{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GSMAY6BM4ZSEJ2GYKVC6GTZUNP","short_pith_number":"pith:GSMAY6BM","canonical_record":{"source":{"id":"1407.2063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-08T12:34:11Z","cross_cats_sorted":[],"title_canon_sha256":"591e5b147d6e5e5c86b110a3deaccf6392b291e5c5e65f43620288fa38570dad","abstract_canon_sha256":"2bcbe0b4d64909a7dfcd5ccce1b03f88c11a4a6f94473fde501af87f103a05e6"},"schema_version":"1.0"},"canonical_sha256":"34980c782ce66444e8d85545e34f346bedf6867008313ec1903e6f1c7b3c3d76","source":{"kind":"arxiv","id":"1407.2063","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2063","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2063v2","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2063","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"GSMAY6BM4ZSE","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GSMAY6BM4ZSEJ2GY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GSMAY6BM","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GSMAY6BM4ZSEJ2GYKVC6GTZUNP","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-08T12:34:11Z","cross_cats_sorted":[],"title_canon_sha256":"591e5b147d6e5e5c86b110a3deaccf6392b291e5c5e65f43620288fa38570dad","abstract_canon_sha256":"2bcbe0b4d64909a7dfcd5ccce1b03f88c11a4a6f94473fde501af87f103a05e6"},"schema_version":"1.0"},"canonical_sha256":"34980c782ce66444e8d85545e34f346bedf6867008313ec1903e6f1c7b3c3d76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:53.589204Z","signature_b64":"8aFFYsFYfRPAbRZxkpieLVQq6+zWIxHUB0dR7KP17PUfNnUpcS37+Zz3+ceAv+h0npm3Cs0X7c0JOJjNAYcMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34980c782ce66444e8d85545e34f346bedf6867008313ec1903e6f1c7b3c3d76","last_reissued_at":"2026-05-18T01:59:53.588690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:53.588690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2063","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":"2026-05-18T01:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRMSJkrwjsF6W6BeE8tpDddR8LsUI25icqC32BKN/5bMMsx8UJVmHEwFWyg+or2p4thwhxf+01A36WLOHcbYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:56:38.587344Z"},"content_sha256":"c087193c8e7896a483873badda68830dba9860c68d660cb74430d21da8646c68","schema_version":"1.0","event_id":"sha256:c087193c8e7896a483873badda68830dba9860c68d660cb74430d21da8646c68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GSMAY6BM4ZSEJ2GYKVC6GTZUNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation and Streaming Algorithms for Projective Clustering via Random Projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Michael Kerber, Sharath Raghvendra","submitted_at":"2014-07-08T12:34:11Z","abstract_excerpt":"Let $P$ be a set of $n$ points in $\\mathbb{R}^d$. In the projective clustering problem, given $k, q$ and norm $\\rho \\in [1,\\infty]$, we have to compute a set $\\mathcal{F}$ of $k$ $q$-dimensional flats such that $(\\sum_{p\\in P}d(p, \\mathcal{F})^\\rho)^{1/\\rho}$ is minimized; here $d(p, \\mathcal{F})$ represents the (Euclidean) distance of $p$ to the closest flat in $\\mathcal{F}$. We let $f_k^q(P,\\rho)$ denote the minimal value and interpret $f_k^q(P,\\infty)$ to be $\\max_{r\\in P}d(r, \\mathcal{F})$. When $\\rho=1,2$ and $\\infty$ and $q=0$, the problem corresponds to the $k$-median, $k$-mean and the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2063","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":""},"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":"2026-05-18T01:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9IHCLiUpqVt3DXfaPQiVCE+FB87C0nXwspseNPsSxm3NP+Im8W/tornRnoo2TOvmzVKSH+FN/X1OICx5eZ8qCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:56:38.587928Z"},"content_sha256":"0d1d9288b44b70627bdeb77e34c4af74b7058ec2269ce49a462cf906718c2c76","schema_version":"1.0","event_id":"sha256:0d1d9288b44b70627bdeb77e34c4af74b7058ec2269ce49a462cf906718c2c76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSMAY6BM4ZSEJ2GYKVC6GTZUNP/bundle.json","state_url":"https://pith.science/pith/GSMAY6BM4ZSEJ2GYKVC6GTZUNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSMAY6BM4ZSEJ2GYKVC6GTZUNP/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":"2026-06-05T03:56:38Z","links":{"resolver":"https://pith.science/pith/GSMAY6BM4ZSEJ2GYKVC6GTZUNP","bundle":"https://pith.science/pith/GSMAY6BM4ZSEJ2GYKVC6GTZUNP/bundle.json","state":"https://pith.science/pith/GSMAY6BM4ZSEJ2GYKVC6GTZUNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSMAY6BM4ZSEJ2GYKVC6GTZUNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GSMAY6BM4ZSEJ2GYKVC6GTZUNP","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":"2bcbe0b4d64909a7dfcd5ccce1b03f88c11a4a6f94473fde501af87f103a05e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-08T12:34:11Z","title_canon_sha256":"591e5b147d6e5e5c86b110a3deaccf6392b291e5c5e65f43620288fa38570dad"},"schema_version":"1.0","source":{"id":"1407.2063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2063","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2063v2","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2063","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"GSMAY6BM4ZSE","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GSMAY6BM4ZSEJ2GY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GSMAY6BM","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:0d1d9288b44b70627bdeb77e34c4af74b7058ec2269ce49a462cf906718c2c76","target":"graph","created_at":"2026-05-18T01:59:53Z","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":"Let $P$ be a set of $n$ points in $\\mathbb{R}^d$. In the projective clustering problem, given $k, q$ and norm $\\rho \\in [1,\\infty]$, we have to compute a set $\\mathcal{F}$ of $k$ $q$-dimensional flats such that $(\\sum_{p\\in P}d(p, \\mathcal{F})^\\rho)^{1/\\rho}$ is minimized; here $d(p, \\mathcal{F})$ represents the (Euclidean) distance of $p$ to the closest flat in $\\mathcal{F}$. We let $f_k^q(P,\\rho)$ denote the minimal value and interpret $f_k^q(P,\\infty)$ to be $\\max_{r\\in P}d(r, \\mathcal{F})$. When $\\rho=1,2$ and $\\infty$ and $q=0$, the problem corresponds to the $k$-median, $k$-mean and the ","authors_text":"Michael Kerber, Sharath Raghvendra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-08T12:34:11Z","title":"Approximation and Streaming Algorithms for Projective Clustering via Random Projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2063","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:c087193c8e7896a483873badda68830dba9860c68d660cb74430d21da8646c68","target":"record","created_at":"2026-05-18T01:59:53Z","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":"2bcbe0b4d64909a7dfcd5ccce1b03f88c11a4a6f94473fde501af87f103a05e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-07-08T12:34:11Z","title_canon_sha256":"591e5b147d6e5e5c86b110a3deaccf6392b291e5c5e65f43620288fa38570dad"},"schema_version":"1.0","source":{"id":"1407.2063","kind":"arxiv","version":2}},"canonical_sha256":"34980c782ce66444e8d85545e34f346bedf6867008313ec1903e6f1c7b3c3d76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34980c782ce66444e8d85545e34f346bedf6867008313ec1903e6f1c7b3c3d76","first_computed_at":"2026-05-18T01:59:53.588690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:53.588690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8aFFYsFYfRPAbRZxkpieLVQq6+zWIxHUB0dR7KP17PUfNnUpcS37+Zz3+ceAv+h0npm3Cs0X7c0JOJjNAYcMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:53.589204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c087193c8e7896a483873badda68830dba9860c68d660cb74430d21da8646c68","sha256:0d1d9288b44b70627bdeb77e34c4af74b7058ec2269ce49a462cf906718c2c76"],"state_sha256":"1b6f6f265958ca181adabbb7024678a74e96e642f6931e70b907fdbfc02d6d39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZzGYgwYcE0sSm4Nx+Grl1ji8SexIL0uKpefNkBj96UZe7MrewZN3g2INqh3ExDLv2yeEkHO6eBlod1g0EtQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:56:38.591438Z","bundle_sha256":"066867e3b6859a1908fdd6759c5e6542f3381010ffb76de57a0f2cacb369c0a6"}}