{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:D7QV3S32CHKS5RVNAHWUQDXLPK","short_pith_number":"pith:D7QV3S32","canonical_record":{"source":{"id":"2605.26035","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T17:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"5d8b8737cdfb43e283e52e3a0dbfffc9cad8213a745d0cdc62cc35e0793ba6b0","abstract_canon_sha256":"29709a7443ac86802046b295149edaa0494e7e6c1c03cba5c73ecebd74beabc1"},"schema_version":"1.0"},"canonical_sha256":"1fe15dcb7a11d52ec6ad01ed480eeb7abf7bb00b5a388c37023f06f56d928b3e","source":{"kind":"arxiv","id":"2605.26035","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26035","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26035v1","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26035","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"D7QV3S32CHKS","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"pith_short_16","alias_value":"D7QV3S32CHKS5RVN","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"pith_short_8","alias_value":"D7QV3S32","created_at":"2026-05-26T02:05:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:D7QV3S32CHKS5RVNAHWUQDXLPK","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26035","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T17:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"5d8b8737cdfb43e283e52e3a0dbfffc9cad8213a745d0cdc62cc35e0793ba6b0","abstract_canon_sha256":"29709a7443ac86802046b295149edaa0494e7e6c1c03cba5c73ecebd74beabc1"},"schema_version":"1.0"},"canonical_sha256":"1fe15dcb7a11d52ec6ad01ed480eeb7abf7bb00b5a388c37023f06f56d928b3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:24.335363Z","signature_b64":"DQkO6f8dQfJUOBDPd16W+/6jAwHTVuROM54d09m2SgsQDtytkgI08aAfhWWNtpWc9SSxyWMlcZa2LQELI2drDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fe15dcb7a11d52ec6ad01ed480eeb7abf7bb00b5a388c37023f06f56d928b3e","last_reissued_at":"2026-05-26T02:05:24.334772Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:24.334772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26035","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":"2026-05-26T02:05:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQNsuXBJlE8PTuE1JQFZ0FY4PHEWNK5HFKEKcc9DBV1cVgzZ4dFvMJsvXLAEgAFMYNShMUaru7qW/BDeC5qOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:37:26.470348Z"},"content_sha256":"035bc46ff86d6652e19414d40f5c91cc7d5f66b4a35435cfab99b0b32db5b752","schema_version":"1.0","event_id":"sha256:035bc46ff86d6652e19414d40f5c91cc7d5f66b4a35435cfab99b0b32db5b752"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:D7QV3S32CHKS5RVNAHWUQDXLPK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Length Generalization with Log-Depth Recurrent Units","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alessandra Russo, Charles Pert, Dalal Alrajeh","submitted_at":"2026-05-25T17:02:29Z","abstract_excerpt":"Length generalization remains a persistent challenge for neural networks: recurrent models tend to suffer from positional biases, while transformers are constrained by fixed computational depth. Regular languages provide a frequently used testbed for evaluating length generalization, as label prediction can be checked for any sequence length. We propose MLP-LDRU, a type of Log-Depth Recurrent Unit, which captures a class of associativity-biased operators designed to approximate recurrence through parallel reduction. We evaluate MLP-LDRU on 21 regular-language tasks, consisting of standard benc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26035","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/2605.26035/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":"2026-05-26T02:05:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7IeETmvD1agYD5PxJGEHdXUUDHWXd0EGJxEdAELl7nDRkR57dl9zNhZ3IcKyaKugi/3uOlfbKau3lOGVMiaTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:37:26.470718Z"},"content_sha256":"23f362a22571044c9858ff87f6008b4f7449fcec5e8d7e2acf3b1a8855a909bb","schema_version":"1.0","event_id":"sha256:23f362a22571044c9858ff87f6008b4f7449fcec5e8d7e2acf3b1a8855a909bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D7QV3S32CHKS5RVNAHWUQDXLPK/bundle.json","state_url":"https://pith.science/pith/D7QV3S32CHKS5RVNAHWUQDXLPK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D7QV3S32CHKS5RVNAHWUQDXLPK/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":"2026-06-20T22:37:26Z","links":{"resolver":"https://pith.science/pith/D7QV3S32CHKS5RVNAHWUQDXLPK","bundle":"https://pith.science/pith/D7QV3S32CHKS5RVNAHWUQDXLPK/bundle.json","state":"https://pith.science/pith/D7QV3S32CHKS5RVNAHWUQDXLPK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D7QV3S32CHKS5RVNAHWUQDXLPK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D7QV3S32CHKS5RVNAHWUQDXLPK","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":"29709a7443ac86802046b295149edaa0494e7e6c1c03cba5c73ecebd74beabc1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T17:02:29Z","title_canon_sha256":"5d8b8737cdfb43e283e52e3a0dbfffc9cad8213a745d0cdc62cc35e0793ba6b0"},"schema_version":"1.0","source":{"id":"2605.26035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26035","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26035v1","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26035","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"D7QV3S32CHKS","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"pith_short_16","alias_value":"D7QV3S32CHKS5RVN","created_at":"2026-05-26T02:05:24Z"},{"alias_kind":"pith_short_8","alias_value":"D7QV3S32","created_at":"2026-05-26T02:05:24Z"}],"graph_snapshots":[{"event_id":"sha256:23f362a22571044c9858ff87f6008b4f7449fcec5e8d7e2acf3b1a8855a909bb","target":"graph","created_at":"2026-05-26T02:05:24Z","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/2605.26035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Length generalization remains a persistent challenge for neural networks: recurrent models tend to suffer from positional biases, while transformers are constrained by fixed computational depth. Regular languages provide a frequently used testbed for evaluating length generalization, as label prediction can be checked for any sequence length. We propose MLP-LDRU, a type of Log-Depth Recurrent Unit, which captures a class of associativity-biased operators designed to approximate recurrence through parallel reduction. We evaluate MLP-LDRU on 21 regular-language tasks, consisting of standard benc","authors_text":"Alessandra Russo, Charles Pert, Dalal Alrajeh","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T17:02:29Z","title":"Length Generalization with Log-Depth Recurrent Units"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26035","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":"sha256:035bc46ff86d6652e19414d40f5c91cc7d5f66b4a35435cfab99b0b32db5b752","target":"record","created_at":"2026-05-26T02:05:24Z","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":"29709a7443ac86802046b295149edaa0494e7e6c1c03cba5c73ecebd74beabc1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T17:02:29Z","title_canon_sha256":"5d8b8737cdfb43e283e52e3a0dbfffc9cad8213a745d0cdc62cc35e0793ba6b0"},"schema_version":"1.0","source":{"id":"2605.26035","kind":"arxiv","version":1}},"canonical_sha256":"1fe15dcb7a11d52ec6ad01ed480eeb7abf7bb00b5a388c37023f06f56d928b3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fe15dcb7a11d52ec6ad01ed480eeb7abf7bb00b5a388c37023f06f56d928b3e","first_computed_at":"2026-05-26T02:05:24.334772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:05:24.334772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DQkO6f8dQfJUOBDPd16W+/6jAwHTVuROM54d09m2SgsQDtytkgI08aAfhWWNtpWc9SSxyWMlcZa2LQELI2drDA==","signature_status":"signed_v1","signed_at":"2026-05-26T02:05:24.335363Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:035bc46ff86d6652e19414d40f5c91cc7d5f66b4a35435cfab99b0b32db5b752","sha256:23f362a22571044c9858ff87f6008b4f7449fcec5e8d7e2acf3b1a8855a909bb"],"state_sha256":"abf88be0f0355b5c7d9d6fddffc0c11bfdfddecc8b606159f53f042f8cc3e943"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6O6EBnKqXGT6L85F91UhyqnCDJTBOohLFtEJHYRoQKBouavYBdINX3i9OtSMkH9s4zwn6GPzNPl2v0WEd/S0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:37:26.472728Z","bundle_sha256":"c5aa4eb81662bac07b5bec4708c2410db433af812e796857a082a7fc5659428c"}}