cdc","target":"record","created_at":"2026-07-05T07:29:08Z","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":"b837d2cee393387a38991efba2fc9ab81033cc7f1ba4cbf6059bc99c93d592e1","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2021-01-01T14:27:45Z","title_canon_sha256":"aaced50acafa916c04a0ec31598fb4a589969a5af38176c240955cf61bb7abbd"},"schema_version":"1.0","source":{"id":"2101.00243","kind":"arxiv","version":6}},"canonical_sha256":"5419f071efe2010e3014e5e887c04a7a093cc893acc8be5f51e05c3f3abe13cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5419f071efe2010e3014e5e887c04a7a093cc893acc8be5f51e05c3f3abe13cc","first_computed_at":"2026-07-05T07:29:08.068866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:29:08.068866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6HRDGdbCPSzwI+aQ9KOrxJPWZGE83xRKvSDUnNvUBinmagTCZBzyExyKOaSEGyBy7c2D6UpDIH77ci45nu9TCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:29:08.069376Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.00243","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af842180bdf82bc78b98a92c76b980c4f611548fb9df45828696aa3861e76cdc","sha256:ccb1836d14fe43b085325916f5e62a269e58cddbe73fc107d9be72ce08c61215"],"state_sha256":"d0c190f5c58522db28b45c2e5759b7c218b2cd42bde2c8ccc8aebab62a18fc78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"msJG5KzOrIr3oyrf9/7+k3oeRq86aPJYR34xNgncybAwFozGI9hlOGoK1mORKlSpcNqzJM2Jj5NfFjMclcoKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T01:05:23.024771Z","bundle_sha256":"a9b2cf6d73a0aa56eb549a4766bf144ec29d4bd9378937819149fef602c0d68d"}}