{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KJB7WZMOBQCWXUZUNBICAP4O5N","short_pith_number":"pith:KJB7WZMO","canonical_record":{"source":{"id":"2603.03612","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-04T00:51:08Z","cross_cats_sorted":["cs.CC","cs.CL","cs.FL"],"title_canon_sha256":"dd0cca411763705e0b5a355d16157da4c2bbb810d059a2139360f94ad427e721","abstract_canon_sha256":"252cfb8436d690dd225dda6a7bcbb07f85d415649a820fbde50fa3c05cdd3a99"},"schema_version":"1.0"},"canonical_sha256":"5243fb658e0c056bd3346850203f8eeb61f36bc0ca4c1ef20644bbfc98cedd5c","source":{"kind":"arxiv","id":"2603.03612","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.03612","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"arxiv_version","alias_value":"2603.03612v3","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03612","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"pith_short_12","alias_value":"KJB7WZMOBQCW","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"pith_short_16","alias_value":"KJB7WZMOBQCWXUZU","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"pith_short_8","alias_value":"KJB7WZMO","created_at":"2026-06-03T01:05:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KJB7WZMOBQCWXUZUNBICAP4O5N","target":"record","payload":{"canonical_record":{"source":{"id":"2603.03612","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-04T00:51:08Z","cross_cats_sorted":["cs.CC","cs.CL","cs.FL"],"title_canon_sha256":"dd0cca411763705e0b5a355d16157da4c2bbb810d059a2139360f94ad427e721","abstract_canon_sha256":"252cfb8436d690dd225dda6a7bcbb07f85d415649a820fbde50fa3c05cdd3a99"},"schema_version":"1.0"},"canonical_sha256":"5243fb658e0c056bd3346850203f8eeb61f36bc0ca4c1ef20644bbfc98cedd5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:11.197345Z","signature_b64":"6MIYhiL2UkXvFbgCIbHREmI+nrevN19VEGTHp/r87v4nPaJK+W70Evdq/j22QqcvM+PefKpgol6uPidGq7iLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5243fb658e0c056bd3346850203f8eeb61f36bc0ca4c1ef20644bbfc98cedd5c","last_reissued_at":"2026-06-03T01:05:11.196866Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:11.196866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.03612","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T01:05:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MslMq33abwDoL95Vx9DPEbzBKN9q2X5hyg0dVK18dnCJYGQZy2JwCD3fqqRO0mfWI8vwUaoqtP9SpBgMfrG9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:57:31.927583Z"},"content_sha256":"00168630d4bae3a5420917679a5181fb56f77aa6f8f110fceb7d3326f2487398","schema_version":"1.0","event_id":"sha256:00168630d4bae3a5420917679a5181fb56f77aa6f8f110fceb7d3326f2487398"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KJB7WZMOBQCWXUZUNBICAP4O5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Why Are Linear RNNs More Parallelizable?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CL","cs.FL"],"primary_cat":"cs.LG","authors_text":"Anthony Lin, Ashish Sabharwal, Hongjian Jiang, William Merrill, Yanhong Li","submitted_at":"2026-03-04T00:51:08Z","abstract_excerpt":"The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what makes LRNNs -- but not traditional, nonlinear RNNs -- as easy to parallelize in practice as transformers. We answer this question by providing a tight connection between types of RNNs and standard complexity classes. We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03612","kind":"arxiv","version":3},"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/2603.03612/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":"2026-06-03T01:05:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cohLp9ki9Cpt4pMqTiAjLoUAWOsZnd4hwmlNXmekew818pMkcF5x6BKy7M1fGHZ4WxQSYS4wO12CvpRSZMvSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:57:31.927973Z"},"content_sha256":"40bb5071dd6f72c74cd7ff680eed4d0f2cd7e0585bcfb80c49b625b0789a6812","schema_version":"1.0","event_id":"sha256:40bb5071dd6f72c74cd7ff680eed4d0f2cd7e0585bcfb80c49b625b0789a6812"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJB7WZMOBQCWXUZUNBICAP4O5N/bundle.json","state_url":"https://pith.science/pith/KJB7WZMOBQCWXUZUNBICAP4O5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJB7WZMOBQCWXUZUNBICAP4O5N/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":"2026-06-20T20:57:31Z","links":{"resolver":"https://pith.science/pith/KJB7WZMOBQCWXUZUNBICAP4O5N","bundle":"https://pith.science/pith/KJB7WZMOBQCWXUZUNBICAP4O5N/bundle.json","state":"https://pith.science/pith/KJB7WZMOBQCWXUZUNBICAP4O5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJB7WZMOBQCWXUZUNBICAP4O5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KJB7WZMOBQCWXUZUNBICAP4O5N","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":"252cfb8436d690dd225dda6a7bcbb07f85d415649a820fbde50fa3c05cdd3a99","cross_cats_sorted":["cs.CC","cs.CL","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-04T00:51:08Z","title_canon_sha256":"dd0cca411763705e0b5a355d16157da4c2bbb810d059a2139360f94ad427e721"},"schema_version":"1.0","source":{"id":"2603.03612","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.03612","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"arxiv_version","alias_value":"2603.03612v3","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03612","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"pith_short_12","alias_value":"KJB7WZMOBQCW","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"pith_short_16","alias_value":"KJB7WZMOBQCWXUZU","created_at":"2026-06-03T01:05:11Z"},{"alias_kind":"pith_short_8","alias_value":"KJB7WZMO","created_at":"2026-06-03T01:05:11Z"}],"graph_snapshots":[{"event_id":"sha256:40bb5071dd6f72c74cd7ff680eed4d0f2cd7e0585bcfb80c49b625b0789a6812","target":"graph","created_at":"2026-06-03T01:05:11Z","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/2603.03612/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what makes LRNNs -- but not traditional, nonlinear RNNs -- as easy to parallelize in practice as transformers. We answer this question by providing a tight connection between types of RNNs and standard complexity classes. We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to ","authors_text":"Anthony Lin, Ashish Sabharwal, Hongjian Jiang, William Merrill, Yanhong Li","cross_cats":["cs.CC","cs.CL","cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-04T00:51:08Z","title":"Why Are Linear RNNs More Parallelizable?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03612","kind":"arxiv","version":3},"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":"sha256:00168630d4bae3a5420917679a5181fb56f77aa6f8f110fceb7d3326f2487398","target":"record","created_at":"2026-06-03T01:05:11Z","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":"252cfb8436d690dd225dda6a7bcbb07f85d415649a820fbde50fa3c05cdd3a99","cross_cats_sorted":["cs.CC","cs.CL","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-04T00:51:08Z","title_canon_sha256":"dd0cca411763705e0b5a355d16157da4c2bbb810d059a2139360f94ad427e721"},"schema_version":"1.0","source":{"id":"2603.03612","kind":"arxiv","version":3}},"canonical_sha256":"5243fb658e0c056bd3346850203f8eeb61f36bc0ca4c1ef20644bbfc98cedd5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5243fb658e0c056bd3346850203f8eeb61f36bc0ca4c1ef20644bbfc98cedd5c","first_computed_at":"2026-06-03T01:05:11.196866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:11.196866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6MIYhiL2UkXvFbgCIbHREmI+nrevN19VEGTHp/r87v4nPaJK+W70Evdq/j22QqcvM+PefKpgol6uPidGq7iLDw==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:11.197345Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.03612","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00168630d4bae3a5420917679a5181fb56f77aa6f8f110fceb7d3326f2487398","sha256:40bb5071dd6f72c74cd7ff680eed4d0f2cd7e0585bcfb80c49b625b0789a6812"],"state_sha256":"6b5fcc05c556dd36f29b8af39351b1c261d2bc9fca72c9711f624a579bad268b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2kebOC53TDaFtK1tYFYWAIpZ0ilca+OPxpKFxJkQMYOzF5qH/wSK8IavlNhxSmQNLSyhYWfx9F2M/ZRt3exDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T20:57:31.930040Z","bundle_sha256":"483e86d9f29b2e6158b76c500b1cb2174d4863fae67c2de0b9b80737fd5d579b"}}