{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:CCVPAIVMYMFLUK4URPLQAPBT3I","short_pith_number":"pith:CCVPAIVM","canonical_record":{"source":{"id":"0706.2316","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2007-06-15T15:28:18Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"d5a3b5b6dd43b35d157d262181a6dd1b730c0f1c851388ff250910783357ff91","abstract_canon_sha256":"0ec58d6a93f1a19d6c20970d365af27da7874930a494346ed6513b0a94758f0d"},"schema_version":"1.0"},"canonical_sha256":"10aaf022acc30aba2b948bd7003c33da35b3a9a53f4eeaf649a861b9caf1a82a","source":{"kind":"arxiv","id":"0706.2316","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.2316","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"0706.2316v2","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.2316","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"CCVPAIVMYMFL","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_16","alias_value":"CCVPAIVMYMFLUK4U","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_8","alias_value":"CCVPAIVM","created_at":"2026-06-03T22:06:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:CCVPAIVMYMFLUK4URPLQAPBT3I","target":"record","payload":{"canonical_record":{"source":{"id":"0706.2316","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2007-06-15T15:28:18Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"d5a3b5b6dd43b35d157d262181a6dd1b730c0f1c851388ff250910783357ff91","abstract_canon_sha256":"0ec58d6a93f1a19d6c20970d365af27da7874930a494346ed6513b0a94758f0d"},"schema_version":"1.0"},"canonical_sha256":"10aaf022acc30aba2b948bd7003c33da35b3a9a53f4eeaf649a861b9caf1a82a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:01.263471Z","signature_b64":"O/jYlaNDClUIsSmxgT55UTpcvxUxfPhHwsoI9AMmC6s5/OL6ZEzA9cQkt+F1V95dvi14PILFERIGqeRaZGt7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10aaf022acc30aba2b948bd7003c33da35b3a9a53f4eeaf649a861b9caf1a82a","last_reissued_at":"2026-06-03T22:06:01.263051Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:01.263051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.2316","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":"2026-06-03T22:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1UxuhaxQLbcLO//1F4VuMd+Z4gGlUAe8nT9xImUgs+3GgLsLiWj9fl7WBuIaB4DI3zwmCu2UsqJX+3tz6WQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:09:42.450610Z"},"content_sha256":"e29590e29a1e03dee893b00a2f60687de1fc453bb69a198e584673b9a96f2c3f","schema_version":"1.0","event_id":"sha256:e29590e29a1e03dee893b00a2f60687de1fc453bb69a198e584673b9a96f2c3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:CCVPAIVMYMFLUK4URPLQAPBT3I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable Border Bases for Ideals of Points","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AC","authors_text":"Claudia Fassino, John Abbott, Maria-Laura Torrente","submitted_at":"2007-06-15T15:28:18Z","abstract_excerpt":"Let $X$ be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal $I(X)$ independent of the data uncertainty. We present a method to compute a polynomial basis $B$ of $I(X)$ which exhibits structural stability, that is, if $\\widetilde X$ is any set of points differing only slightly from $X$, there exists a polynomial set $\\widetilde B$ structurally similar to $B$, which is a basis of the perturbed ideal $ I(\\widetilde X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2316","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0706.2316/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":"2026-06-03T22:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpl+QULTC4UP7Z+1sjp4JAbSVXYeGlt1uSJbVS5THLsyyxE5x04d4TFWWDsNh2jSxOmHFQnVJPRSqwfORcP8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:09:42.450976Z"},"content_sha256":"50d0f330c858ed8abeb8548f6229e2fcaba4f94e9816615648db5faa8f925eb0","schema_version":"1.0","event_id":"sha256:50d0f330c858ed8abeb8548f6229e2fcaba4f94e9816615648db5faa8f925eb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCVPAIVMYMFLUK4URPLQAPBT3I/bundle.json","state_url":"https://pith.science/pith/CCVPAIVMYMFLUK4URPLQAPBT3I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCVPAIVMYMFLUK4URPLQAPBT3I/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":"2026-06-20T22:09:42Z","links":{"resolver":"https://pith.science/pith/CCVPAIVMYMFLUK4URPLQAPBT3I","bundle":"https://pith.science/pith/CCVPAIVMYMFLUK4URPLQAPBT3I/bundle.json","state":"https://pith.science/pith/CCVPAIVMYMFLUK4URPLQAPBT3I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCVPAIVMYMFLUK4URPLQAPBT3I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:CCVPAIVMYMFLUK4URPLQAPBT3I","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":"0ec58d6a93f1a19d6c20970d365af27da7874930a494346ed6513b0a94758f0d","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AC","submitted_at":"2007-06-15T15:28:18Z","title_canon_sha256":"d5a3b5b6dd43b35d157d262181a6dd1b730c0f1c851388ff250910783357ff91"},"schema_version":"1.0","source":{"id":"0706.2316","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.2316","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"0706.2316v2","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.2316","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"CCVPAIVMYMFL","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_16","alias_value":"CCVPAIVMYMFLUK4U","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_8","alias_value":"CCVPAIVM","created_at":"2026-06-03T22:06:01Z"}],"graph_snapshots":[{"event_id":"sha256:50d0f330c858ed8abeb8548f6229e2fcaba4f94e9816615648db5faa8f925eb0","target":"graph","created_at":"2026-06-03T22:06:01Z","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/0706.2316/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal $I(X)$ independent of the data uncertainty. We present a method to compute a polynomial basis $B$ of $I(X)$ which exhibits structural stability, that is, if $\\widetilde X$ is any set of points differing only slightly from $X$, there exists a polynomial set $\\widetilde B$ structurally similar to $B$, which is a basis of the perturbed ideal $ I(\\widetilde X)$.","authors_text":"Claudia Fassino, John Abbott, Maria-Laura Torrente","cross_cats":["cs.NA","math.NA"],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"2007-06-15T15:28:18Z","title":"Stable Border Bases for Ideals of Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2316","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:e29590e29a1e03dee893b00a2f60687de1fc453bb69a198e584673b9a96f2c3f","target":"record","created_at":"2026-06-03T22:06:01Z","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":"0ec58d6a93f1a19d6c20970d365af27da7874930a494346ed6513b0a94758f0d","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AC","submitted_at":"2007-06-15T15:28:18Z","title_canon_sha256":"d5a3b5b6dd43b35d157d262181a6dd1b730c0f1c851388ff250910783357ff91"},"schema_version":"1.0","source":{"id":"0706.2316","kind":"arxiv","version":2}},"canonical_sha256":"10aaf022acc30aba2b948bd7003c33da35b3a9a53f4eeaf649a861b9caf1a82a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10aaf022acc30aba2b948bd7003c33da35b3a9a53f4eeaf649a861b9caf1a82a","first_computed_at":"2026-06-03T22:06:01.263051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:01.263051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O/jYlaNDClUIsSmxgT55UTpcvxUxfPhHwsoI9AMmC6s5/OL6ZEzA9cQkt+F1V95dvi14PILFERIGqeRaZGt7BA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:01.263471Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.2316","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e29590e29a1e03dee893b00a2f60687de1fc453bb69a198e584673b9a96f2c3f","sha256:50d0f330c858ed8abeb8548f6229e2fcaba4f94e9816615648db5faa8f925eb0"],"state_sha256":"729541073e4e6e9693bb512026e6cf1f8e8f9c3515fc010a7734e1c3c02a2dca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4OTwkCZUAnBW8I3A0N9C2qMgHEQumDgrdR6pnpuByKITmvyvNzHQSiXbLiFCdJwGbdQZjPBEiVexXwL0+6KFCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:09:42.452944Z","bundle_sha256":"832791da142d1aac199e6d99a16204daff7c81fd631ce2679791d50609be5b1e"}}