{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:N23I3SJ7KXAUPINPYYPNPYLT4C","short_pith_number":"pith:N23I3SJ7","canonical_record":{"source":{"id":"2308.03212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2023-08-06T21:23:22Z","cross_cats_sorted":["cs.CC","cs.LG"],"title_canon_sha256":"c79ae45ca7ffe7c2c43d79fe90157e4d6a8f501007765be146c284d90e85ac17","abstract_canon_sha256":"cb93f92f82b71f2f4d71afdcb9a98949cc169727d844093d9359d880e00cd93a"},"schema_version":"1.0"},"canonical_sha256":"6eb68dc93f55c147a1afc61ed7e173e0bc7363090757ac65a2718691dcfb82de","source":{"kind":"arxiv","id":"2308.03212","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.03212","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"2308.03212v2","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.03212","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"N23I3SJ7KXAU","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"pith_short_16","alias_value":"N23I3SJ7KXAUPINP","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"pith_short_8","alias_value":"N23I3SJ7","created_at":"2026-07-05T06:43:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:N23I3SJ7KXAUPINPYYPNPYLT4C","target":"record","payload":{"canonical_record":{"source":{"id":"2308.03212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2023-08-06T21:23:22Z","cross_cats_sorted":["cs.CC","cs.LG"],"title_canon_sha256":"c79ae45ca7ffe7c2c43d79fe90157e4d6a8f501007765be146c284d90e85ac17","abstract_canon_sha256":"cb93f92f82b71f2f4d71afdcb9a98949cc169727d844093d9359d880e00cd93a"},"schema_version":"1.0"},"canonical_sha256":"6eb68dc93f55c147a1afc61ed7e173e0bc7363090757ac65a2718691dcfb82de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:43:24.738292Z","signature_b64":"GXEupmih2kRomIUTgFL4ys/inEexkFGwPSl/Kk6uSV7o5HE0E/y3ktPSKLGNhpwS6wPbCROZk1QQIXz43zNzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6eb68dc93f55c147a1afc61ed7e173e0bc7363090757ac65a2718691dcfb82de","last_reissued_at":"2026-07-05T06:43:24.737916Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:43:24.737916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.03212","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":"2026-07-05T06:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rxZk6gkPf65AgPk9SuQw6PP4F1NWcSVhiLg9XejLwR2o6wFt3CjllpdrapccuEj576k3hIjY/dW6yAQTiY31BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:59:31.354694Z"},"content_sha256":"a779a954eee81d7b3e9b08d71ec648cdb58671d17579e5ce28c2144076f41a1b","schema_version":"1.0","event_id":"sha256:a779a954eee81d7b3e9b08d71ec648cdb58671d17579e5ce28c2144076f41a1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:N23I3SJ7KXAUPINPYYPNPYLT4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG"],"primary_cat":"cs.CL","authors_text":"Lena Strobl","submitted_at":"2023-08-06T21:23:22Z","abstract_excerpt":"Transformers have emerged as a widely used neural network model for various natural language processing tasks. Previous research explored their relationship with constant-depth threshold circuits, making two assumptions: average-hard attention and logarithmic precision for internal computations relative to input length. Merrill et al. (2022) prove that average-hard attention transformers recognize languages that fall within the complexity class TC0, denoting the set of languages that can be recognized by constant-depth polynomial-size threshold circuits. Likewise, Merrill and Sabharwal (2023) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.03212","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/2308.03212/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":"2026-07-05T06:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bP8Egsv7/ugChDWpMrzk/mkscNnD3WgHk1ZvOAUFJUvjYd7Ge3XmXd5GXismxkgloYgNdFutNOJrCNW3GbmwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:59:31.355200Z"},"content_sha256":"ddae97a4b66ee0526069f47335fa2f94a5dde090c3c83de640eea3d6a1640a95","schema_version":"1.0","event_id":"sha256:ddae97a4b66ee0526069f47335fa2f94a5dde090c3c83de640eea3d6a1640a95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N23I3SJ7KXAUPINPYYPNPYLT4C/bundle.json","state_url":"https://pith.science/pith/N23I3SJ7KXAUPINPYYPNPYLT4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N23I3SJ7KXAUPINPYYPNPYLT4C/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":"2026-08-09T07:59:31Z","links":{"resolver":"https://pith.science/pith/N23I3SJ7KXAUPINPYYPNPYLT4C","bundle":"https://pith.science/pith/N23I3SJ7KXAUPINPYYPNPYLT4C/bundle.json","state":"https://pith.science/pith/N23I3SJ7KXAUPINPYYPNPYLT4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N23I3SJ7KXAUPINPYYPNPYLT4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:N23I3SJ7KXAUPINPYYPNPYLT4C","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":"cb93f92f82b71f2f4d71afdcb9a98949cc169727d844093d9359d880e00cd93a","cross_cats_sorted":["cs.CC","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2023-08-06T21:23:22Z","title_canon_sha256":"c79ae45ca7ffe7c2c43d79fe90157e4d6a8f501007765be146c284d90e85ac17"},"schema_version":"1.0","source":{"id":"2308.03212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.03212","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"2308.03212v2","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.03212","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"N23I3SJ7KXAU","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"pith_short_16","alias_value":"N23I3SJ7KXAUPINP","created_at":"2026-07-05T06:43:24Z"},{"alias_kind":"pith_short_8","alias_value":"N23I3SJ7","created_at":"2026-07-05T06:43:24Z"}],"graph_snapshots":[{"event_id":"sha256:ddae97a4b66ee0526069f47335fa2f94a5dde090c3c83de640eea3d6a1640a95","target":"graph","created_at":"2026-07-05T06:43:24Z","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/2308.03212/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transformers have emerged as a widely used neural network model for various natural language processing tasks. Previous research explored their relationship with constant-depth threshold circuits, making two assumptions: average-hard attention and logarithmic precision for internal computations relative to input length. Merrill et al. (2022) prove that average-hard attention transformers recognize languages that fall within the complexity class TC0, denoting the set of languages that can be recognized by constant-depth polynomial-size threshold circuits. Likewise, Merrill and Sabharwal (2023) ","authors_text":"Lena Strobl","cross_cats":["cs.CC","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2023-08-06T21:23:22Z","title":"Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.03212","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:a779a954eee81d7b3e9b08d71ec648cdb58671d17579e5ce28c2144076f41a1b","target":"record","created_at":"2026-07-05T06:43:24Z","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":"cb93f92f82b71f2f4d71afdcb9a98949cc169727d844093d9359d880e00cd93a","cross_cats_sorted":["cs.CC","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2023-08-06T21:23:22Z","title_canon_sha256":"c79ae45ca7ffe7c2c43d79fe90157e4d6a8f501007765be146c284d90e85ac17"},"schema_version":"1.0","source":{"id":"2308.03212","kind":"arxiv","version":2}},"canonical_sha256":"6eb68dc93f55c147a1afc61ed7e173e0bc7363090757ac65a2718691dcfb82de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6eb68dc93f55c147a1afc61ed7e173e0bc7363090757ac65a2718691dcfb82de","first_computed_at":"2026-07-05T06:43:24.737916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:43:24.737916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GXEupmih2kRomIUTgFL4ys/inEexkFGwPSl/Kk6uSV7o5HE0E/y3ktPSKLGNhpwS6wPbCROZk1QQIXz43zNzDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:43:24.738292Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.03212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a779a954eee81d7b3e9b08d71ec648cdb58671d17579e5ce28c2144076f41a1b","sha256:ddae97a4b66ee0526069f47335fa2f94a5dde090c3c83de640eea3d6a1640a95"],"state_sha256":"9a9e5ba1885d643baf15cc07a808c1bd0514e659ee9042f2f8c5d43d2f1326ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9akF62KWaApHiEsrLftdVbbxzw2c6cn9Cb+kvKMRjvGuzozw+0f4COWi06lbCF0RqrTQPnfdiXZFSS5wGVWAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:59:31.359141Z","bundle_sha256":"8139e1ec6161f7846dd29c5a172d256bc881771799bf18f17b6fec2d28d8dbda"}}