{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PSX4EFBCIN5PS4OFLRIWWOUMIM","short_pith_number":"pith:PSX4EFBC","canonical_record":{"source":{"id":"1809.05043","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-09-13T16:22:19Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5c623184dec78f0dfe1c0fdb4c71eb3d7ab6d85cc028d781a7d6618899ffb702","abstract_canon_sha256":"3c67c22ac85aa25d5e5c8cf72cf9058bffca21056aaed89c43116f13e0f4b354"},"schema_version":"1.0"},"canonical_sha256":"7cafc21422437af971c55c516b3a8c43309cbddfc9779684cfbdf2e8481efba3","source":{"kind":"arxiv","id":"1809.05043","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05043","created_at":"2026-05-18T00:00:18Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05043v4","created_at":"2026-05-18T00:00:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05043","created_at":"2026-05-18T00:00:18Z"},{"alias_kind":"pith_short_12","alias_value":"PSX4EFBCIN5P","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PSX4EFBCIN5PS4OF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PSX4EFBC","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PSX4EFBCIN5PS4OFLRIWWOUMIM","target":"record","payload":{"canonical_record":{"source":{"id":"1809.05043","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-09-13T16:22:19Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5c623184dec78f0dfe1c0fdb4c71eb3d7ab6d85cc028d781a7d6618899ffb702","abstract_canon_sha256":"3c67c22ac85aa25d5e5c8cf72cf9058bffca21056aaed89c43116f13e0f4b354"},"schema_version":"1.0"},"canonical_sha256":"7cafc21422437af971c55c516b3a8c43309cbddfc9779684cfbdf2e8481efba3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:18.051999Z","signature_b64":"QefOC2S0T3mH03ChYgBhAuTQVBkrmttN/5eN9JrodANuF9SZ51VmAZHTKkPVnwBNhY2mlpo6SFgteRrPmzFGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cafc21422437af971c55c516b3a8c43309cbddfc9779684cfbdf2e8481efba3","last_reissued_at":"2026-05-18T00:00:18.051328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:18.051328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.05043","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVT+BuQb+hLME5Pqbyvbc427hQR/W+KP0qE/O6gwfLbKD7+nk9CDNHVx2VvMiLXIKEsUZ3DXp0vm3jdGcFBVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:28:40.757759Z"},"content_sha256":"c88c8289e5dda16d2d32961724c390a57bf80b87c2fd0968a142b9b03d6132bb","schema_version":"1.0","event_id":"sha256:c88c8289e5dda16d2d32961724c390a57bf80b87c2fd0968a142b9b03d6132bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PSX4EFBCIN5PS4OFLRIWWOUMIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PhD Dissertation: Generalized Independent Components Analysis Over Finite Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Amichai Painsky","submitted_at":"2018-09-13T16:22:19Z","abstract_excerpt":"Independent component analysis (ICA) is a statistical method for transforming an observable multi-dimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes a model according to which the observations are generated (such as a linear transformation with additive noise). ICA over finite fields is a special case of ICA in which both the observations and the independent components are over a finite alphabet. In this thesis we consider a formulation of the finite-field case in which an observation vector is decompos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05043","kind":"arxiv","version":4},"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":"2026-05-18T00:00:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W6tzDqFs6RGwShSxeq6ZS097G2nFtL2vmCmCgHvppSVrJIDX41PhpJEOS9hzSetRK/rvMGmUYmdUebu8/ChjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:28:40.758131Z"},"content_sha256":"07b00e84babf54c6b91645bf9ab4bf96a9c534578a7c3b49f4cf5b476884a866","schema_version":"1.0","event_id":"sha256:07b00e84babf54c6b91645bf9ab4bf96a9c534578a7c3b49f4cf5b476884a866"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSX4EFBCIN5PS4OFLRIWWOUMIM/bundle.json","state_url":"https://pith.science/pith/PSX4EFBCIN5PS4OFLRIWWOUMIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSX4EFBCIN5PS4OFLRIWWOUMIM/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":"2026-05-31T14:28:40Z","links":{"resolver":"https://pith.science/pith/PSX4EFBCIN5PS4OFLRIWWOUMIM","bundle":"https://pith.science/pith/PSX4EFBCIN5PS4OFLRIWWOUMIM/bundle.json","state":"https://pith.science/pith/PSX4EFBCIN5PS4OFLRIWWOUMIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSX4EFBCIN5PS4OFLRIWWOUMIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PSX4EFBCIN5PS4OFLRIWWOUMIM","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":"3c67c22ac85aa25d5e5c8cf72cf9058bffca21056aaed89c43116f13e0f4b354","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-09-13T16:22:19Z","title_canon_sha256":"5c623184dec78f0dfe1c0fdb4c71eb3d7ab6d85cc028d781a7d6618899ffb702"},"schema_version":"1.0","source":{"id":"1809.05043","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05043","created_at":"2026-05-18T00:00:18Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05043v4","created_at":"2026-05-18T00:00:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05043","created_at":"2026-05-18T00:00:18Z"},{"alias_kind":"pith_short_12","alias_value":"PSX4EFBCIN5P","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PSX4EFBCIN5PS4OF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PSX4EFBC","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:07b00e84babf54c6b91645bf9ab4bf96a9c534578a7c3b49f4cf5b476884a866","target":"graph","created_at":"2026-05-18T00:00:18Z","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":"Independent component analysis (ICA) is a statistical method for transforming an observable multi-dimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes a model according to which the observations are generated (such as a linear transformation with additive noise). ICA over finite fields is a special case of ICA in which both the observations and the independent components are over a finite alphabet. In this thesis we consider a formulation of the finite-field case in which an observation vector is decompos","authors_text":"Amichai Painsky","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-09-13T16:22:19Z","title":"PhD Dissertation: Generalized Independent Components Analysis Over Finite Alphabets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05043","kind":"arxiv","version":4},"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:c88c8289e5dda16d2d32961724c390a57bf80b87c2fd0968a142b9b03d6132bb","target":"record","created_at":"2026-05-18T00:00:18Z","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":"3c67c22ac85aa25d5e5c8cf72cf9058bffca21056aaed89c43116f13e0f4b354","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-09-13T16:22:19Z","title_canon_sha256":"5c623184dec78f0dfe1c0fdb4c71eb3d7ab6d85cc028d781a7d6618899ffb702"},"schema_version":"1.0","source":{"id":"1809.05043","kind":"arxiv","version":4}},"canonical_sha256":"7cafc21422437af971c55c516b3a8c43309cbddfc9779684cfbdf2e8481efba3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cafc21422437af971c55c516b3a8c43309cbddfc9779684cfbdf2e8481efba3","first_computed_at":"2026-05-18T00:00:18.051328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:18.051328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QefOC2S0T3mH03ChYgBhAuTQVBkrmttN/5eN9JrodANuF9SZ51VmAZHTKkPVnwBNhY2mlpo6SFgteRrPmzFGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:18.051999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.05043","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c88c8289e5dda16d2d32961724c390a57bf80b87c2fd0968a142b9b03d6132bb","sha256:07b00e84babf54c6b91645bf9ab4bf96a9c534578a7c3b49f4cf5b476884a866"],"state_sha256":"c1a763583e6461df022103df5d3c9a7bb5e959b08e255068a1d6aabd927cfa3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fIq08e0FtEMCA+hsl/ztVZmDA6yC8Yzi2hxrdPacUDhGiCTD82RpfKyIbDsgDx2/Z38pif6nz55Atrpm2h53CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:28:40.760716Z","bundle_sha256":"8b39f9639dd4c191d52c83ca625eb615344dc7a8bfe9f0a31981f14422b341d3"}}