{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BY75C7AMWGUAH65235HMM2FUJ5","short_pith_number":"pith:BY75C7AM","canonical_record":{"source":{"id":"1504.02118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T20:29:02Z","cross_cats_sorted":[],"title_canon_sha256":"662c8283cdc176162d9be9038e57b5407f7d89caa4fbadf50841937e3262df35","abstract_canon_sha256":"638d65a357c84f182a107634e0b0e2c23a915ea11484262b09987029801dc311"},"schema_version":"1.0"},"canonical_sha256":"0e3fd17c0cb1a803fbbadf4ec668b44f720b9c7808484bd75b587546333918d4","source":{"kind":"arxiv","id":"1504.02118","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02118","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02118v3","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02118","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"pith_short_12","alias_value":"BY75C7AMWGUA","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BY75C7AMWGUAH652","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BY75C7AM","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BY75C7AMWGUAH65235HMM2FUJ5","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T20:29:02Z","cross_cats_sorted":[],"title_canon_sha256":"662c8283cdc176162d9be9038e57b5407f7d89caa4fbadf50841937e3262df35","abstract_canon_sha256":"638d65a357c84f182a107634e0b0e2c23a915ea11484262b09987029801dc311"},"schema_version":"1.0"},"canonical_sha256":"0e3fd17c0cb1a803fbbadf4ec668b44f720b9c7808484bd75b587546333918d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:03.678163Z","signature_b64":"tQj20jz0fa4Wnn+ISS4/PAXMvPUblB3slvS5hIkWe6B9EyFJGCGfeclQWX/pbvimhi/wxj1GCr4nJhX6HRRGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e3fd17c0cb1a803fbbadf4ec668b44f720b9c7808484bd75b587546333918d4","last_reissued_at":"2026-05-18T01:37:03.677521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:03.677521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02118","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":"2026-05-18T01:37:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBHAU5Qy/QnVuVZH2/bAu1ubDru1v48si12Z2MzJvjKBPyhUuAjkBLOcB9NRxaTQZD7+UYlYwRwGT3167RNtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:25:32.170175Z"},"content_sha256":"67556d33f14ef0bebb9829913759a4c6e17b718a16ea41673616f7c0ed444331","schema_version":"1.0","event_id":"sha256:67556d33f14ef0bebb9829913759a4c6e17b718a16ea41673616f7c0ed444331"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BY75C7AMWGUAH65235HMM2FUJ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Bad Are Vandermonde Matrices?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Victor Y. Pan","submitted_at":"2015-04-08T20:29:02Z","abstract_excerpt":"The work on the estimation of the condition numbers of Vandermonde matrices, motivated by applications to interpolation and quadrature, can be traced back at least to the 1970s. Empirical study has shown consistently that Vandermonde matrices tend to be badly ill-conditioned, with a narrow class of notable exceptions, such as the matrices of the discrete Fourier transform (hereafter referred to as DFT). So far formal support for this empirical observation, however, has been limited to the matrices defined by the real set of knots. We prove that, more generally, any Vandermonde matrix of a larg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02118","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":"2026-05-18T01:37:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fbuhUBS6Us1s0CLIyNMo/Q3xVRZx6BCLQ6uEhB0Y2pUep6R0JNAid63DkHAvP58ON2wXKHkQsBGOzTOAmikLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:25:32.170772Z"},"content_sha256":"0e7da8b71f2e73f59824e21103fa6602de8adaa8689bbc2512e2179cf0ba4c5e","schema_version":"1.0","event_id":"sha256:0e7da8b71f2e73f59824e21103fa6602de8adaa8689bbc2512e2179cf0ba4c5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BY75C7AMWGUAH65235HMM2FUJ5/bundle.json","state_url":"https://pith.science/pith/BY75C7AMWGUAH65235HMM2FUJ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BY75C7AMWGUAH65235HMM2FUJ5/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":"2026-06-11T14:25:32Z","links":{"resolver":"https://pith.science/pith/BY75C7AMWGUAH65235HMM2FUJ5","bundle":"https://pith.science/pith/BY75C7AMWGUAH65235HMM2FUJ5/bundle.json","state":"https://pith.science/pith/BY75C7AMWGUAH65235HMM2FUJ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BY75C7AMWGUAH65235HMM2FUJ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BY75C7AMWGUAH65235HMM2FUJ5","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":"638d65a357c84f182a107634e0b0e2c23a915ea11484262b09987029801dc311","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T20:29:02Z","title_canon_sha256":"662c8283cdc176162d9be9038e57b5407f7d89caa4fbadf50841937e3262df35"},"schema_version":"1.0","source":{"id":"1504.02118","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02118","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02118v3","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02118","created_at":"2026-05-18T01:37:03Z"},{"alias_kind":"pith_short_12","alias_value":"BY75C7AMWGUA","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BY75C7AMWGUAH652","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BY75C7AM","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:0e7da8b71f2e73f59824e21103fa6602de8adaa8689bbc2512e2179cf0ba4c5e","target":"graph","created_at":"2026-05-18T01:37:03Z","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":"The work on the estimation of the condition numbers of Vandermonde matrices, motivated by applications to interpolation and quadrature, can be traced back at least to the 1970s. Empirical study has shown consistently that Vandermonde matrices tend to be badly ill-conditioned, with a narrow class of notable exceptions, such as the matrices of the discrete Fourier transform (hereafter referred to as DFT). So far formal support for this empirical observation, however, has been limited to the matrices defined by the real set of knots. We prove that, more generally, any Vandermonde matrix of a larg","authors_text":"Victor Y. Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T20:29:02Z","title":"How Bad Are Vandermonde Matrices?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02118","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":"sha256:67556d33f14ef0bebb9829913759a4c6e17b718a16ea41673616f7c0ed444331","target":"record","created_at":"2026-05-18T01:37:03Z","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":"638d65a357c84f182a107634e0b0e2c23a915ea11484262b09987029801dc311","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T20:29:02Z","title_canon_sha256":"662c8283cdc176162d9be9038e57b5407f7d89caa4fbadf50841937e3262df35"},"schema_version":"1.0","source":{"id":"1504.02118","kind":"arxiv","version":3}},"canonical_sha256":"0e3fd17c0cb1a803fbbadf4ec668b44f720b9c7808484bd75b587546333918d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e3fd17c0cb1a803fbbadf4ec668b44f720b9c7808484bd75b587546333918d4","first_computed_at":"2026-05-18T01:37:03.677521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:03.677521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tQj20jz0fa4Wnn+ISS4/PAXMvPUblB3slvS5hIkWe6B9EyFJGCGfeclQWX/pbvimhi/wxj1GCr4nJhX6HRRGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:03.678163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02118","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67556d33f14ef0bebb9829913759a4c6e17b718a16ea41673616f7c0ed444331","sha256:0e7da8b71f2e73f59824e21103fa6602de8adaa8689bbc2512e2179cf0ba4c5e"],"state_sha256":"dc1db832d8f662253afa6bc78d68580d460027f83cacb0547c1f27a03cf8f5f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzP6gJq/eO1NgD07NBrGzDGXQ+yNJ3jsF8KcL/5hd1pGaodSm80Kyer4yTjn7eSuokB21pxTMnKOJaJBGKhbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:25:32.173535Z","bundle_sha256":"ceb20b8e9402d1afe82baf08a9b29f8cf34f15678b0301b62ce97985fd5d3436"}}