{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SQS2RDZFXYQNJDKIWTA4MG2VY3","short_pith_number":"pith:SQS2RDZF","canonical_record":{"source":{"id":"1410.0642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-09-27T12:59:55Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"e5bf107d745d81826988dfed91cc1d83dbad61639c671c948739499449973b83","abstract_canon_sha256":"5cc814c8dff858d859357c2f5bcecbdd47ce3da598a5e74a9662bd793d3c65a7"},"schema_version":"1.0"},"canonical_sha256":"9425a88f25be20d48d48b4c1c61b55c6fd2ebe06fd75b6067d04f1477eeb16bf","source":{"kind":"arxiv","id":"1410.0642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0642","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0642v1","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0642","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"SQS2RDZFXYQN","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SQS2RDZFXYQNJDKI","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SQS2RDZF","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SQS2RDZFXYQNJDKIWTA4MG2VY3","target":"record","payload":{"canonical_record":{"source":{"id":"1410.0642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-09-27T12:59:55Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"e5bf107d745d81826988dfed91cc1d83dbad61639c671c948739499449973b83","abstract_canon_sha256":"5cc814c8dff858d859357c2f5bcecbdd47ce3da598a5e74a9662bd793d3c65a7"},"schema_version":"1.0"},"canonical_sha256":"9425a88f25be20d48d48b4c1c61b55c6fd2ebe06fd75b6067d04f1477eeb16bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:10.572224Z","signature_b64":"8ZG+M7ex8sqWtDFqMh8KlV33pclQoussrHGE3/NBgdqHc+QHlAwlFur6XsCZqh0MTlibEc9G9fM6LVjmuaqPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9425a88f25be20d48d48b4c1c61b55c6fd2ebe06fd75b6067d04f1477eeb16bf","last_reissued_at":"2026-05-18T02:41:10.571656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:10.571656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.0642","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":"2026-05-18T02:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"siO8GrHcTMLvzUiLVajhffFWxFyVp8WOqqPt6axGvqVmpafu0BOXnwkI7d3ykYaAcvraAN3GHb3DB/aFwedQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:06:04.147526Z"},"content_sha256":"5dffed99eb977c3db7b1678abc3a82d7f987007c924ed71a2cde1b8ed71a8c88","schema_version":"1.0","event_id":"sha256:5dffed99eb977c3db7b1678abc3a82d7f987007c924ed71a2cde1b8ed71a8c88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SQS2RDZFXYQNJDKIWTA4MG2VY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Archetypal Analysis and the Approximation of Convex Hulls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.NA","authors_text":"Christian Bauckhage","submitted_at":"2014-09-27T12:59:55Z","abstract_excerpt":"We briefly review the basic ideas behind archetypal analysis for matrix factorization and discuss its behavior in approximating the convex hull of a data sample. We then ask how good such approximations can be and consider different cases. Understanding archetypal analysis as the problem of computing a convexity constrained low-rank approximation of the identity matrix provides estimates for archetypal analysis and the SiVM heuristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0642","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":"2026-05-18T02:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oa2xph1yuIXDbIG+SrPoqE7prMOxdDgn6Zy67e1lBZUvCniS3MHpvNGCHEZEN9DRGEQfvSpR0E2kU4TOnwrxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:06:04.148265Z"},"content_sha256":"faca00cab93ddf2357c11fce1c17c582988fb588b3071881000dec26c27c4f03","schema_version":"1.0","event_id":"sha256:faca00cab93ddf2357c11fce1c17c582988fb588b3071881000dec26c27c4f03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQS2RDZFXYQNJDKIWTA4MG2VY3/bundle.json","state_url":"https://pith.science/pith/SQS2RDZFXYQNJDKIWTA4MG2VY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQS2RDZFXYQNJDKIWTA4MG2VY3/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":"2026-06-11T04:06:04Z","links":{"resolver":"https://pith.science/pith/SQS2RDZFXYQNJDKIWTA4MG2VY3","bundle":"https://pith.science/pith/SQS2RDZFXYQNJDKIWTA4MG2VY3/bundle.json","state":"https://pith.science/pith/SQS2RDZFXYQNJDKIWTA4MG2VY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQS2RDZFXYQNJDKIWTA4MG2VY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SQS2RDZFXYQNJDKIWTA4MG2VY3","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":"5cc814c8dff858d859357c2f5bcecbdd47ce3da598a5e74a9662bd793d3c65a7","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-09-27T12:59:55Z","title_canon_sha256":"e5bf107d745d81826988dfed91cc1d83dbad61639c671c948739499449973b83"},"schema_version":"1.0","source":{"id":"1410.0642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0642","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0642v1","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0642","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"SQS2RDZFXYQN","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SQS2RDZFXYQNJDKI","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SQS2RDZF","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:faca00cab93ddf2357c11fce1c17c582988fb588b3071881000dec26c27c4f03","target":"graph","created_at":"2026-05-18T02:41:10Z","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 briefly review the basic ideas behind archetypal analysis for matrix factorization and discuss its behavior in approximating the convex hull of a data sample. We then ask how good such approximations can be and consider different cases. Understanding archetypal analysis as the problem of computing a convexity constrained low-rank approximation of the identity matrix provides estimates for archetypal analysis and the SiVM heuristic.","authors_text":"Christian Bauckhage","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-09-27T12:59:55Z","title":"A Note on Archetypal Analysis and the Approximation of Convex Hulls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0642","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":"sha256:5dffed99eb977c3db7b1678abc3a82d7f987007c924ed71a2cde1b8ed71a8c88","target":"record","created_at":"2026-05-18T02:41:10Z","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":"5cc814c8dff858d859357c2f5bcecbdd47ce3da598a5e74a9662bd793d3c65a7","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-09-27T12:59:55Z","title_canon_sha256":"e5bf107d745d81826988dfed91cc1d83dbad61639c671c948739499449973b83"},"schema_version":"1.0","source":{"id":"1410.0642","kind":"arxiv","version":1}},"canonical_sha256":"9425a88f25be20d48d48b4c1c61b55c6fd2ebe06fd75b6067d04f1477eeb16bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9425a88f25be20d48d48b4c1c61b55c6fd2ebe06fd75b6067d04f1477eeb16bf","first_computed_at":"2026-05-18T02:41:10.571656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:10.571656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ZG+M7ex8sqWtDFqMh8KlV33pclQoussrHGE3/NBgdqHc+QHlAwlFur6XsCZqh0MTlibEc9G9fM6LVjmuaqPAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:10.572224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dffed99eb977c3db7b1678abc3a82d7f987007c924ed71a2cde1b8ed71a8c88","sha256:faca00cab93ddf2357c11fce1c17c582988fb588b3071881000dec26c27c4f03"],"state_sha256":"a2e0c0273615a50ef695c32a23b32bb2b61b7b4ce3e78fc03f5dca1c9c13f4b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N41cRL9zhtOhmL9uPqG1RoXw5hIfm2DErf07oCUUvARyl0NIpjwfxcr/sxHrpakdqMSZ7T5RsFNeEwYAnvrrBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T04:06:04.152022Z","bundle_sha256":"ed678fc0be57a9620a587395c597ae60ede0ec8542c6ebf01cbf4f1220e4212a"}}