{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MAJVHFOLUDWOFILNWNJIJTGGPK","short_pith_number":"pith:MAJVHFOL","canonical_record":{"source":{"id":"1209.6281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-27T16:46:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"deb9f67ebfc55a0185c316f8becfe64dd649e0478fdfe4c6e89c8455aa44e7b5","abstract_canon_sha256":"3f41c35cd7c501b13bb0f82a373a6388703ede9ef28f1a88a3f25be35f8673b2"},"schema_version":"1.0"},"canonical_sha256":"60135395cba0ece2a16db35284ccc67a85c7f411b6143e39362c958858e4521f","source":{"kind":"arxiv","id":"1209.6281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6281","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6281v1","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6281","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"pith_short_12","alias_value":"MAJVHFOLUDWO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MAJVHFOLUDWOFILN","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MAJVHFOL","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MAJVHFOLUDWOFILNWNJIJTGGPK","target":"record","payload":{"canonical_record":{"source":{"id":"1209.6281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-27T16:46:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"deb9f67ebfc55a0185c316f8becfe64dd649e0478fdfe4c6e89c8455aa44e7b5","abstract_canon_sha256":"3f41c35cd7c501b13bb0f82a373a6388703ede9ef28f1a88a3f25be35f8673b2"},"schema_version":"1.0"},"canonical_sha256":"60135395cba0ece2a16db35284ccc67a85c7f411b6143e39362c958858e4521f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:34.738992Z","signature_b64":"xZEnJCtxgYsiyo04GL0dhMeDkgHJ4+nnhE3Zn0o/4Qxxn5Z1+JFI7Ok+bQb9EA4W+UeDVGdm7PFvDOJqLW+/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60135395cba0ece2a16db35284ccc67a85c7f411b6143e39362c958858e4521f","last_reissued_at":"2026-05-18T03:44:34.738171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:34.738171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.6281","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":"2026-05-18T03:44:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fny9IGGJ3YqYOiZY0mx98n+VjSrYhjIyCcXwYJbjZ792wl0ptfcvwhU4/uqDbeWMdndb2sMGcyhNtNyjLRh/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:52:42.476493Z"},"content_sha256":"4e523f43b15f779d7a4042fb90f0d5665be81c0b06a153b8847fbc44bf5a1b64","schema_version":"1.0","event_id":"sha256:4e523f43b15f779d7a4042fb90f0d5665be81c0b06a153b8847fbc44bf5a1b64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MAJVHFOLUDWOFILNWNJIJTGGPK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On approximations by projections of polytopes with few facets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Alexander E. Litvak, Mark Rudelson, Nicole Tomczak-Jaegermann","submitted_at":"2012-09-27T16:46:07Z","abstract_excerpt":"We provide an affirmative answer to a problem posed by Barvinok and Veomett, showing that in general an n-dimensional convex body cannot be approximated by a projection of a section of a simplex of a sub-exponential dimension. Moreover, we establish a lower bound of the Banach-Mazur distance between n-dimensional projections of sections of an N-dimensional simplex and a certain convex symmetric body, which is sharp up to a logarithmic factor for all N>n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6281","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":"2026-05-18T03:44:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jTaxoDLRJYOsC+xhzX324pgwxktXkQeKllQQ7kZwmjqU5rMf/uTIA4OMzLnuEw9AwcwaD8KciHulqpvVCA4vDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:52:42.476844Z"},"content_sha256":"a9cdf8fcaa0aec00493525f7c802262f25852bc653da8864054bc98f09f65aa5","schema_version":"1.0","event_id":"sha256:a9cdf8fcaa0aec00493525f7c802262f25852bc653da8864054bc98f09f65aa5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MAJVHFOLUDWOFILNWNJIJTGGPK/bundle.json","state_url":"https://pith.science/pith/MAJVHFOLUDWOFILNWNJIJTGGPK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MAJVHFOLUDWOFILNWNJIJTGGPK/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":"2026-06-02T13:52:42Z","links":{"resolver":"https://pith.science/pith/MAJVHFOLUDWOFILNWNJIJTGGPK","bundle":"https://pith.science/pith/MAJVHFOLUDWOFILNWNJIJTGGPK/bundle.json","state":"https://pith.science/pith/MAJVHFOLUDWOFILNWNJIJTGGPK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MAJVHFOLUDWOFILNWNJIJTGGPK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MAJVHFOLUDWOFILNWNJIJTGGPK","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":"3f41c35cd7c501b13bb0f82a373a6388703ede9ef28f1a88a3f25be35f8673b2","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-27T16:46:07Z","title_canon_sha256":"deb9f67ebfc55a0185c316f8becfe64dd649e0478fdfe4c6e89c8455aa44e7b5"},"schema_version":"1.0","source":{"id":"1209.6281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6281","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6281v1","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6281","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"pith_short_12","alias_value":"MAJVHFOLUDWO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MAJVHFOLUDWOFILN","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MAJVHFOL","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:a9cdf8fcaa0aec00493525f7c802262f25852bc653da8864054bc98f09f65aa5","target":"graph","created_at":"2026-05-18T03:44:34Z","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 provide an affirmative answer to a problem posed by Barvinok and Veomett, showing that in general an n-dimensional convex body cannot be approximated by a projection of a section of a simplex of a sub-exponential dimension. Moreover, we establish a lower bound of the Banach-Mazur distance between n-dimensional projections of sections of an N-dimensional simplex and a certain convex symmetric body, which is sharp up to a logarithmic factor for all N>n.","authors_text":"Alexander E. Litvak, Mark Rudelson, Nicole Tomczak-Jaegermann","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-27T16:46:07Z","title":"On approximations by projections of polytopes with few facets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6281","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":"sha256:4e523f43b15f779d7a4042fb90f0d5665be81c0b06a153b8847fbc44bf5a1b64","target":"record","created_at":"2026-05-18T03:44:34Z","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":"3f41c35cd7c501b13bb0f82a373a6388703ede9ef28f1a88a3f25be35f8673b2","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-27T16:46:07Z","title_canon_sha256":"deb9f67ebfc55a0185c316f8becfe64dd649e0478fdfe4c6e89c8455aa44e7b5"},"schema_version":"1.0","source":{"id":"1209.6281","kind":"arxiv","version":1}},"canonical_sha256":"60135395cba0ece2a16db35284ccc67a85c7f411b6143e39362c958858e4521f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60135395cba0ece2a16db35284ccc67a85c7f411b6143e39362c958858e4521f","first_computed_at":"2026-05-18T03:44:34.738171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:34.738171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xZEnJCtxgYsiyo04GL0dhMeDkgHJ4+nnhE3Zn0o/4Qxxn5Z1+JFI7Ok+bQb9EA4W+UeDVGdm7PFvDOJqLW+/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:34.738992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.6281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e523f43b15f779d7a4042fb90f0d5665be81c0b06a153b8847fbc44bf5a1b64","sha256:a9cdf8fcaa0aec00493525f7c802262f25852bc653da8864054bc98f09f65aa5"],"state_sha256":"c4b9e4de45ceccbbb0b22fe0b36b94d2b1696f3447e9758a2c91b43e2c8f5b0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XoBDwtvDILwoiBTr/riVitxWExrTEoa0XfNZmq8CSA2x5DAOVMaQiX0nCAMwBJJVDJRgIEdcTCDYsIhOWKaRDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:52:42.478856Z","bundle_sha256":"d27b9f3e326f275227ee5a933e6be0970fc675afd84a3445c1be43e6aad68c4e"}}