{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UW7GOQ7WWRHNXZM4UC5QT4Y2BL","short_pith_number":"pith:UW7GOQ7W","canonical_record":{"source":{"id":"1008.0274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-02T10:20:11Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"80919e7b2828681fafb27b6bf9bc956a943229d8718356fffa7f8f9bcda38211","abstract_canon_sha256":"ecbca073c7fe389bab7b8be0fd9713a7812351754354171b8c3eaf85d34d17bd"},"schema_version":"1.0"},"canonical_sha256":"a5be6743f6b44edbe59ca0bb09f31a0afaba56d72d1496b1673bc422db8c0be9","source":{"kind":"arxiv","id":"1008.0274","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0274","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0274v2","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0274","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"UW7GOQ7WWRHN","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UW7GOQ7WWRHNXZM4","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UW7GOQ7W","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UW7GOQ7WWRHNXZM4UC5QT4Y2BL","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-02T10:20:11Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"80919e7b2828681fafb27b6bf9bc956a943229d8718356fffa7f8f9bcda38211","abstract_canon_sha256":"ecbca073c7fe389bab7b8be0fd9713a7812351754354171b8c3eaf85d34d17bd"},"schema_version":"1.0"},"canonical_sha256":"a5be6743f6b44edbe59ca0bb09f31a0afaba56d72d1496b1673bc422db8c0be9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:12.087710Z","signature_b64":"sCunM7Dl5ppmtQPq4k/uBOZ/8KIwRszQX6x+S9Z8SmDNvQxjA92GwXvle62KaM9UMzAo0zbFPuLYMJ92BoVlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5be6743f6b44edbe59ca0bb09f31a0afaba56d72d1496b1673bc422db8c0be9","last_reissued_at":"2026-05-18T04:02:12.087027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:12.087027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0274","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":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzfmufFbHHys6+V5sTYHIVL8C9Hs/J3VCCCUxA6iTzSO69yCGHBfm0cNC+4LULA7qKB4j1AA+moxruArWtguCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:40:12.625079Z"},"content_sha256":"5aa0b937f06a9b1b8594122a3aa3051bba0e999bbcd2ca05570deced3fb4f3ca","schema_version":"1.0","event_id":"sha256:5aa0b937f06a9b1b8594122a3aa3051bba0e999bbcd2ca05570deced3fb4f3ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UW7GOQ7WWRHNXZM4UC5QT4Y2BL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple Approximate Varieties for Sets of Empirical Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AC","authors_text":"Claudia Fassino, Maria-Laura Torrente","submitted_at":"2010-08-02T10:20:11Z","abstract_excerpt":"We present a symbolic-numeric approach for the analysis of a given set of noisy data, represented as a finite set $\\X$ of limited precision points. Starting from $\\X$ and a permitted tolerance $\\varepsilon$ on its coordinates, our method automatically determines a low degree monic polynomial whose associated variety passes close to each point of $\\X$ by less than the given tolerance $\\varepsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0274","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":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e72Y1h4UtfzfBVxNhZ1eocAZQG1Wcitmbd2XzGyonAdB9RZ+njqEVJOoRx2Y6rmYeTFzjKxxvxRE/e871GY7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:40:12.625477Z"},"content_sha256":"67b203288f38a571e63830181cb50f7348ffc78ce8211d8314a15ef65bcce7df","schema_version":"1.0","event_id":"sha256:67b203288f38a571e63830181cb50f7348ffc78ce8211d8314a15ef65bcce7df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UW7GOQ7WWRHNXZM4UC5QT4Y2BL/bundle.json","state_url":"https://pith.science/pith/UW7GOQ7WWRHNXZM4UC5QT4Y2BL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UW7GOQ7WWRHNXZM4UC5QT4Y2BL/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":"2026-05-31T06:40:12Z","links":{"resolver":"https://pith.science/pith/UW7GOQ7WWRHNXZM4UC5QT4Y2BL","bundle":"https://pith.science/pith/UW7GOQ7WWRHNXZM4UC5QT4Y2BL/bundle.json","state":"https://pith.science/pith/UW7GOQ7WWRHNXZM4UC5QT4Y2BL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UW7GOQ7WWRHNXZM4UC5QT4Y2BL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UW7GOQ7WWRHNXZM4UC5QT4Y2BL","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":"ecbca073c7fe389bab7b8be0fd9713a7812351754354171b8c3eaf85d34d17bd","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-02T10:20:11Z","title_canon_sha256":"80919e7b2828681fafb27b6bf9bc956a943229d8718356fffa7f8f9bcda38211"},"schema_version":"1.0","source":{"id":"1008.0274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0274","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0274v2","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0274","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"UW7GOQ7WWRHN","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UW7GOQ7WWRHNXZM4","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UW7GOQ7W","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:67b203288f38a571e63830181cb50f7348ffc78ce8211d8314a15ef65bcce7df","target":"graph","created_at":"2026-05-18T04:02:12Z","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 present a symbolic-numeric approach for the analysis of a given set of noisy data, represented as a finite set $\\X$ of limited precision points. Starting from $\\X$ and a permitted tolerance $\\varepsilon$ on its coordinates, our method automatically determines a low degree monic polynomial whose associated variety passes close to each point of $\\X$ by less than the given tolerance $\\varepsilon$.","authors_text":"Claudia Fassino, Maria-Laura Torrente","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-02T10:20:11Z","title":"Simple Approximate Varieties for Sets of Empirical Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0274","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":"sha256:5aa0b937f06a9b1b8594122a3aa3051bba0e999bbcd2ca05570deced3fb4f3ca","target":"record","created_at":"2026-05-18T04:02:12Z","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":"ecbca073c7fe389bab7b8be0fd9713a7812351754354171b8c3eaf85d34d17bd","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-02T10:20:11Z","title_canon_sha256":"80919e7b2828681fafb27b6bf9bc956a943229d8718356fffa7f8f9bcda38211"},"schema_version":"1.0","source":{"id":"1008.0274","kind":"arxiv","version":2}},"canonical_sha256":"a5be6743f6b44edbe59ca0bb09f31a0afaba56d72d1496b1673bc422db8c0be9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5be6743f6b44edbe59ca0bb09f31a0afaba56d72d1496b1673bc422db8c0be9","first_computed_at":"2026-05-18T04:02:12.087027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:12.087027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sCunM7Dl5ppmtQPq4k/uBOZ/8KIwRszQX6x+S9Z8SmDNvQxjA92GwXvle62KaM9UMzAo0zbFPuLYMJ92BoVlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:12.087710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aa0b937f06a9b1b8594122a3aa3051bba0e999bbcd2ca05570deced3fb4f3ca","sha256:67b203288f38a571e63830181cb50f7348ffc78ce8211d8314a15ef65bcce7df"],"state_sha256":"b720bd2f583d41d12fe7f0b3bcefeeba4ce9d818aab4923377b6fea81a7823fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPh7C2n5i9Lo1SQRhkyNEsqcH0UcbGUrArWSKy/UKb1ny1ql4I+Etuzo3DrWFY8x/SZtVKn1r6UzcqSZjowNCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:40:12.628031Z","bundle_sha256":"2c33c90a017bab3a8fc7afa3c9501bcf60adcfac02f2d61ef56c05403cc491f8"}}