{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HUYCVFX4Q2ZSLRXPH7FQNBRHKY","short_pith_number":"pith:HUYCVFX4","canonical_record":{"source":{"id":"1810.02429","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T21:22:22Z","cross_cats_sorted":[],"title_canon_sha256":"053204500a73b5c55cc0ebd6cbfaf474d419b328637acaf1bff2dc5302b4c565","abstract_canon_sha256":"b6411eef94f52d1829ee60b20be651491e9452d139b91ec1f6604735718cbe09"},"schema_version":"1.0"},"canonical_sha256":"3d302a96fc86b325c6ef3fcb0686275632142aab2e7c7408ba1d65fbb737e0ea","source":{"kind":"arxiv","id":"1810.02429","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02429","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02429v4","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02429","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"HUYCVFX4Q2ZS","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"pith_short_16","alias_value":"HUYCVFX4Q2ZSLRXP","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"pith_short_8","alias_value":"HUYCVFX4","created_at":"2026-07-05T03:23:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HUYCVFX4Q2ZSLRXPH7FQNBRHKY","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02429","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T21:22:22Z","cross_cats_sorted":[],"title_canon_sha256":"053204500a73b5c55cc0ebd6cbfaf474d419b328637acaf1bff2dc5302b4c565","abstract_canon_sha256":"b6411eef94f52d1829ee60b20be651491e9452d139b91ec1f6604735718cbe09"},"schema_version":"1.0"},"canonical_sha256":"3d302a96fc86b325c6ef3fcb0686275632142aab2e7c7408ba1d65fbb737e0ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:23:35.396799Z","signature_b64":"CdDlFGOFK04Sy5XX7g7CW+p3A14r6wgS5ltLL6EFcRu2c7ThRCNioi4kknHR/RBcoT2EdmPYqSjD+/gjT2FKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d302a96fc86b325c6ef3fcb0686275632142aab2e7c7408ba1d65fbb737e0ea","last_reissued_at":"2026-07-05T03:23:35.396347Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:23:35.396347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02429","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":"2026-07-05T03:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VAKCEAQrlYeKoOp5bWSyA5v1awnKDBzsDBubh51IrLCkjNs+5ulFgg5FfHHty3uOAq7KmNUR5QgyulLLOczNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T20:04:12.210591Z"},"content_sha256":"97bf6ca27269d9d19cc88096e75320e4d6d4827dbb76cb74edb182a336b4ef8d","schema_version":"1.0","event_id":"sha256:97bf6ca27269d9d19cc88096e75320e4d6d4827dbb76cb74edb182a336b4ef8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HUYCVFX4Q2ZSLRXPH7FQNBRHKY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Restarting Frank-Wolfe: Faster Rates Under H\\\"olderian Error Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexandre d'Aspremont, Sebastian Pokutta, Thomas Kerdreux","submitted_at":"2018-10-04T21:22:22Z","abstract_excerpt":"Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While the vanilla Frank-Wolfe algorithm only ensures a worst-case rate of $\\mathcal{O}(1/\\epsilon)$, various recent results have shown that for strongly convex functions on polytopes, the method can be slightly modified to achieve linear convergence. However, this still leaves a huge gap between sublinear $\\mathcal{O}(1/\\epsilon)$ convergence and linear $\\mathcal{O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02429","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.02429/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4OKGyEwnqF3BThwlf3awNgx+R9ZBDiwiykpdBPPSI16GFzfG14FoknEiiAG9tefUMResya0piL+NgvDtNIqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T20:04:12.210961Z"},"content_sha256":"76447f84baa82604b8963a889b25106784da66e20ba1e3fd111e02a8eca97d97","schema_version":"1.0","event_id":"sha256:76447f84baa82604b8963a889b25106784da66e20ba1e3fd111e02a8eca97d97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUYCVFX4Q2ZSLRXPH7FQNBRHKY/bundle.json","state_url":"https://pith.science/pith/HUYCVFX4Q2ZSLRXPH7FQNBRHKY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUYCVFX4Q2ZSLRXPH7FQNBRHKY/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":"2026-07-20T20:04:12Z","links":{"resolver":"https://pith.science/pith/HUYCVFX4Q2ZSLRXPH7FQNBRHKY","bundle":"https://pith.science/pith/HUYCVFX4Q2ZSLRXPH7FQNBRHKY/bundle.json","state":"https://pith.science/pith/HUYCVFX4Q2ZSLRXPH7FQNBRHKY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUYCVFX4Q2ZSLRXPH7FQNBRHKY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HUYCVFX4Q2ZSLRXPH7FQNBRHKY","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":"b6411eef94f52d1829ee60b20be651491e9452d139b91ec1f6604735718cbe09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T21:22:22Z","title_canon_sha256":"053204500a73b5c55cc0ebd6cbfaf474d419b328637acaf1bff2dc5302b4c565"},"schema_version":"1.0","source":{"id":"1810.02429","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02429","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02429v4","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02429","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"HUYCVFX4Q2ZS","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"pith_short_16","alias_value":"HUYCVFX4Q2ZSLRXP","created_at":"2026-07-05T03:23:35Z"},{"alias_kind":"pith_short_8","alias_value":"HUYCVFX4","created_at":"2026-07-05T03:23:35Z"}],"graph_snapshots":[{"event_id":"sha256:76447f84baa82604b8963a889b25106784da66e20ba1e3fd111e02a8eca97d97","target":"graph","created_at":"2026-07-05T03:23:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1810.02429/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While the vanilla Frank-Wolfe algorithm only ensures a worst-case rate of $\\mathcal{O}(1/\\epsilon)$, various recent results have shown that for strongly convex functions on polytopes, the method can be slightly modified to achieve linear convergence. However, this still leaves a huge gap between sublinear $\\mathcal{O}(1/\\epsilon)$ convergence and linear $\\mathcal{O","authors_text":"Alexandre d'Aspremont, Sebastian Pokutta, Thomas Kerdreux","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T21:22:22Z","title":"Restarting Frank-Wolfe: Faster Rates Under H\\\"olderian Error Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02429","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":"sha256:97bf6ca27269d9d19cc88096e75320e4d6d4827dbb76cb74edb182a336b4ef8d","target":"record","created_at":"2026-07-05T03:23:35Z","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":"b6411eef94f52d1829ee60b20be651491e9452d139b91ec1f6604735718cbe09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T21:22:22Z","title_canon_sha256":"053204500a73b5c55cc0ebd6cbfaf474d419b328637acaf1bff2dc5302b4c565"},"schema_version":"1.0","source":{"id":"1810.02429","kind":"arxiv","version":4}},"canonical_sha256":"3d302a96fc86b325c6ef3fcb0686275632142aab2e7c7408ba1d65fbb737e0ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d302a96fc86b325c6ef3fcb0686275632142aab2e7c7408ba1d65fbb737e0ea","first_computed_at":"2026-07-05T03:23:35.396347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:23:35.396347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CdDlFGOFK04Sy5XX7g7CW+p3A14r6wgS5ltLL6EFcRu2c7ThRCNioi4kknHR/RBcoT2EdmPYqSjD+/gjT2FKCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:23:35.396799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02429","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97bf6ca27269d9d19cc88096e75320e4d6d4827dbb76cb74edb182a336b4ef8d","sha256:76447f84baa82604b8963a889b25106784da66e20ba1e3fd111e02a8eca97d97"],"state_sha256":"8d589bb0db0a58e7c005b67347c0ffc2a8b05fca5ae34ce8be620d2b307f3405"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kM/rx5fQG2fjWTxny3eBWcWtuo8nxJUdIYihgSLnpYOGCcGR58PCw9oJgQE7WAN1Oz1Q7eKwQKx1bi3LvYgCCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-20T20:04:12.213100Z","bundle_sha256":"52403492bdfb3806c51a3ba5d448d621463ce66ae4afb8f5d7fd4dee24839922"}}