{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2Q2KOZ5P5RKBLV5JCPGWAPLLYH","short_pith_number":"pith:2Q2KOZ5P","canonical_record":{"source":{"id":"1709.06533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-19T17:03:17Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"357cd4e4c63ad57e13e526adf7a95efd61c771c9d0c44cce612e6fd398d0ec2b","abstract_canon_sha256":"462d7384eef324314b11c4ea3e3c446af8d15aaf3545ad5b6e536bdb03973383"},"schema_version":"1.0"},"canonical_sha256":"d434a767afec5415d7a913cd603d6bc1f095bbfc973ee6a61683499d40b895a3","source":{"kind":"arxiv","id":"1709.06533","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06533","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06533v1","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06533","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"2Q2KOZ5P5RKB","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2Q2KOZ5P5RKBLV5J","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2Q2KOZ5P","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2Q2KOZ5P5RKBLV5JCPGWAPLLYH","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-19T17:03:17Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"357cd4e4c63ad57e13e526adf7a95efd61c771c9d0c44cce612e6fd398d0ec2b","abstract_canon_sha256":"462d7384eef324314b11c4ea3e3c446af8d15aaf3545ad5b6e536bdb03973383"},"schema_version":"1.0"},"canonical_sha256":"d434a767afec5415d7a913cd603d6bc1f095bbfc973ee6a61683499d40b895a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:45.450631Z","signature_b64":"ddmBpYq1cZ6oJFgnQ+nqYOdX+OxlGZpFYFzHUn3yn2nEVLanoz7qRT1JFvngABFNlIsGx4rockErzUVZNsmhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d434a767afec5415d7a913cd603d6bc1f095bbfc973ee6a61683499d40b895a3","last_reissued_at":"2026-05-18T00:34:45.449778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:45.449778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06533","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":"2026-05-18T00:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/XL7Wbxy4gAzPvQ6otUzQT9ilPS0jJ0+wvijQylw932ptMzlFOfXXCD46A7mn3moGM2w4gL36k8Tw70Gt0zlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:27:54.761957Z"},"content_sha256":"e054c9440d8f9ab90099e8350a13bd902d1244290c8deb11d77b78285d37354b","schema_version":"1.0","event_id":"sha256:e054c9440d8f9ab90099e8350a13bd902d1244290c8deb11d77b78285d37354b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2Q2KOZ5P5RKBLV5JCPGWAPLLYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Christopher Grimm, Michael L. Littman, Yuhang Song","submitted_at":"2017-09-19T17:03:17Z","abstract_excerpt":"Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing these probabilities, GANs learn a generator that can match the given probabilistic source. This paper looks particularly at this matching capability in the context of problems with one-dimensional outputs. We identify a class of function decompositions with properties that make them well suited to the critic role in a leading approach to GANs known as Wassers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06533","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":"2026-05-18T00:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxn3su4QdMxjZ2heXm3bW00U2F30R4u0HpTk4lSUh+dtwepMLZlQl04l9bvvVayxJM5h7aMRXgqiyqAQl/2ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:27:54.762567Z"},"content_sha256":"495b384ef305718cbcbd42a31a35088d2fb15aa53a869d7e41e9d9f425e49435","schema_version":"1.0","event_id":"sha256:495b384ef305718cbcbd42a31a35088d2fb15aa53a869d7e41e9d9f425e49435"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2Q2KOZ5P5RKBLV5JCPGWAPLLYH/bundle.json","state_url":"https://pith.science/pith/2Q2KOZ5P5RKBLV5JCPGWAPLLYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2Q2KOZ5P5RKBLV5JCPGWAPLLYH/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":"2026-05-30T12:27:54Z","links":{"resolver":"https://pith.science/pith/2Q2KOZ5P5RKBLV5JCPGWAPLLYH","bundle":"https://pith.science/pith/2Q2KOZ5P5RKBLV5JCPGWAPLLYH/bundle.json","state":"https://pith.science/pith/2Q2KOZ5P5RKBLV5JCPGWAPLLYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2Q2KOZ5P5RKBLV5JCPGWAPLLYH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2Q2KOZ5P5RKBLV5JCPGWAPLLYH","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":"462d7384eef324314b11c4ea3e3c446af8d15aaf3545ad5b6e536bdb03973383","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-19T17:03:17Z","title_canon_sha256":"357cd4e4c63ad57e13e526adf7a95efd61c771c9d0c44cce612e6fd398d0ec2b"},"schema_version":"1.0","source":{"id":"1709.06533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06533","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06533v1","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06533","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"2Q2KOZ5P5RKB","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2Q2KOZ5P5RKBLV5J","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2Q2KOZ5P","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:495b384ef305718cbcbd42a31a35088d2fb15aa53a869d7e41e9d9f425e49435","target":"graph","created_at":"2026-05-18T00:34:45Z","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":"Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing these probabilities, GANs learn a generator that can match the given probabilistic source. This paper looks particularly at this matching capability in the context of problems with one-dimensional outputs. We identify a class of function decompositions with properties that make them well suited to the critic role in a leading approach to GANs known as Wassers","authors_text":"Christopher Grimm, Michael L. Littman, Yuhang Song","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-19T17:03:17Z","title":"Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06533","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:e054c9440d8f9ab90099e8350a13bd902d1244290c8deb11d77b78285d37354b","target":"record","created_at":"2026-05-18T00:34:45Z","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":"462d7384eef324314b11c4ea3e3c446af8d15aaf3545ad5b6e536bdb03973383","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-19T17:03:17Z","title_canon_sha256":"357cd4e4c63ad57e13e526adf7a95efd61c771c9d0c44cce612e6fd398d0ec2b"},"schema_version":"1.0","source":{"id":"1709.06533","kind":"arxiv","version":1}},"canonical_sha256":"d434a767afec5415d7a913cd603d6bc1f095bbfc973ee6a61683499d40b895a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d434a767afec5415d7a913cd603d6bc1f095bbfc973ee6a61683499d40b895a3","first_computed_at":"2026-05-18T00:34:45.449778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:45.449778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ddmBpYq1cZ6oJFgnQ+nqYOdX+OxlGZpFYFzHUn3yn2nEVLanoz7qRT1JFvngABFNlIsGx4rockErzUVZNsmhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:45.450631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e054c9440d8f9ab90099e8350a13bd902d1244290c8deb11d77b78285d37354b","sha256:495b384ef305718cbcbd42a31a35088d2fb15aa53a869d7e41e9d9f425e49435"],"state_sha256":"2fcd57a72d767ab1c39111ceb1f95fa2f81a7eb8c036a1c85c994054b7b7b9ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3GNuR7NWb3BjvilDZ1NREoYSlb7tvao2j4BHoHJUa5e2nOw1YUQi25TCuVrurEThmLtjnequrKjQ3OTQps5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:27:54.765736Z","bundle_sha256":"a32ab86af32d0410b210a1c6a89dd39cdc15c170132dd0470f553ab4966ed8dc"}}