{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JQQ2KTVMTTYWWMIXLC3PK5T5ED","short_pith_number":"pith:JQQ2KTVM","canonical_record":{"source":{"id":"2607.27680","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-30T04:56:27Z","cross_cats_sorted":["cs.CL"],"title_canon_sha256":"149a7f82d80415e9fde51b0ebff4e3672d4ad5ae50d912c8a30a970e18adf547","abstract_canon_sha256":"cb007abb7c98b6c7438e56ea13b32fbec6e9c47c80f5ca60abe8edf2043bace4"},"schema_version":"1.0"},"canonical_sha256":"4c21a54eac9cf16b311758b6f5767d20f63bbdf095d890fd9cc85bff615cf8a5","source":{"kind":"arxiv","id":"2607.27680","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27680","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27680v1","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27680","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"pith_short_12","alias_value":"JQQ2KTVMTTYW","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"JQQ2KTVMTTYWWMIX","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"JQQ2KTVM","created_at":"2026-07-31T01:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JQQ2KTVMTTYWWMIXLC3PK5T5ED","target":"record","payload":{"canonical_record":{"source":{"id":"2607.27680","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-30T04:56:27Z","cross_cats_sorted":["cs.CL"],"title_canon_sha256":"149a7f82d80415e9fde51b0ebff4e3672d4ad5ae50d912c8a30a970e18adf547","abstract_canon_sha256":"cb007abb7c98b6c7438e56ea13b32fbec6e9c47c80f5ca60abe8edf2043bace4"},"schema_version":"1.0"},"canonical_sha256":"4c21a54eac9cf16b311758b6f5767d20f63bbdf095d890fd9cc85bff615cf8a5","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c21a54eac9cf16b311758b6f5767d20f63bbdf095d890fd9cc85bff615cf8a5","last_reissued_at":"2026-07-31T01:29:42.861396Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:29:42.861396Z"},"source_kind":"arxiv","source_id":"2607.27680","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":"2026-07-31T01:29:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J2w1tUdm4JILvtRFHkfTIru6Iu56mPUHVlnqbFHLqAOpHQy5AHJdUr96xA1m9qTPmrW0pLwjSRDWmTEf97doAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:35:23.063662Z"},"content_sha256":"3743417e33f4cf733b14d203193c9167b63b292aa99daf8334dd763c78500d55","schema_version":"1.0","event_id":"sha256:3743417e33f4cf733b14d203193c9167b63b292aa99daf8334dd763c78500d55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JQQ2KTVMTTYWWMIXLC3PK5T5ED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight Sample Complexity for Low-Rank Adaptation: Matching Bounds and Rank Selection","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CL"],"primary_cat":"cs.LG","authors_text":"Arunan J","submitted_at":"2026-07-30T04:56:27Z","abstract_excerpt":"Low-Rank Adaptation (LoRA) has become the standard mechanism for fine-tuning large pretrained models, yet its statistical properties remain only partially understood. Existing generalization results provide upper bounds of the form O~(sqrt(rd/n)) or O~(rd/n), but a matching lower bound is missing, and the question of how to choose the LoRA rank r has no formal answer. Both gaps are closed here. A local Rademacher argument establishes an upper bound of O~(rd/n) on the excess risk of the empirical risk minimizer over rank-r LoRA, whenever the target adaptation has rank at most r. A matching mini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27680","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/2607.27680/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":"2026-07-31T01:29:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAwUB01JYEF75cicdLfLV8Y66rAiJN410aHVZRygzEK4zCBSA0dSz9TSRoSfrHCp/+EDtaefuFL3vDTYQrjACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:35:23.064444Z"},"content_sha256":"c9c6b140cf69f7e0a6c789e04bcf975da2384d8ba2b66c34f0ff76d409c4bb28","schema_version":"1.0","event_id":"sha256:c9c6b140cf69f7e0a6c789e04bcf975da2384d8ba2b66c34f0ff76d409c4bb28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQQ2KTVMTTYWWMIXLC3PK5T5ED/bundle.json","state_url":"https://pith.science/pith/JQQ2KTVMTTYWWMIXLC3PK5T5ED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQQ2KTVMTTYWWMIXLC3PK5T5ED/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":"2026-08-09T02:35:23Z","links":{"resolver":"https://pith.science/pith/JQQ2KTVMTTYWWMIXLC3PK5T5ED","bundle":"https://pith.science/pith/JQQ2KTVMTTYWWMIXLC3PK5T5ED/bundle.json","state":"https://pith.science/pith/JQQ2KTVMTTYWWMIXLC3PK5T5ED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQQ2KTVMTTYWWMIXLC3PK5T5ED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JQQ2KTVMTTYWWMIXLC3PK5T5ED","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":"cb007abb7c98b6c7438e56ea13b32fbec6e9c47c80f5ca60abe8edf2043bace4","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-30T04:56:27Z","title_canon_sha256":"149a7f82d80415e9fde51b0ebff4e3672d4ad5ae50d912c8a30a970e18adf547"},"schema_version":"1.0","source":{"id":"2607.27680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27680","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27680v1","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27680","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"pith_short_12","alias_value":"JQQ2KTVMTTYW","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"JQQ2KTVMTTYWWMIX","created_at":"2026-07-31T01:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"JQQ2KTVM","created_at":"2026-07-31T01:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:c9c6b140cf69f7e0a6c789e04bcf975da2384d8ba2b66c34f0ff76d409c4bb28","target":"graph","created_at":"2026-07-31T01:29:42Z","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/2607.27680/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low-Rank Adaptation (LoRA) has become the standard mechanism for fine-tuning large pretrained models, yet its statistical properties remain only partially understood. Existing generalization results provide upper bounds of the form O~(sqrt(rd/n)) or O~(rd/n), but a matching lower bound is missing, and the question of how to choose the LoRA rank r has no formal answer. Both gaps are closed here. A local Rademacher argument establishes an upper bound of O~(rd/n) on the excess risk of the empirical risk minimizer over rank-r LoRA, whenever the target adaptation has rank at most r. A matching mini","authors_text":"Arunan J","cross_cats":["cs.CL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-30T04:56:27Z","title":"Tight Sample Complexity for Low-Rank Adaptation: Matching Bounds and Rank Selection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27680","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":"sha256:3743417e33f4cf733b14d203193c9167b63b292aa99daf8334dd763c78500d55","target":"record","created_at":"2026-07-31T01:29:42Z","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":"cb007abb7c98b6c7438e56ea13b32fbec6e9c47c80f5ca60abe8edf2043bace4","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-30T04:56:27Z","title_canon_sha256":"149a7f82d80415e9fde51b0ebff4e3672d4ad5ae50d912c8a30a970e18adf547"},"schema_version":"1.0","source":{"id":"2607.27680","kind":"arxiv","version":1}},"canonical_sha256":"4c21a54eac9cf16b311758b6f5767d20f63bbdf095d890fd9cc85bff615cf8a5","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c21a54eac9cf16b311758b6f5767d20f63bbdf095d890fd9cc85bff615cf8a5","first_computed_at":"2026-07-31T01:29:42.861396Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:29:42.861396Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3743417e33f4cf733b14d203193c9167b63b292aa99daf8334dd763c78500d55","sha256:c9c6b140cf69f7e0a6c789e04bcf975da2384d8ba2b66c34f0ff76d409c4bb28"],"state_sha256":"4c7286a1967b78c0130a939a34b0bdbc6e4f5f97c435e9ba5769da7832997d22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7OdHokR7/CQnb0NWIoD7Sd4w8v4EohSJtkhroE1ELq5hS5hYX+imexhzE0jLjOLvE02w2CiMh7czmBY2o44Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T02:35:23.069585Z","bundle_sha256":"5b51aaa1c4149f2068b410518e0b4f1327bd59f09b9fad41303c60b7baef0240"}}