{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EXSAHHJ6V3HJHRO6LYR22DMWQT","short_pith_number":"pith:EXSAHHJ6","canonical_record":{"source":{"id":"1108.0858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-03T14:49:59Z","cross_cats_sorted":[],"title_canon_sha256":"f572ffac09c39516f988c2eae5329e9985d1883d2557708a0d47a9e542c2c013","abstract_canon_sha256":"1fd767dca72a1992740b1981729c6843ac4f486f4641fb08f32a682d9ec9c33f"},"schema_version":"1.0"},"canonical_sha256":"25e4039d3eaece93c5de5e23ad0d9684e55b40552d36fa6121158bbfa0fc8be8","source":{"kind":"arxiv","id":"1108.0858","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0858","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0858v1","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0858","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"EXSAHHJ6V3HJ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EXSAHHJ6V3HJHRO6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EXSAHHJ6","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EXSAHHJ6V3HJHRO6LYR22DMWQT","target":"record","payload":{"canonical_record":{"source":{"id":"1108.0858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-03T14:49:59Z","cross_cats_sorted":[],"title_canon_sha256":"f572ffac09c39516f988c2eae5329e9985d1883d2557708a0d47a9e542c2c013","abstract_canon_sha256":"1fd767dca72a1992740b1981729c6843ac4f486f4641fb08f32a682d9ec9c33f"},"schema_version":"1.0"},"canonical_sha256":"25e4039d3eaece93c5de5e23ad0d9684e55b40552d36fa6121158bbfa0fc8be8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:21.877795Z","signature_b64":"nDgULhlVWc8+DAuGxKwP53quyoMiMTglgEkaxQMX2HyCl4DTraDogkWLswaJWRYyVp2m4JqfxR2SvtjGgBu4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25e4039d3eaece93c5de5e23ad0d9684e55b40552d36fa6121158bbfa0fc8be8","last_reissued_at":"2026-05-18T04:16:21.877340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:21.877340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.0858","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WP2OP0cgYJo2ZIObAz8S3aHoXLltsumtaxb0nabU3faLGnWp+Zdh5kqLTf+hvfXQr124G6QcqQE/2xRig8iDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:00:01.137004Z"},"content_sha256":"7cd4e7ec0196a459cfe3d6435226ef11d0305fa39877d70f3caea543bd48bddd","schema_version":"1.0","event_id":"sha256:7cd4e7ec0196a459cfe3d6435226ef11d0305fa39877d70f3caea543bd48bddd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EXSAHHJ6V3HJHRO6LYR22DMWQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Best Approximation Pair of Two Linear Varieties via an (In)Equality by (Fan-Todd) Beesack","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Cecilia Costa, Fernando Martins, Jose Vitoria, M. A. Facas Vicente","submitted_at":"2011-08-03T14:49:59Z","abstract_excerpt":"The closest point of a linear variety to an external point is found by using the equality case of an Ostrowski's type inequality. This point is given in closed form as the quotient of a (formal) and a (scalar) Gram determinant. Then, the best approximation pair of points onto two linear varieties is given, as well as characterization of this pair of best approximation points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0858","kind":"arxiv","version":1},"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":"2026-05-18T04:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F9mOF1HhkaiVm7H6O1bUMD+6Te07nQUlLFV8w3ts9g+/hyl22xTJ40B6D6iCgGo0Bf86+i2hiuhcnPor/0DoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:00:01.137457Z"},"content_sha256":"f33ee1d90e22264a5ef9dcb057855bb062f1b750aa35cfca44ae1085ad0261c8","schema_version":"1.0","event_id":"sha256:f33ee1d90e22264a5ef9dcb057855bb062f1b750aa35cfca44ae1085ad0261c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXSAHHJ6V3HJHRO6LYR22DMWQT/bundle.json","state_url":"https://pith.science/pith/EXSAHHJ6V3HJHRO6LYR22DMWQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXSAHHJ6V3HJHRO6LYR22DMWQT/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":"2026-08-03T19:00:01Z","links":{"resolver":"https://pith.science/pith/EXSAHHJ6V3HJHRO6LYR22DMWQT","bundle":"https://pith.science/pith/EXSAHHJ6V3HJHRO6LYR22DMWQT/bundle.json","state":"https://pith.science/pith/EXSAHHJ6V3HJHRO6LYR22DMWQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXSAHHJ6V3HJHRO6LYR22DMWQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EXSAHHJ6V3HJHRO6LYR22DMWQT","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":"1fd767dca72a1992740b1981729c6843ac4f486f4641fb08f32a682d9ec9c33f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-03T14:49:59Z","title_canon_sha256":"f572ffac09c39516f988c2eae5329e9985d1883d2557708a0d47a9e542c2c013"},"schema_version":"1.0","source":{"id":"1108.0858","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0858","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0858v1","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0858","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"EXSAHHJ6V3HJ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EXSAHHJ6V3HJHRO6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EXSAHHJ6","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:f33ee1d90e22264a5ef9dcb057855bb062f1b750aa35cfca44ae1085ad0261c8","target":"graph","created_at":"2026-05-18T04:16:21Z","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 closest point of a linear variety to an external point is found by using the equality case of an Ostrowski's type inequality. This point is given in closed form as the quotient of a (formal) and a (scalar) Gram determinant. Then, the best approximation pair of points onto two linear varieties is given, as well as characterization of this pair of best approximation points.","authors_text":"Cecilia Costa, Fernando Martins, Jose Vitoria, M. A. Facas Vicente","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-03T14:49:59Z","title":"Best Approximation Pair of Two Linear Varieties via an (In)Equality by (Fan-Todd) Beesack"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0858","kind":"arxiv","version":1},"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":"sha256:7cd4e7ec0196a459cfe3d6435226ef11d0305fa39877d70f3caea543bd48bddd","target":"record","created_at":"2026-05-18T04:16:21Z","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":"1fd767dca72a1992740b1981729c6843ac4f486f4641fb08f32a682d9ec9c33f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-03T14:49:59Z","title_canon_sha256":"f572ffac09c39516f988c2eae5329e9985d1883d2557708a0d47a9e542c2c013"},"schema_version":"1.0","source":{"id":"1108.0858","kind":"arxiv","version":1}},"canonical_sha256":"25e4039d3eaece93c5de5e23ad0d9684e55b40552d36fa6121158bbfa0fc8be8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25e4039d3eaece93c5de5e23ad0d9684e55b40552d36fa6121158bbfa0fc8be8","first_computed_at":"2026-05-18T04:16:21.877340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:21.877340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nDgULhlVWc8+DAuGxKwP53quyoMiMTglgEkaxQMX2HyCl4DTraDogkWLswaJWRYyVp2m4JqfxR2SvtjGgBu4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:21.877795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0858","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cd4e7ec0196a459cfe3d6435226ef11d0305fa39877d70f3caea543bd48bddd","sha256:f33ee1d90e22264a5ef9dcb057855bb062f1b750aa35cfca44ae1085ad0261c8"],"state_sha256":"a049aa504c4c2b3f045298880251827290f2f46fe605abfb2f3d4a9b6396c03a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IvsOa8q+roMZGFys3T+MXJke5NWq+YOnpJMaB7sFEAHvKVPjFoWJOGBVcjQ5E3Oq0d3Ub9B0jKfJ7Yu/TR8bDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T19:00:01.142359Z","bundle_sha256":"72f3c1a44e318849e9917e82ea75d78b29bb838e35c4df5064c5a5dc0e8fe8b5"}}