{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DU5WZNXVQNDTVHEZSIAAYV2EAP","short_pith_number":"pith:DU5WZNXV","canonical_record":{"source":{"id":"2607.21975","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T04:41:26Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"09ab28e1f7de202517b986a6522ab2944b172b7d62027a05b67b3a7570be734e","abstract_canon_sha256":"d4b0471a56e490fdfaa929102010f84c303b988a31d6ee860dd5e3ac6b4afb67"},"schema_version":"1.0"},"canonical_sha256":"1d3b6cb6f583473a9c9992000c574403fb0ebf04e683028c053f91bf62b67213","source":{"kind":"arxiv","id":"2607.21975","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21975","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21975v1","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21975","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"pith_short_12","alias_value":"DU5WZNXVQNDT","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"pith_short_16","alias_value":"DU5WZNXVQNDTVHEZ","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"pith_short_8","alias_value":"DU5WZNXV","created_at":"2026-07-27T00:20:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DU5WZNXVQNDTVHEZSIAAYV2EAP","target":"record","payload":{"canonical_record":{"source":{"id":"2607.21975","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T04:41:26Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"09ab28e1f7de202517b986a6522ab2944b172b7d62027a05b67b3a7570be734e","abstract_canon_sha256":"d4b0471a56e490fdfaa929102010f84c303b988a31d6ee860dd5e3ac6b4afb67"},"schema_version":"1.0"},"canonical_sha256":"1d3b6cb6f583473a9c9992000c574403fb0ebf04e683028c053f91bf62b67213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-27T00:20:30.864996Z","signature_b64":"qwj7pTbek9u4PfOQ8Dv0pbepu5d0X6jrYtNcepmUYEFwj0+AEWXDyAnHxtDe3IWasuiwaHWfAJ7ME6/7rPtUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d3b6cb6f583473a9c9992000c574403fb0ebf04e683028c053f91bf62b67213","last_reissued_at":"2026-07-27T00:20:30.864187Z","signature_status":"signed_v1","first_computed_at":"2026-07-27T00:20:30.864187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.21975","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":"2026-07-27T00:20:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5S/RbIziEO+va2e0lNCG4wQuf6gH6FRY9LfcCq5KCp3tWBQfyVJ1gu0bmUZMfDygbMzm18DIok+l10uvHao0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:16:18.017540Z"},"content_sha256":"944e5a58d8cb2c701ef5723e1b666fc6dff84eaae0a22eed27866abfbf04406a","schema_version":"1.0","event_id":"sha256:944e5a58d8cb2c701ef5723e1b666fc6dff84eaae0a22eed27866abfbf04406a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DU5WZNXVQNDTVHEZSIAAYV2EAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Convergence of Stochastic Low-Rank Adaptation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Chengchang Liu, John C.S. Lui, Ru Wang","submitted_at":"2026-07-24T04:41:26Z","abstract_excerpt":"Low-rank adaptation (LoRA) optimizes $J(B,A)=\\mathcal L(W_\\mathrm{base}+sBA)$ over two adapters $B \\in \\mathbb{R}^{m \\times r}$ and $A \\in \\mathbb{R}^{r \\times n}$ that form a low-rank update to a frozen pretrained weight matrix $W_\\mathrm{base} \\in \\mathbb{R}^{m \\times n}$. The prior analysis shows LoRA-GD takes $\\exp\\{\\mathcal{O}(\\epsilon^{-2})\\}$ oracle calls to find an $\\epsilon$-stationary point such that $\\|\\nabla J(B,A)\\|\\leq \\epsilon$ in the deterministic setting. We sharpen the analysis and show that $\\mathcal{O}(\\epsilon^{-4})$ full-gradient evaluations suffice for the same first-ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21975","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.21975/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":"2026-07-27T00:20:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xD2wOY9Nm7/g+BozWnWvT0umOi//ygMkM0LYE38XNd8JY0Cu+ZCe2g453jAs6oQqwgWdBZoyzkehnw/m27X4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:16:18.018067Z"},"content_sha256":"422546789c19f8c223d61e5568d89553437c2e7a32d59356cd620bbf0c60c927","schema_version":"1.0","event_id":"sha256:422546789c19f8c223d61e5568d89553437c2e7a32d59356cd620bbf0c60c927"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DU5WZNXVQNDTVHEZSIAAYV2EAP/bundle.json","state_url":"https://pith.science/pith/DU5WZNXVQNDTVHEZSIAAYV2EAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DU5WZNXVQNDTVHEZSIAAYV2EAP/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":"2026-08-19T22:16:18Z","links":{"resolver":"https://pith.science/pith/DU5WZNXVQNDTVHEZSIAAYV2EAP","bundle":"https://pith.science/pith/DU5WZNXVQNDTVHEZSIAAYV2EAP/bundle.json","state":"https://pith.science/pith/DU5WZNXVQNDTVHEZSIAAYV2EAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DU5WZNXVQNDTVHEZSIAAYV2EAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DU5WZNXVQNDTVHEZSIAAYV2EAP","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":"d4b0471a56e490fdfaa929102010f84c303b988a31d6ee860dd5e3ac6b4afb67","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T04:41:26Z","title_canon_sha256":"09ab28e1f7de202517b986a6522ab2944b172b7d62027a05b67b3a7570be734e"},"schema_version":"1.0","source":{"id":"2607.21975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21975","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21975v1","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21975","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"pith_short_12","alias_value":"DU5WZNXVQNDT","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"pith_short_16","alias_value":"DU5WZNXVQNDTVHEZ","created_at":"2026-07-27T00:20:30Z"},{"alias_kind":"pith_short_8","alias_value":"DU5WZNXV","created_at":"2026-07-27T00:20:30Z"}],"graph_snapshots":[{"event_id":"sha256:422546789c19f8c223d61e5568d89553437c2e7a32d59356cd620bbf0c60c927","target":"graph","created_at":"2026-07-27T00:20:30Z","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/2607.21975/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low-rank adaptation (LoRA) optimizes $J(B,A)=\\mathcal L(W_\\mathrm{base}+sBA)$ over two adapters $B \\in \\mathbb{R}^{m \\times r}$ and $A \\in \\mathbb{R}^{r \\times n}$ that form a low-rank update to a frozen pretrained weight matrix $W_\\mathrm{base} \\in \\mathbb{R}^{m \\times n}$. The prior analysis shows LoRA-GD takes $\\exp\\{\\mathcal{O}(\\epsilon^{-2})\\}$ oracle calls to find an $\\epsilon$-stationary point such that $\\|\\nabla J(B,A)\\|\\leq \\epsilon$ in the deterministic setting. We sharpen the analysis and show that $\\mathcal{O}(\\epsilon^{-4})$ full-gradient evaluations suffice for the same first-ord","authors_text":"Chengchang Liu, John C.S. Lui, Ru Wang","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T04:41:26Z","title":"On the Convergence of Stochastic Low-Rank Adaptation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21975","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":"sha256:944e5a58d8cb2c701ef5723e1b666fc6dff84eaae0a22eed27866abfbf04406a","target":"record","created_at":"2026-07-27T00:20:30Z","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":"d4b0471a56e490fdfaa929102010f84c303b988a31d6ee860dd5e3ac6b4afb67","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T04:41:26Z","title_canon_sha256":"09ab28e1f7de202517b986a6522ab2944b172b7d62027a05b67b3a7570be734e"},"schema_version":"1.0","source":{"id":"2607.21975","kind":"arxiv","version":1}},"canonical_sha256":"1d3b6cb6f583473a9c9992000c574403fb0ebf04e683028c053f91bf62b67213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d3b6cb6f583473a9c9992000c574403fb0ebf04e683028c053f91bf62b67213","first_computed_at":"2026-07-27T00:20:30.864187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T00:20:30.864187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwj7pTbek9u4PfOQ8Dv0pbepu5d0X6jrYtNcepmUYEFwj0+AEWXDyAnHxtDe3IWasuiwaHWfAJ7ME6/7rPtUBw==","signature_status":"signed_v1","signed_at":"2026-07-27T00:20:30.864996Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:944e5a58d8cb2c701ef5723e1b666fc6dff84eaae0a22eed27866abfbf04406a","sha256:422546789c19f8c223d61e5568d89553437c2e7a32d59356cd620bbf0c60c927"],"state_sha256":"3346ab18b0fbb1ce832b17c8260d374490926ae7ec44c25a56c368f198265d3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oje3z+cev7elxym9WpDtDGKUVgLeJKJXfjnJ3wm2Or8pMldkU6TFjnnhE04qYYMOzXr66j6i6LRbt+Rt0GSDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:16:18.022688Z","bundle_sha256":"39fea5740aa9701bd243a0a1e63d8c83a2e67383f9ff1242185cc97fb57c69d4"}}