{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5HZO665VX7246XWAQY4MN5CMJD","short_pith_number":"pith:5HZO665V","canonical_record":{"source":{"id":"1708.04733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-16T01:10:49Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"51297e13a4331fb78bc47248a6927188e163746cbce8ebe47b16132abfade433","abstract_canon_sha256":"360f52ef418a01fa79892f717a8f4f36100a83865de1826b85a39eb6baf473c5"},"schema_version":"1.0"},"canonical_sha256":"e9f2ef7bb5bff5cf5ec08638c6f44c48fbb91f5f69357754c0495785253ab465","source":{"kind":"arxiv","id":"1708.04733","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04733","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04733v2","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04733","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"5HZO665VX724","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5HZO665VX7246XWA","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5HZO665V","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5HZO665VX7246XWAQY4MN5CMJD","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-16T01:10:49Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"51297e13a4331fb78bc47248a6927188e163746cbce8ebe47b16132abfade433","abstract_canon_sha256":"360f52ef418a01fa79892f717a8f4f36100a83865de1826b85a39eb6baf473c5"},"schema_version":"1.0"},"canonical_sha256":"e9f2ef7bb5bff5cf5ec08638c6f44c48fbb91f5f69357754c0495785253ab465","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:54.133792Z","signature_b64":"8ld7WCjR7Bm0NJmT1L41d/06jC4VpBON9m4t9NK1I2+heEdxH1O4IuKy/Q2l5eLofBf82UuFqiliHQw/xW/NBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9f2ef7bb5bff5cf5ec08638c6f44c48fbb91f5f69357754c0495785253ab465","last_reissued_at":"2026-05-18T00:37:54.133148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:54.133148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04733","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":"2026-05-18T00:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w1Mjcucj+ruI/BP1Jm7KpJiXsps76jkBfOU3jzqTCniiA5TK7lrALwngj/lhdruqGwpe7Q04IynFChCNkbMSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:44:40.049972Z"},"content_sha256":"17b6c5ae952912eca611917b202335a5809635b6fe7052486ac2b799bb293ecd","schema_version":"1.0","event_id":"sha256:17b6c5ae952912eca611917b202335a5809635b6fe7052486ac2b799bb293ecd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5HZO665VX7246XWAQY4MN5CMJD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Enclosing Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Dinh Phung, Hung Vu, Trung Le, Tu Dinh Nguyen","submitted_at":"2017-08-16T01:10:49Z","abstract_excerpt":"Training model to generate data has increasingly attracted research attention and become important in modern world applications. We propose in this paper a new geometry-based optimization approach to address this problem. Orthogonal to current state-of-the-art density-based approaches, most notably VAE and GAN, we present a fresh new idea that borrows the principle of minimal enclosing ball to train a generator G\\left(\\bz\\right) in such a way that both training and generated data, after being mapped to the feature space, are enclosed in the same sphere. We develop theory to guarantee that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04733","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":"2026-05-18T00:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3gwWb1+nvxjTMV3OLc/AlNlmCD8RKJPAyYGBnMFPbwyVdXQv5fOX109x6jWgyu3YwUl91JlIiFG1D7Wf9AVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:44:40.050697Z"},"content_sha256":"b38c83bda7f9275af76f173a299ec3d8c53d89e83cd48e5460f0ea2038db8a43","schema_version":"1.0","event_id":"sha256:b38c83bda7f9275af76f173a299ec3d8c53d89e83cd48e5460f0ea2038db8a43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HZO665VX7246XWAQY4MN5CMJD/bundle.json","state_url":"https://pith.science/pith/5HZO665VX7246XWAQY4MN5CMJD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HZO665VX7246XWAQY4MN5CMJD/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":"2026-06-04T20:44:40Z","links":{"resolver":"https://pith.science/pith/5HZO665VX7246XWAQY4MN5CMJD","bundle":"https://pith.science/pith/5HZO665VX7246XWAQY4MN5CMJD/bundle.json","state":"https://pith.science/pith/5HZO665VX7246XWAQY4MN5CMJD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HZO665VX7246XWAQY4MN5CMJD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5HZO665VX7246XWAQY4MN5CMJD","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":"360f52ef418a01fa79892f717a8f4f36100a83865de1826b85a39eb6baf473c5","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-16T01:10:49Z","title_canon_sha256":"51297e13a4331fb78bc47248a6927188e163746cbce8ebe47b16132abfade433"},"schema_version":"1.0","source":{"id":"1708.04733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04733","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04733v2","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04733","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"5HZO665VX724","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5HZO665VX7246XWA","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5HZO665V","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:b38c83bda7f9275af76f173a299ec3d8c53d89e83cd48e5460f0ea2038db8a43","target":"graph","created_at":"2026-05-18T00:37:54Z","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":"Training model to generate data has increasingly attracted research attention and become important in modern world applications. We propose in this paper a new geometry-based optimization approach to address this problem. Orthogonal to current state-of-the-art density-based approaches, most notably VAE and GAN, we present a fresh new idea that borrows the principle of minimal enclosing ball to train a generator G\\left(\\bz\\right) in such a way that both training and generated data, after being mapped to the feature space, are enclosed in the same sphere. We develop theory to guarantee that the ","authors_text":"Dinh Phung, Hung Vu, Trung Le, Tu Dinh Nguyen","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-16T01:10:49Z","title":"Geometric Enclosing Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04733","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":"sha256:17b6c5ae952912eca611917b202335a5809635b6fe7052486ac2b799bb293ecd","target":"record","created_at":"2026-05-18T00:37:54Z","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":"360f52ef418a01fa79892f717a8f4f36100a83865de1826b85a39eb6baf473c5","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-16T01:10:49Z","title_canon_sha256":"51297e13a4331fb78bc47248a6927188e163746cbce8ebe47b16132abfade433"},"schema_version":"1.0","source":{"id":"1708.04733","kind":"arxiv","version":2}},"canonical_sha256":"e9f2ef7bb5bff5cf5ec08638c6f44c48fbb91f5f69357754c0495785253ab465","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9f2ef7bb5bff5cf5ec08638c6f44c48fbb91f5f69357754c0495785253ab465","first_computed_at":"2026-05-18T00:37:54.133148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:54.133148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ld7WCjR7Bm0NJmT1L41d/06jC4VpBON9m4t9NK1I2+heEdxH1O4IuKy/Q2l5eLofBf82UuFqiliHQw/xW/NBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:54.133792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17b6c5ae952912eca611917b202335a5809635b6fe7052486ac2b799bb293ecd","sha256:b38c83bda7f9275af76f173a299ec3d8c53d89e83cd48e5460f0ea2038db8a43"],"state_sha256":"50c37b65a778861f4d9c2ab14c9b24034b1085f1a0870721a2218f1af84542b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kxn0EZv4nR1JYwXiKvfgBah6lBz+6CRRh1raDkmv8IW/SneDX6I9n3oWcUnPYgNhM/iApLu/WosMwqu3uu7PCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:44:40.054251Z","bundle_sha256":"e6d4af29a7a335875d3451a3cb2a079f87116c8ae71ca604a23d79a5f65df79e"}}