{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6ZGIODOWTW64VKSLYQJQXTZBAU","short_pith_number":"pith:6ZGIODOW","canonical_record":{"source":{"id":"2410.19730","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2024-10-25T17:56:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"f57311b895fc617097065d2ca9d347fcc31f0d3fd115a805d3863eb8091454e1","abstract_canon_sha256":"3450f1782ed50416f5ef7a2115aefae55f5cd4470e640d7531d26c8dbd00982c"},"schema_version":"1.0"},"canonical_sha256":"f64c870dd69dbdcaaa4bc4130bcf21050f85ca932064b41495624d087706e911","source":{"kind":"arxiv","id":"2410.19730","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19730","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19730v2","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19730","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_12","alias_value":"6ZGIODOWTW64","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"6ZGIODOWTW64VKSL","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"6ZGIODOW","created_at":"2026-07-05T09:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6ZGIODOWTW64VKSLYQJQXTZBAU","target":"record","payload":{"canonical_record":{"source":{"id":"2410.19730","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2024-10-25T17:56:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"f57311b895fc617097065d2ca9d347fcc31f0d3fd115a805d3863eb8091454e1","abstract_canon_sha256":"3450f1782ed50416f5ef7a2115aefae55f5cd4470e640d7531d26c8dbd00982c"},"schema_version":"1.0"},"canonical_sha256":"f64c870dd69dbdcaaa4bc4130bcf21050f85ca932064b41495624d087706e911","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:27:25.748860Z","signature_b64":"5aQG0MpLcw+Lr9HejYcyfyxTzQTALXeNic5mwPJstjemCvLn3QMrPqJXi3tkGah7WI22zrpqIK5MGDUBzFf0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f64c870dd69dbdcaaa4bc4130bcf21050f85ca932064b41495624d087706e911","last_reissued_at":"2026-07-05T09:27:25.748253Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:27:25.748253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.19730","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":"2026-07-05T09:27:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOic14UYS7MfWjDnF+Bo+XFRQaGIgze2padjIKR5yTv4Vitm5Kj8qLNRZozW/AWsZ940bOPUmrN5ndtdqTTpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T08:01:09.369820Z"},"content_sha256":"381510ca70f3f75c7ef68b581bc6bda6eb3cac97f0d5fe3ca42db97dd528bfe5","schema_version":"1.0","event_id":"sha256:381510ca70f3f75c7ef68b581bc6bda6eb3cac97f0d5fe3ca42db97dd528bfe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6ZGIODOWTW64VKSLYQJQXTZBAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting Ability of Large Language Models and Impact of Tokenization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.CL","authors_text":"Chenyu You, Juntai Cao, Xiang Zhang","submitted_at":"2024-10-25T17:56:24Z","abstract_excerpt":"Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to constant-depth computation. This restriction places them in the complexity class TC$^0$, making them theoretically incapable of solving tasks that demand increasingly deep reasoning as input length grows. Counting, a fundamental component of many reasoning tasks, also requires reasoning depth to grow linearly to be performed inductively. While previous studies ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19730","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/2410.19730/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":"2026-07-05T09:27:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3LiOLkc/JEB6yj7QHkbp/i6VhjcWOPUxqeTIaEraN8KG8d7z9zDC/R3rWrRwt55+RHSxL4N+rzx46i+P+O9iBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T08:01:09.370194Z"},"content_sha256":"7521b6a826d2277fad9e8cc2bb541ee9bedce36051f04ab44b84003767eabffa","schema_version":"1.0","event_id":"sha256:7521b6a826d2277fad9e8cc2bb541ee9bedce36051f04ab44b84003767eabffa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZGIODOWTW64VKSLYQJQXTZBAU/bundle.json","state_url":"https://pith.science/pith/6ZGIODOWTW64VKSLYQJQXTZBAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZGIODOWTW64VKSLYQJQXTZBAU/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":"2026-07-18T08:01:09Z","links":{"resolver":"https://pith.science/pith/6ZGIODOWTW64VKSLYQJQXTZBAU","bundle":"https://pith.science/pith/6ZGIODOWTW64VKSLYQJQXTZBAU/bundle.json","state":"https://pith.science/pith/6ZGIODOWTW64VKSLYQJQXTZBAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZGIODOWTW64VKSLYQJQXTZBAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6ZGIODOWTW64VKSLYQJQXTZBAU","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":"3450f1782ed50416f5ef7a2115aefae55f5cd4470e640d7531d26c8dbd00982c","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2024-10-25T17:56:24Z","title_canon_sha256":"f57311b895fc617097065d2ca9d347fcc31f0d3fd115a805d3863eb8091454e1"},"schema_version":"1.0","source":{"id":"2410.19730","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19730","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19730v2","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19730","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_12","alias_value":"6ZGIODOWTW64","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"6ZGIODOWTW64VKSL","created_at":"2026-07-05T09:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"6ZGIODOW","created_at":"2026-07-05T09:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:7521b6a826d2277fad9e8cc2bb541ee9bedce36051f04ab44b84003767eabffa","target":"graph","created_at":"2026-07-05T09:27:25Z","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/2410.19730/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to constant-depth computation. This restriction places them in the complexity class TC$^0$, making them theoretically incapable of solving tasks that demand increasingly deep reasoning as input length grows. Counting, a fundamental component of many reasoning tasks, also requires reasoning depth to grow linearly to be performed inductively. While previous studies ha","authors_text":"Chenyu You, Juntai Cao, Xiang Zhang","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2024-10-25T17:56:24Z","title":"Counting Ability of Large Language Models and Impact of Tokenization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19730","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":"sha256:381510ca70f3f75c7ef68b581bc6bda6eb3cac97f0d5fe3ca42db97dd528bfe5","target":"record","created_at":"2026-07-05T09:27:25Z","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":"3450f1782ed50416f5ef7a2115aefae55f5cd4470e640d7531d26c8dbd00982c","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2024-10-25T17:56:24Z","title_canon_sha256":"f57311b895fc617097065d2ca9d347fcc31f0d3fd115a805d3863eb8091454e1"},"schema_version":"1.0","source":{"id":"2410.19730","kind":"arxiv","version":2}},"canonical_sha256":"f64c870dd69dbdcaaa4bc4130bcf21050f85ca932064b41495624d087706e911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f64c870dd69dbdcaaa4bc4130bcf21050f85ca932064b41495624d087706e911","first_computed_at":"2026-07-05T09:27:25.748253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:27:25.748253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5aQG0MpLcw+Lr9HejYcyfyxTzQTALXeNic5mwPJstjemCvLn3QMrPqJXi3tkGah7WI22zrpqIK5MGDUBzFf0BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:27:25.748860Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.19730","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:381510ca70f3f75c7ef68b581bc6bda6eb3cac97f0d5fe3ca42db97dd528bfe5","sha256:7521b6a826d2277fad9e8cc2bb541ee9bedce36051f04ab44b84003767eabffa"],"state_sha256":"b837abec57095c18c132b5e7c82a448b1c40ed2d643568f6630279245e8479ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5U0karV95hM9MzdtveKNCNUlMnWUQgjvThyFedyvkfNkhqPl97uw+W4xDKzCIus8JjFczKPRSOUC1VcJ37bDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-18T08:01:09.372402Z","bundle_sha256":"96f0d02bed4a98849b9cf9da7db4b0408a0dfe2ddbb727e21cb39fbd76dfdbbd"}}