{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XV2CVNBDWF7D5IQGUVGQRRGSA2","short_pith_number":"pith:XV2CVNBD","canonical_record":{"source":{"id":"1608.01844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SD","submitted_at":"2016-08-05T11:48:58Z","cross_cats_sorted":[],"title_canon_sha256":"2b6ab342c27b5d5b77362b19527080500716bfe01bda1c6d9a25cd1fb0929a7c","abstract_canon_sha256":"9ab43bed93117253e72852954117c92a902e67b6cdd8dd8bc16fe839e78e3124"},"schema_version":"1.0"},"canonical_sha256":"bd742ab423b17e3ea206a54d08c4d206bfa6fe0e49d0c03748eac0d0a87b93a0","source":{"kind":"arxiv","id":"1608.01844","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01844","created_at":"2026-05-18T00:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01844v2","created_at":"2026-05-18T00:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01844","created_at":"2026-05-18T00:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"XV2CVNBDWF7D","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XV2CVNBDWF7D5IQG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XV2CVNBD","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XV2CVNBDWF7D5IQGUVGQRRGSA2","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SD","submitted_at":"2016-08-05T11:48:58Z","cross_cats_sorted":[],"title_canon_sha256":"2b6ab342c27b5d5b77362b19527080500716bfe01bda1c6d9a25cd1fb0929a7c","abstract_canon_sha256":"9ab43bed93117253e72852954117c92a902e67b6cdd8dd8bc16fe839e78e3124"},"schema_version":"1.0"},"canonical_sha256":"bd742ab423b17e3ea206a54d08c4d206bfa6fe0e49d0c03748eac0d0a87b93a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:57.618338Z","signature_b64":"mp/hhM2KWcafkp7jz3diO8HxBi76wDUoA6w9GBzSn8wBT16+G/vRpmC49bkJROTB4DgXMUJQ3EFqJKOdUtftBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd742ab423b17e3ea206a54d08c4d206bfa6fe0e49d0c03748eac0d0a87b93a0","last_reissued_at":"2026-05-18T00:59:57.617866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:57.617866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01844","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":"2026-05-18T00:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BOkF4mLQvnsntgpYbEQpa5XLFhrdeektpYaPgd+s4WW+cSvkna2qiNWOqP1mg1zhGucTSB730ITt0die8wRZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:13:50.525543Z"},"content_sha256":"955f4174b7caca3d4bdf0b7a44d69319bb40d05f9bc53ebc283ab9ffcb8787a5","schema_version":"1.0","event_id":"sha256:955f4174b7caca3d4bdf0b7a44d69319bb40d05f9bc53ebc283ab9ffcb8787a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XV2CVNBDWF7D5IQGUVGQRRGSA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"L\\'evy NMF for robust nonnegative source separation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SD","authors_text":"Antoine Liutkus, Paul Magron, Roland Badeau","submitted_at":"2016-08-05T11:48:58Z","abstract_excerpt":"Source separation, which consists in decomposing data into meaningful structured components, is an active research topic in many areas, such as music and image signal processing, applied physics and text mining. In this paper, we introduce the Positive $\\alpha$-stable (P$\\alpha$S) distributions to model the latent sources, which are a subclass of the stable distributions family. They notably permit us to model random variables that are both nonnegative and impulsive. Considering the L\\'evy distribution, the only P$\\alpha$S distribution whose density is tractable, we propose a mixture model cal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01844","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":"2026-05-18T00:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OXl0um43++NTXksWYhFpliEINvHsNihFg9fKXAo3sw7mIPJWb7bmYoHl9ItfKjHjmhSOhdP0mUr+pZKjxeEqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:13:50.525892Z"},"content_sha256":"828b2b86a4893cbb0900fa3db7c3917bcb727338c77d2839b63dad8436d314fb","schema_version":"1.0","event_id":"sha256:828b2b86a4893cbb0900fa3db7c3917bcb727338c77d2839b63dad8436d314fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XV2CVNBDWF7D5IQGUVGQRRGSA2/bundle.json","state_url":"https://pith.science/pith/XV2CVNBDWF7D5IQGUVGQRRGSA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XV2CVNBDWF7D5IQGUVGQRRGSA2/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":"2026-06-03T16:13:50Z","links":{"resolver":"https://pith.science/pith/XV2CVNBDWF7D5IQGUVGQRRGSA2","bundle":"https://pith.science/pith/XV2CVNBDWF7D5IQGUVGQRRGSA2/bundle.json","state":"https://pith.science/pith/XV2CVNBDWF7D5IQGUVGQRRGSA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XV2CVNBDWF7D5IQGUVGQRRGSA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XV2CVNBDWF7D5IQGUVGQRRGSA2","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":"9ab43bed93117253e72852954117c92a902e67b6cdd8dd8bc16fe839e78e3124","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SD","submitted_at":"2016-08-05T11:48:58Z","title_canon_sha256":"2b6ab342c27b5d5b77362b19527080500716bfe01bda1c6d9a25cd1fb0929a7c"},"schema_version":"1.0","source":{"id":"1608.01844","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01844","created_at":"2026-05-18T00:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01844v2","created_at":"2026-05-18T00:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01844","created_at":"2026-05-18T00:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"XV2CVNBDWF7D","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XV2CVNBDWF7D5IQG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XV2CVNBD","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:828b2b86a4893cbb0900fa3db7c3917bcb727338c77d2839b63dad8436d314fb","target":"graph","created_at":"2026-05-18T00:59:57Z","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":"Source separation, which consists in decomposing data into meaningful structured components, is an active research topic in many areas, such as music and image signal processing, applied physics and text mining. In this paper, we introduce the Positive $\\alpha$-stable (P$\\alpha$S) distributions to model the latent sources, which are a subclass of the stable distributions family. They notably permit us to model random variables that are both nonnegative and impulsive. Considering the L\\'evy distribution, the only P$\\alpha$S distribution whose density is tractable, we propose a mixture model cal","authors_text":"Antoine Liutkus, Paul Magron, Roland Badeau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SD","submitted_at":"2016-08-05T11:48:58Z","title":"L\\'evy NMF for robust nonnegative source separation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01844","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":"sha256:955f4174b7caca3d4bdf0b7a44d69319bb40d05f9bc53ebc283ab9ffcb8787a5","target":"record","created_at":"2026-05-18T00:59:57Z","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":"9ab43bed93117253e72852954117c92a902e67b6cdd8dd8bc16fe839e78e3124","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SD","submitted_at":"2016-08-05T11:48:58Z","title_canon_sha256":"2b6ab342c27b5d5b77362b19527080500716bfe01bda1c6d9a25cd1fb0929a7c"},"schema_version":"1.0","source":{"id":"1608.01844","kind":"arxiv","version":2}},"canonical_sha256":"bd742ab423b17e3ea206a54d08c4d206bfa6fe0e49d0c03748eac0d0a87b93a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd742ab423b17e3ea206a54d08c4d206bfa6fe0e49d0c03748eac0d0a87b93a0","first_computed_at":"2026-05-18T00:59:57.617866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:57.617866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mp/hhM2KWcafkp7jz3diO8HxBi76wDUoA6w9GBzSn8wBT16+G/vRpmC49bkJROTB4DgXMUJQ3EFqJKOdUtftBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:57.618338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01844","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:955f4174b7caca3d4bdf0b7a44d69319bb40d05f9bc53ebc283ab9ffcb8787a5","sha256:828b2b86a4893cbb0900fa3db7c3917bcb727338c77d2839b63dad8436d314fb"],"state_sha256":"d1aa3ee273fc1a27c314954b2b0595dc4ec3b7609ef4f72ea17a5d9ade23b27c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2iKFl3F/N2WMhz8jXidsFS4Nzw3utktlMXrLgfBZfAxdbJVBCYOkcNeOni33O01/e7hvlLeI3my1iKsjmi3SCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:13:50.527848Z","bundle_sha256":"38a7a05a76e324765c6ecffff3f0006d88901de0b2a02f63997b6517db855424"}}