{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CBYCBP2HPJWZ74RKEBYMUGDQSL","short_pith_number":"pith:CBYCBP2H","canonical_record":{"source":{"id":"2608.11716","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:57:08Z","cross_cats_sorted":[],"title_canon_sha256":"9fbbf72009440bd6069f1cd0b524c600fdbae5f8c68ff7218099066456a304d1","abstract_canon_sha256":"6de17064f398282fb39b145d3dc9b7eaf3bdf17e9cc66944045b28d6c4e05b0f"},"schema_version":"1.0"},"canonical_sha256":"107020bf477a6d9ff22a2070ca187092d222811367044dfd091c60eb5e3347cc","source":{"kind":"arxiv","id":"2608.11716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11716","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11716v1","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11716","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"pith_short_12","alias_value":"CBYCBP2HPJWZ","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"CBYCBP2HPJWZ74RK","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"CBYCBP2H","created_at":"2026-08-13T01:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CBYCBP2HPJWZ74RKEBYMUGDQSL","target":"record","payload":{"canonical_record":{"source":{"id":"2608.11716","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:57:08Z","cross_cats_sorted":[],"title_canon_sha256":"9fbbf72009440bd6069f1cd0b524c600fdbae5f8c68ff7218099066456a304d1","abstract_canon_sha256":"6de17064f398282fb39b145d3dc9b7eaf3bdf17e9cc66944045b28d6c4e05b0f"},"schema_version":"1.0"},"canonical_sha256":"107020bf477a6d9ff22a2070ca187092d222811367044dfd091c60eb5e3347cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T01:27:54.751000Z","signature_b64":"3MvCxMjvnXH9KmXBQGHJpy/6QkyGF2AkAh3kTew7uK4IXoa6x6m9bbLr+8LAZaufBaXtxmaFC1EzRMaPTdRgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"107020bf477a6d9ff22a2070ca187092d222811367044dfd091c60eb5e3347cc","last_reissued_at":"2026-08-13T01:27:54.748514Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T01:27:54.748514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.11716","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":"2026-08-13T01:27:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mwNI0Y1sAYzi8pswR94EDf5vTcyPI3Kf0YoCtSwFZxlLQ0uMGpi450oe6ojeimYpbDL2ehZR4cBsgnvt17rcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T04:11:04.619559Z"},"content_sha256":"a09494bcada02b057171bc8fd119781d5e8a1eed392c8ff458f6055386bc47ba","schema_version":"1.0","event_id":"sha256:a09494bcada02b057171bc8fd119781d5e8a1eed392c8ff458f6055386bc47ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CBYCBP2HPJWZ74RKEBYMUGDQSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chain-of-Thought Shows the Path to a Tree: Realizing Branching Complexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Anish Chakrabarty, Debanjan Dutta, Swagatam Das","submitted_at":"2026-08-12T06:57:08Z","abstract_excerpt":"Chain of Thought (CoT) lifts the expressive ceiling of bounded-depth Transformers, with characterizations tying the number of CoT steps to circuit complexity classes. What remains largely missing are concrete instantiations with explicit, depth-bounded constructions, and the traversal procedures such characterizations presuppose. We close this gap for branching complexity. We give CoT realizations of depth-first search (DFS) and of Dijkstra algorithm, the latter subsuming breadth-first search, by unique hard-attention decoders of at most two layers, and use them as a shared computational subst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11716","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/2608.11716/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":"2026-08-13T01:27:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bf5x0yvk5w4aWow0cVKsUaMxjsAfldERdECu/2Ez0AF4rPYiax4H4bfkIl+y0Urw31OGquBHX4Ad1pTDTFDwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T04:11:04.620385Z"},"content_sha256":"1b28c1fc82e81c72eda43686c669feb8b0835120a13d2c1a77c406bf4186de22","schema_version":"1.0","event_id":"sha256:1b28c1fc82e81c72eda43686c669feb8b0835120a13d2c1a77c406bf4186de22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBYCBP2HPJWZ74RKEBYMUGDQSL/bundle.json","state_url":"https://pith.science/pith/CBYCBP2HPJWZ74RKEBYMUGDQSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBYCBP2HPJWZ74RKEBYMUGDQSL/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":"2026-08-21T04:11:04Z","links":{"resolver":"https://pith.science/pith/CBYCBP2HPJWZ74RKEBYMUGDQSL","bundle":"https://pith.science/pith/CBYCBP2HPJWZ74RKEBYMUGDQSL/bundle.json","state":"https://pith.science/pith/CBYCBP2HPJWZ74RKEBYMUGDQSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBYCBP2HPJWZ74RKEBYMUGDQSL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CBYCBP2HPJWZ74RKEBYMUGDQSL","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":"6de17064f398282fb39b145d3dc9b7eaf3bdf17e9cc66944045b28d6c4e05b0f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:57:08Z","title_canon_sha256":"9fbbf72009440bd6069f1cd0b524c600fdbae5f8c68ff7218099066456a304d1"},"schema_version":"1.0","source":{"id":"2608.11716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11716","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11716v1","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11716","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"pith_short_12","alias_value":"CBYCBP2HPJWZ","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"CBYCBP2HPJWZ74RK","created_at":"2026-08-13T01:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"CBYCBP2H","created_at":"2026-08-13T01:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:1b28c1fc82e81c72eda43686c669feb8b0835120a13d2c1a77c406bf4186de22","target":"graph","created_at":"2026-08-13T01:27:54Z","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/2608.11716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Chain of Thought (CoT) lifts the expressive ceiling of bounded-depth Transformers, with characterizations tying the number of CoT steps to circuit complexity classes. What remains largely missing are concrete instantiations with explicit, depth-bounded constructions, and the traversal procedures such characterizations presuppose. We close this gap for branching complexity. We give CoT realizations of depth-first search (DFS) and of Dijkstra algorithm, the latter subsuming breadth-first search, by unique hard-attention decoders of at most two layers, and use them as a shared computational subst","authors_text":"Anish Chakrabarty, Debanjan Dutta, Swagatam Das","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:57:08Z","title":"Chain-of-Thought Shows the Path to a Tree: Realizing Branching Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11716","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:a09494bcada02b057171bc8fd119781d5e8a1eed392c8ff458f6055386bc47ba","target":"record","created_at":"2026-08-13T01:27:54Z","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":"6de17064f398282fb39b145d3dc9b7eaf3bdf17e9cc66944045b28d6c4e05b0f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-08-12T06:57:08Z","title_canon_sha256":"9fbbf72009440bd6069f1cd0b524c600fdbae5f8c68ff7218099066456a304d1"},"schema_version":"1.0","source":{"id":"2608.11716","kind":"arxiv","version":1}},"canonical_sha256":"107020bf477a6d9ff22a2070ca187092d222811367044dfd091c60eb5e3347cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"107020bf477a6d9ff22a2070ca187092d222811367044dfd091c60eb5e3347cc","first_computed_at":"2026-08-13T01:27:54.748514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-13T01:27:54.748514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3MvCxMjvnXH9KmXBQGHJpy/6QkyGF2AkAh3kTew7uK4IXoa6x6m9bbLr+8LAZaufBaXtxmaFC1EzRMaPTdRgBw==","signature_status":"signed_v1","signed_at":"2026-08-13T01:27:54.751000Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.11716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a09494bcada02b057171bc8fd119781d5e8a1eed392c8ff458f6055386bc47ba","sha256:1b28c1fc82e81c72eda43686c669feb8b0835120a13d2c1a77c406bf4186de22"],"state_sha256":"bd0f13863cf23b11109bb75979a058e9b42f370ea0a82961df719dbbf7d2114d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/eSXYk1y0OMuvBxKl0SQMzo8JNN2M3L1xHMBnECy/GjSPGAXD/BlJ6RPuv3gjdIaQauJEWu9UUhL1DlrjodFAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T04:11:04.625406Z","bundle_sha256":"383e6f262424c531204188fcb5d26eb4e3d8b4958f67fdb97b653f1687950c33"}}