{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SBJ5TP3FMK6XYQVJRMNKVF67ZT","short_pith_number":"pith:SBJ5TP3F","canonical_record":{"source":{"id":"1311.6455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-25T20:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"a069a52d9c22726fbf1df78185f3be4fb25ed7cb21e09dd0bcb7dedf75aa272f","abstract_canon_sha256":"44332410d0c3a6f1d8f137223d43c4eb6de139499fab27fe0b3bd0d114adc911"},"schema_version":"1.0"},"canonical_sha256":"9053d9bf6562bd7c42a98b1aaa97dfccc207b6b2c42c27e48b4eef92b2922239","source":{"kind":"arxiv","id":"1311.6455","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6455","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6455v3","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6455","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"SBJ5TP3FMK6X","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SBJ5TP3FMK6XYQVJ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SBJ5TP3F","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SBJ5TP3FMK6XYQVJRMNKVF67ZT","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-25T20:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"a069a52d9c22726fbf1df78185f3be4fb25ed7cb21e09dd0bcb7dedf75aa272f","abstract_canon_sha256":"44332410d0c3a6f1d8f137223d43c4eb6de139499fab27fe0b3bd0d114adc911"},"schema_version":"1.0"},"canonical_sha256":"9053d9bf6562bd7c42a98b1aaa97dfccc207b6b2c42c27e48b4eef92b2922239","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:43.720571Z","signature_b64":"3+rN/oSroeqgcs0PbApUCr3RUSK41m4fDevR+it0+5GIfjVbLCTnuXWj1BCAroYXWV+Hic41Dr6BUOQDHEbrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9053d9bf6562bd7c42a98b1aaa97dfccc207b6b2c42c27e48b4eef92b2922239","last_reissued_at":"2026-05-18T02:56:43.720116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:43.720116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6455","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":"2026-05-18T02:56:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xH1bLomJgp6LStMyrGz7Vy9gaWigSjN/iYDGKWQ+CWTSin13DNxT7sWxHUb7WgyVZCaw32qxLQIodT11ai5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:00:06.982528Z"},"content_sha256":"20d828b163204a245664a6a5ac2ef21127c8c8d30f2ee6e2f89114e753effbed","schema_version":"1.0","event_id":"sha256:20d828b163204a245664a6a5ac2ef21127c8c8d30f2ee6e2f89114e753effbed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SBJ5TP3FMK6XYQVJRMNKVF67ZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On certain multivariate Vandermonde determinants whose variables separate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Konstantin Usevich, Stefano De Marchi","submitted_at":"2013-11-25T20:47:25Z","abstract_excerpt":"We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma 1, L. Bos et al. (2009), Dolomites Research Notes on Approximation, 2:1-15]. As a special case, we apply the result to Padua and Padua-like points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6455","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":"2026-05-18T02:56:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MFLQ044ydV2egXXXO6uIxZ4smg9gy19dNbOLSU/A0ISM4QLGIjPYbDv3YYe5CGY5JCGo2zY3W/B+tm8p/9NsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:00:06.983094Z"},"content_sha256":"e4411bb2fd86c426327d2b1ffdc8f8c7335cd9d325e0e6bf3239cb23a6ca7fbe","schema_version":"1.0","event_id":"sha256:e4411bb2fd86c426327d2b1ffdc8f8c7335cd9d325e0e6bf3239cb23a6ca7fbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBJ5TP3FMK6XYQVJRMNKVF67ZT/bundle.json","state_url":"https://pith.science/pith/SBJ5TP3FMK6XYQVJRMNKVF67ZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBJ5TP3FMK6XYQVJRMNKVF67ZT/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":"2026-06-09T07:00:06Z","links":{"resolver":"https://pith.science/pith/SBJ5TP3FMK6XYQVJRMNKVF67ZT","bundle":"https://pith.science/pith/SBJ5TP3FMK6XYQVJRMNKVF67ZT/bundle.json","state":"https://pith.science/pith/SBJ5TP3FMK6XYQVJRMNKVF67ZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBJ5TP3FMK6XYQVJRMNKVF67ZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SBJ5TP3FMK6XYQVJRMNKVF67ZT","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":"44332410d0c3a6f1d8f137223d43c4eb6de139499fab27fe0b3bd0d114adc911","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-25T20:47:25Z","title_canon_sha256":"a069a52d9c22726fbf1df78185f3be4fb25ed7cb21e09dd0bcb7dedf75aa272f"},"schema_version":"1.0","source":{"id":"1311.6455","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6455","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6455v3","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6455","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"SBJ5TP3FMK6X","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SBJ5TP3FMK6XYQVJ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SBJ5TP3F","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:e4411bb2fd86c426327d2b1ffdc8f8c7335cd9d325e0e6bf3239cb23a6ca7fbe","target":"graph","created_at":"2026-05-18T02:56:43Z","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 prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma 1, L. Bos et al. (2009), Dolomites Research Notes on Approximation, 2:1-15]. As a special case, we apply the result to Padua and Padua-like points.","authors_text":"Konstantin Usevich, Stefano De Marchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-25T20:47:25Z","title":"On certain multivariate Vandermonde determinants whose variables separate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6455","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":"sha256:20d828b163204a245664a6a5ac2ef21127c8c8d30f2ee6e2f89114e753effbed","target":"record","created_at":"2026-05-18T02:56:43Z","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":"44332410d0c3a6f1d8f137223d43c4eb6de139499fab27fe0b3bd0d114adc911","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-25T20:47:25Z","title_canon_sha256":"a069a52d9c22726fbf1df78185f3be4fb25ed7cb21e09dd0bcb7dedf75aa272f"},"schema_version":"1.0","source":{"id":"1311.6455","kind":"arxiv","version":3}},"canonical_sha256":"9053d9bf6562bd7c42a98b1aaa97dfccc207b6b2c42c27e48b4eef92b2922239","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9053d9bf6562bd7c42a98b1aaa97dfccc207b6b2c42c27e48b4eef92b2922239","first_computed_at":"2026-05-18T02:56:43.720116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:43.720116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3+rN/oSroeqgcs0PbApUCr3RUSK41m4fDevR+it0+5GIfjVbLCTnuXWj1BCAroYXWV+Hic41Dr6BUOQDHEbrAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:43.720571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6455","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20d828b163204a245664a6a5ac2ef21127c8c8d30f2ee6e2f89114e753effbed","sha256:e4411bb2fd86c426327d2b1ffdc8f8c7335cd9d325e0e6bf3239cb23a6ca7fbe"],"state_sha256":"ba6e55c4e679675e08008f8bdf8c1ec8d7f6a62543d3b1d495f00d44035d282b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+NPIkvvcgdRXMW4+3t7kIc9BjdFCJF2R0SDoM7d1HXY8KKP2R96lplMz6BOaeSU7rROVsfanETTXQ8JibpT/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:00:06.986780Z","bundle_sha256":"db2eeed3e6fbc9649f69f5a54baa5305156bc8ac8520218ec47d6032d843cab5"}}