{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LJ24NCQT2DRMOD4DHMJFZ2Q2YE","short_pith_number":"pith:LJ24NCQT","canonical_record":{"source":{"id":"2305.16186","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T15:43:07Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"6dca9eb5ddf51e92fb503afeb8f6f8d531afc9c522298f811acd927f09187bad","abstract_canon_sha256":"f4afc24142f8dad6f4d9a35bd3c359ad234eb467d9303db10f8179ccb98c5f44"},"schema_version":"1.0"},"canonical_sha256":"5a75c68a13d0e2c70f833b125cea1ac132c541d16b984bc62275b27a7b363e97","source":{"kind":"arxiv","id":"2305.16186","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.16186","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"2305.16186v2","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16186","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"LJ24NCQT2DRM","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"LJ24NCQT2DRMOD4D","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"LJ24NCQT","created_at":"2026-07-05T07:06:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LJ24NCQT2DRMOD4DHMJFZ2Q2YE","target":"record","payload":{"canonical_record":{"source":{"id":"2305.16186","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T15:43:07Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"6dca9eb5ddf51e92fb503afeb8f6f8d531afc9c522298f811acd927f09187bad","abstract_canon_sha256":"f4afc24142f8dad6f4d9a35bd3c359ad234eb467d9303db10f8179ccb98c5f44"},"schema_version":"1.0"},"canonical_sha256":"5a75c68a13d0e2c70f833b125cea1ac132c541d16b984bc62275b27a7b363e97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:06:27.822405Z","signature_b64":"KuotxG+SuzRyDcjh2UaD8B7hjV6y6l/EBNCk60XM9tVaC3hLHh5qk5aWWDFu+yhHoyIUOJ9s+v012x+EgwyXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a75c68a13d0e2c70f833b125cea1ac132c541d16b984bc62275b27a7b363e97","last_reissued_at":"2026-07-05T07:06:27.821923Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:06:27.821923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.16186","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":"2026-07-05T07:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vsdLZJgI9YQ6dIc/IqwXFsDUqP1omCh9w57JM45g+Y8Q7usu4qCY7/iEiHHE14QRRJ7rijCDhjHFhem9I3NzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:10:14.529605Z"},"content_sha256":"d718f4f3a03afb7b8b6750df9d94435615c70a1ffe3b2d5e6f716d75fc1f7425","schema_version":"1.0","event_id":"sha256:d718f4f3a03afb7b8b6750df9d94435615c70a1ffe3b2d5e6f716d75fc1f7425"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LJ24NCQT2DRMOD4DHMJFZ2Q2YE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Christopher Criscitiello, Christophe Roux, David Mart\\'inez-Rubio, Sebastian Pokutta","submitted_at":"2023-05-25T15:43:07Z","abstract_excerpt":"In this work, we study optimization problems of the form $\\min_x \\max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\\mathcal{M} \\times \\mathcal{N}$ and is $\\mu_x$-strongly geodesically convex (g-convex) in $x$ and $\\mu_y$-strongly g-concave in $y$, for $\\mu_x, \\mu_y \\geq 0$. We design accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\\mathcal{M}$, $\\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16186","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.16186/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":"2026-07-05T07:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FiMTAjVHZZ53M7YbPYEQ5Wulr1mP1sqkBImGUVpMucTnXs0/Z3Ptr2xB8oaAw/ZzSnUepf5VhRHIzDVOhpcWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:10:14.529983Z"},"content_sha256":"7eafc8fe09caa6232171cfa7187bb4ff8dfa71d41d0af92f5bc569d44f3783a7","schema_version":"1.0","event_id":"sha256:7eafc8fe09caa6232171cfa7187bb4ff8dfa71d41d0af92f5bc569d44f3783a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJ24NCQT2DRMOD4DHMJFZ2Q2YE/bundle.json","state_url":"https://pith.science/pith/LJ24NCQT2DRMOD4DHMJFZ2Q2YE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJ24NCQT2DRMOD4DHMJFZ2Q2YE/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":"2026-07-06T15:10:14Z","links":{"resolver":"https://pith.science/pith/LJ24NCQT2DRMOD4DHMJFZ2Q2YE","bundle":"https://pith.science/pith/LJ24NCQT2DRMOD4DHMJFZ2Q2YE/bundle.json","state":"https://pith.science/pith/LJ24NCQT2DRMOD4DHMJFZ2Q2YE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJ24NCQT2DRMOD4DHMJFZ2Q2YE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LJ24NCQT2DRMOD4DHMJFZ2Q2YE","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":"f4afc24142f8dad6f4d9a35bd3c359ad234eb467d9303db10f8179ccb98c5f44","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T15:43:07Z","title_canon_sha256":"6dca9eb5ddf51e92fb503afeb8f6f8d531afc9c522298f811acd927f09187bad"},"schema_version":"1.0","source":{"id":"2305.16186","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.16186","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"2305.16186v2","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16186","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"LJ24NCQT2DRM","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"LJ24NCQT2DRMOD4D","created_at":"2026-07-05T07:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"LJ24NCQT","created_at":"2026-07-05T07:06:27Z"}],"graph_snapshots":[{"event_id":"sha256:7eafc8fe09caa6232171cfa7187bb4ff8dfa71d41d0af92f5bc569d44f3783a7","target":"graph","created_at":"2026-07-05T07:06:27Z","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/2305.16186/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we study optimization problems of the form $\\min_x \\max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\\mathcal{M} \\times \\mathcal{N}$ and is $\\mu_x$-strongly geodesically convex (g-convex) in $x$ and $\\mu_y$-strongly g-concave in $y$, for $\\mu_x, \\mu_y \\geq 0$. We design accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\\mathcal{M}$, $\\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve ","authors_text":"Christopher Criscitiello, Christophe Roux, David Mart\\'inez-Rubio, Sebastian Pokutta","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T15:43:07Z","title":"Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16186","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:d718f4f3a03afb7b8b6750df9d94435615c70a1ffe3b2d5e6f716d75fc1f7425","target":"record","created_at":"2026-07-05T07:06:27Z","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":"f4afc24142f8dad6f4d9a35bd3c359ad234eb467d9303db10f8179ccb98c5f44","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-25T15:43:07Z","title_canon_sha256":"6dca9eb5ddf51e92fb503afeb8f6f8d531afc9c522298f811acd927f09187bad"},"schema_version":"1.0","source":{"id":"2305.16186","kind":"arxiv","version":2}},"canonical_sha256":"5a75c68a13d0e2c70f833b125cea1ac132c541d16b984bc62275b27a7b363e97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a75c68a13d0e2c70f833b125cea1ac132c541d16b984bc62275b27a7b363e97","first_computed_at":"2026-07-05T07:06:27.821923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:06:27.821923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KuotxG+SuzRyDcjh2UaD8B7hjV6y6l/EBNCk60XM9tVaC3hLHh5qk5aWWDFu+yhHoyIUOJ9s+v012x+EgwyXDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:06:27.822405Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.16186","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d718f4f3a03afb7b8b6750df9d94435615c70a1ffe3b2d5e6f716d75fc1f7425","sha256:7eafc8fe09caa6232171cfa7187bb4ff8dfa71d41d0af92f5bc569d44f3783a7"],"state_sha256":"b81c0aef7b004fc064ff94a9d551bfa29a4343c4770cbedcea753acd903aeb24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zBnlIsuNVxRPgO5rBMcFPkIdFs1kVCNSSMxaaxYsTKLJFJTYPhiGsEgv5vGWTJXUpsJPmGRKUC3p9VxvbUW+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:10:14.531958Z","bundle_sha256":"4ccd5af606a0cb489a98294f285c7444a4a994500a91d1924ebe0f3e69a53c61"}}