{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:M63RUUFDS74L56SFEU62TFWHK6","short_pith_number":"pith:M63RUUFD","canonical_record":{"source":{"id":"1810.04321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-10T00:56:59Z","cross_cats_sorted":["cs.CG","math.FA","math.MG"],"title_canon_sha256":"447fab118f675a23ad64579dcba2db52b4f8646023bb93d89f9fcfbdcb295c2a","abstract_canon_sha256":"19301ae29481082bc3a97f771ca94c72be8b1fb4963866716528bbf54c04b4d9"},"schema_version":"1.0"},"canonical_sha256":"67b71a50a397f8befa45253da996c757826c2e49d6d25e06dc1cc3f29cd7d2aa","source":{"kind":"arxiv","id":"1810.04321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04321","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04321v1","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04321","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"M63RUUFDS74L","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M63RUUFDS74L56SF","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M63RUUFD","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:M63RUUFDS74L56SFEU62TFWHK6","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-10T00:56:59Z","cross_cats_sorted":["cs.CG","math.FA","math.MG"],"title_canon_sha256":"447fab118f675a23ad64579dcba2db52b4f8646023bb93d89f9fcfbdcb295c2a","abstract_canon_sha256":"19301ae29481082bc3a97f771ca94c72be8b1fb4963866716528bbf54c04b4d9"},"schema_version":"1.0"},"canonical_sha256":"67b71a50a397f8befa45253da996c757826c2e49d6d25e06dc1cc3f29cd7d2aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:40.395519Z","signature_b64":"OisGemf09WZDkf4Q8OJpYu78zvH73IG+KyeiMtGhacwqYJmgh5yMmkuoRFbo5sv6mBXCEwd9KPpuGf284oQACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67b71a50a397f8befa45253da996c757826c2e49d6d25e06dc1cc3f29cd7d2aa","last_reissued_at":"2026-05-18T00:03:40.395044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:40.395044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04321","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":"2026-05-18T00:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upjFHZc0T9vmBir0lvtSpb3cFOPd/dPRAPOhU/iOUsXv69tO6y8CXKUNPJucHSIqYjazcxfsCDvChsBX76pdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:37:53.781601Z"},"content_sha256":"fa48b9fe97b711a7542965c32de7c7b9865da6c0843e8fc921251d8ad618c817","schema_version":"1.0","event_id":"sha256:fa48b9fe97b711a7542965c32de7c7b9865da6c0843e8fc921251d8ad618c817"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:M63RUUFDS74L56SFEU62TFWHK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Andoni--Krauthgamer--Razenshteyn characterization of sketchable norms fails for sketchable metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.FA","math.MG"],"primary_cat":"cs.DS","authors_text":"Assaf Naor, Subhash Khot","submitted_at":"2018-10-10T00:56:59Z","abstract_excerpt":"Andoni, Krauthgamer and Razenshteyn (AKR) proved (STOC 2015) that a finite-dimensional normed space $(X,\\|\\cdot\\|_X)$ admits a $O(1)$ sketching algorithm (namely, with $O(1)$ sketch size and $O(1)$ approximation) if and only if for every $\\varepsilon\\in (0,1)$ there exist $\\alpha\\geqslant 1$ and an embedding $f:X\\to \\ell_{1-\\varepsilon}$ such that $\\|x-y\\|_X\\leqslant \\|f(x)-f(y)\\|_{1-\\varepsilon}\\leqslant \\alpha \\|x-y\\|_X$ for all $x,y\\in X$. The \"if part\" of this theorem follows from a sketching algorithm of Indyk (FOCS 2000). The contribution of AKR is therefore to demonstrate that the mere "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04321","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":"2026-05-18T00:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UBbY0vw9puIAdccr/bzqHXi79d9jmoyn6FgJRK7oMdUxECxdB8iLE4VbZjYKzvBCtdXIGzAFVLwb043XQwuWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:37:53.781955Z"},"content_sha256":"82e00780d6b7d04c981bc2e10fae32990b6b1d1702e835845b3ed18d8b0719ef","schema_version":"1.0","event_id":"sha256:82e00780d6b7d04c981bc2e10fae32990b6b1d1702e835845b3ed18d8b0719ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/bundle.json","state_url":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M63RUUFDS74L56SFEU62TFWHK6/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":"2026-06-23T14:37:53Z","links":{"resolver":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6","bundle":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/bundle.json","state":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M63RUUFDS74L56SFEU62TFWHK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:M63RUUFDS74L56SFEU62TFWHK6","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":"19301ae29481082bc3a97f771ca94c72be8b1fb4963866716528bbf54c04b4d9","cross_cats_sorted":["cs.CG","math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-10T00:56:59Z","title_canon_sha256":"447fab118f675a23ad64579dcba2db52b4f8646023bb93d89f9fcfbdcb295c2a"},"schema_version":"1.0","source":{"id":"1810.04321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04321","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04321v1","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04321","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"M63RUUFDS74L","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M63RUUFDS74L56SF","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M63RUUFD","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:82e00780d6b7d04c981bc2e10fae32990b6b1d1702e835845b3ed18d8b0719ef","target":"graph","created_at":"2026-05-18T00:03:40Z","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":"Andoni, Krauthgamer and Razenshteyn (AKR) proved (STOC 2015) that a finite-dimensional normed space $(X,\\|\\cdot\\|_X)$ admits a $O(1)$ sketching algorithm (namely, with $O(1)$ sketch size and $O(1)$ approximation) if and only if for every $\\varepsilon\\in (0,1)$ there exist $\\alpha\\geqslant 1$ and an embedding $f:X\\to \\ell_{1-\\varepsilon}$ such that $\\|x-y\\|_X\\leqslant \\|f(x)-f(y)\\|_{1-\\varepsilon}\\leqslant \\alpha \\|x-y\\|_X$ for all $x,y\\in X$. The \"if part\" of this theorem follows from a sketching algorithm of Indyk (FOCS 2000). The contribution of AKR is therefore to demonstrate that the mere ","authors_text":"Assaf Naor, Subhash Khot","cross_cats":["cs.CG","math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-10T00:56:59Z","title":"The Andoni--Krauthgamer--Razenshteyn characterization of sketchable norms fails for sketchable metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04321","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:fa48b9fe97b711a7542965c32de7c7b9865da6c0843e8fc921251d8ad618c817","target":"record","created_at":"2026-05-18T00:03:40Z","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":"19301ae29481082bc3a97f771ca94c72be8b1fb4963866716528bbf54c04b4d9","cross_cats_sorted":["cs.CG","math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-10T00:56:59Z","title_canon_sha256":"447fab118f675a23ad64579dcba2db52b4f8646023bb93d89f9fcfbdcb295c2a"},"schema_version":"1.0","source":{"id":"1810.04321","kind":"arxiv","version":1}},"canonical_sha256":"67b71a50a397f8befa45253da996c757826c2e49d6d25e06dc1cc3f29cd7d2aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67b71a50a397f8befa45253da996c757826c2e49d6d25e06dc1cc3f29cd7d2aa","first_computed_at":"2026-05-18T00:03:40.395044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:40.395044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OisGemf09WZDkf4Q8OJpYu78zvH73IG+KyeiMtGhacwqYJmgh5yMmkuoRFbo5sv6mBXCEwd9KPpuGf284oQACA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:40.395519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa48b9fe97b711a7542965c32de7c7b9865da6c0843e8fc921251d8ad618c817","sha256:82e00780d6b7d04c981bc2e10fae32990b6b1d1702e835845b3ed18d8b0719ef"],"state_sha256":"ea583403487973600cbc453fd21bd674c968f1f563980b9614d0b65fd3c7fd13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iV+SoJ6hDtoMLndORuS/mqPZPDDpqMaOHuW5Rc5ghRZNjKd06wqbDGzQFBD2cJmtwJKRquo2L2pOJ74c37ByBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:37:53.783980Z","bundle_sha256":"e6e2f05449131c7e62b7d24b23e4042aa13759b1266bedf0a5ee3710275a23fe"}}