{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TRXBELS2K5ZD2CW6L4MN3INVI7","short_pith_number":"pith:TRXBELS2","canonical_record":{"source":{"id":"1607.04331","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-14T21:43:39Z","cross_cats_sorted":["cs.LG","q-bio.NC"],"title_canon_sha256":"d84b65ffb2db6342866aafd415f104a7aeeccad462532d84d1a4137f10e63749","abstract_canon_sha256":"7b9aebc8e1d7d296f3ae2ae8c64fdd5d079a6dccb210845284201397b1784e10"},"schema_version":"1.0"},"canonical_sha256":"9c6e122e5a57723d0ade5f18dda1b547e3f908ff7a29855ae0affaf1fb4c0e41","source":{"kind":"arxiv","id":"1607.04331","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04331","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04331v2","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04331","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"TRXBELS2K5ZD","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRXBELS2K5ZD2CW6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRXBELS2","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TRXBELS2K5ZD2CW6L4MN3INVI7","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04331","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-14T21:43:39Z","cross_cats_sorted":["cs.LG","q-bio.NC"],"title_canon_sha256":"d84b65ffb2db6342866aafd415f104a7aeeccad462532d84d1a4137f10e63749","abstract_canon_sha256":"7b9aebc8e1d7d296f3ae2ae8c64fdd5d079a6dccb210845284201397b1784e10"},"schema_version":"1.0"},"canonical_sha256":"9c6e122e5a57723d0ade5f18dda1b547e3f908ff7a29855ae0affaf1fb4c0e41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:49.590583Z","signature_b64":"YLQPzVzKfyV47CiV2fzfqufP9zL52tNKdrYNNhpN84Q2uAkRZAIsNY0F0mef6nKSQmXFRXXmmC+tl5omoGyXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c6e122e5a57723d0ade5f18dda1b547e3f908ff7a29855ae0affaf1fb4c0e41","last_reissued_at":"2026-05-18T01:04:49.590220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:49.590220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04331","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":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUxyvZw44P5sJr4DbSyih1yPPSKh8s/zyEro703qICc8pR3iX/rfVk41lgU/tSEJqdDxMi6sigVjc319DpfJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:21:40.615074Z"},"content_sha256":"5e3794ac4ec856077de6b3384abb2950e73ff986798f719151494b6ad2a7e08c","schema_version":"1.0","event_id":"sha256:5e3794ac4ec856077de6b3384abb2950e73ff986798f719151494b6ad2a7e08c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TRXBELS2K5ZD2CW6L4MN3INVI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random projections of random manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","q-bio.NC"],"primary_cat":"stat.ML","authors_text":"Peiran Gao, Subhaneil Lahiri, Surya Ganguli","submitted_at":"2016-07-14T21:43:39Z","abstract_excerpt":"Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on how many projections are needed to accurately preserve the geometry of these manifolds, given their intrinsic dimensionality, volume and curvature. However, such works employ definitions of volume and curvature that are inherently difficult to compute. Therefore such theory cannot be easily tested against numerical simulations to understand the tightness of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04331","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":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FlUjuBjvPwkYvKIXfhcIHWY5q0jmbzgIPnb2hxL774CTMfL2Nm5gOy/cqt28deoIQBvurZqplVhpkuyvJXByBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:21:40.615826Z"},"content_sha256":"85047576d723e0708c484f7373349fb5d3604c961af8e59572a10597e633fc98","schema_version":"1.0","event_id":"sha256:85047576d723e0708c484f7373349fb5d3604c961af8e59572a10597e633fc98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRXBELS2K5ZD2CW6L4MN3INVI7/bundle.json","state_url":"https://pith.science/pith/TRXBELS2K5ZD2CW6L4MN3INVI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRXBELS2K5ZD2CW6L4MN3INVI7/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":"2026-06-06T12:21:40Z","links":{"resolver":"https://pith.science/pith/TRXBELS2K5ZD2CW6L4MN3INVI7","bundle":"https://pith.science/pith/TRXBELS2K5ZD2CW6L4MN3INVI7/bundle.json","state":"https://pith.science/pith/TRXBELS2K5ZD2CW6L4MN3INVI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRXBELS2K5ZD2CW6L4MN3INVI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TRXBELS2K5ZD2CW6L4MN3INVI7","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":"7b9aebc8e1d7d296f3ae2ae8c64fdd5d079a6dccb210845284201397b1784e10","cross_cats_sorted":["cs.LG","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-14T21:43:39Z","title_canon_sha256":"d84b65ffb2db6342866aafd415f104a7aeeccad462532d84d1a4137f10e63749"},"schema_version":"1.0","source":{"id":"1607.04331","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04331","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04331v2","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04331","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"TRXBELS2K5ZD","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRXBELS2K5ZD2CW6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRXBELS2","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:85047576d723e0708c484f7373349fb5d3604c961af8e59572a10597e633fc98","target":"graph","created_at":"2026-05-18T01:04:49Z","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":"Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on how many projections are needed to accurately preserve the geometry of these manifolds, given their intrinsic dimensionality, volume and curvature. However, such works employ definitions of volume and curvature that are inherently difficult to compute. Therefore such theory cannot be easily tested against numerical simulations to understand the tightness of ","authors_text":"Peiran Gao, Subhaneil Lahiri, Surya Ganguli","cross_cats":["cs.LG","q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-14T21:43:39Z","title":"Random projections of random manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04331","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":"sha256:5e3794ac4ec856077de6b3384abb2950e73ff986798f719151494b6ad2a7e08c","target":"record","created_at":"2026-05-18T01:04:49Z","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":"7b9aebc8e1d7d296f3ae2ae8c64fdd5d079a6dccb210845284201397b1784e10","cross_cats_sorted":["cs.LG","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-14T21:43:39Z","title_canon_sha256":"d84b65ffb2db6342866aafd415f104a7aeeccad462532d84d1a4137f10e63749"},"schema_version":"1.0","source":{"id":"1607.04331","kind":"arxiv","version":2}},"canonical_sha256":"9c6e122e5a57723d0ade5f18dda1b547e3f908ff7a29855ae0affaf1fb4c0e41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c6e122e5a57723d0ade5f18dda1b547e3f908ff7a29855ae0affaf1fb4c0e41","first_computed_at":"2026-05-18T01:04:49.590220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:49.590220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YLQPzVzKfyV47CiV2fzfqufP9zL52tNKdrYNNhpN84Q2uAkRZAIsNY0F0mef6nKSQmXFRXXmmC+tl5omoGyXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:49.590583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04331","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e3794ac4ec856077de6b3384abb2950e73ff986798f719151494b6ad2a7e08c","sha256:85047576d723e0708c484f7373349fb5d3604c961af8e59572a10597e633fc98"],"state_sha256":"b375bfe843957c14a6ef0fa866f197d0b9e27e8fe203002c0b39099f693a4587"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yYFvp2aF0x+I8g3SGD5HqHiz3iFv4dmfZOXXv9y8rd5r1z3fRPqchaUk2QqEqIT1b5zmNF96KdpR3z6XkyLWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T12:21:40.619809Z","bundle_sha256":"832d1e23cf14a775aa76eeffe40a8c4120a4a3d570ebeadcf0f0bb5e7f8aa244"}}