{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:X5TLISQWDRZCQTR35GMTEG3J6V","short_pith_number":"pith:X5TLISQW","canonical_record":{"source":{"id":"2506.04374","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-06-04T18:43:23Z","cross_cats_sorted":["cs.CL"],"title_canon_sha256":"e5410164d72bb27c97f06d48155d7593095046a233e176d00f018109381f4a87","abstract_canon_sha256":"e7e16af3ffcab4b275a4c0fcf170c13bad9d6761367d2c22760dbe77532144b5"},"schema_version":"1.0"},"canonical_sha256":"bf66b44a161c72284e3be999321b69f5532b1f883de7de54ca6733ef6ce9f6c1","source":{"kind":"arxiv","id":"2506.04374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04374","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04374v1","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04374","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"pith_short_12","alias_value":"X5TLISQWDRZC","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"pith_short_16","alias_value":"X5TLISQWDRZCQTR3","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"pith_short_8","alias_value":"X5TLISQW","created_at":"2026-07-05T11:16:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:X5TLISQWDRZCQTR35GMTEG3J6V","target":"record","payload":{"canonical_record":{"source":{"id":"2506.04374","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-06-04T18:43:23Z","cross_cats_sorted":["cs.CL"],"title_canon_sha256":"e5410164d72bb27c97f06d48155d7593095046a233e176d00f018109381f4a87","abstract_canon_sha256":"e7e16af3ffcab4b275a4c0fcf170c13bad9d6761367d2c22760dbe77532144b5"},"schema_version":"1.0"},"canonical_sha256":"bf66b44a161c72284e3be999321b69f5532b1f883de7de54ca6733ef6ce9f6c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:36.429894Z","signature_b64":"Y03msOrxJoIaPfKDh6cBhd7v2rPYP0KVjL6e8XrUK7DGd2wY1AU4ElUQRV0B691yfVauNO7XEKDHqchLZ2chAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf66b44a161c72284e3be999321b69f5532b1f883de7de54ca6733ef6ce9f6c1","last_reissued_at":"2026-07-05T11:16:36.429305Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:36.429305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.04374","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":"2026-07-05T11:16:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OYf5/L+Obu8EMhx/FQDgA4cQhRHNXYWNeM5NawXznLDeKAIMKzjvM6goyk9364bv6k6xeT9lQxJoTvraWRZABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:54.943555Z"},"content_sha256":"63c0a08cf7d29e877e284c40efe3e35322ed9874b662f493d2ad0e8755b49907","schema_version":"1.0","event_id":"sha256:63c0a08cf7d29e877e284c40efe3e35322ed9874b662f493d2ad0e8755b49907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:X5TLISQWDRZCQTR35GMTEG3J6V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Statistical Physics of Language Model Reasoning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CL"],"primary_cat":"cs.AI","authors_text":"Amir Reisizadeh, Jack David Carson","submitted_at":"2025-06-04T18:43:23Z","abstract_excerpt":"Transformer LMs show emergent reasoning that resists mechanistic understanding. We offer a statistical physics framework for continuous-time chain-of-thought reasoning dynamics. We model sentence-level hidden state trajectories as a stochastic dynamical system on a lower-dimensional manifold. This drift-diffusion system uses latent regime switching to capture diverse reasoning phases, including misaligned states or failures. Empirical trajectories (8 models, 7 benchmarks) show a rank-40 projection (balancing variance capture and feasibility) explains ~50% variance. We find four latent reasonin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04374","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/2506.04374/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":"2026-07-05T11:16:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2k0s3UDu44glCOWNtpTjQf6pCW9m3tyNBdE9jv2ttGU7Eq13nwnpRb5Dsrc8wKNMOgE8Vx5k7eMisGkbfBeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:54.944066Z"},"content_sha256":"8fbc48cff3fac9ae5a7ecf32db7681589441997b5a18309cc45238754d1399b6","schema_version":"1.0","event_id":"sha256:8fbc48cff3fac9ae5a7ecf32db7681589441997b5a18309cc45238754d1399b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5TLISQWDRZCQTR35GMTEG3J6V/bundle.json","state_url":"https://pith.science/pith/X5TLISQWDRZCQTR35GMTEG3J6V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5TLISQWDRZCQTR35GMTEG3J6V/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":"2026-08-08T11:24:54Z","links":{"resolver":"https://pith.science/pith/X5TLISQWDRZCQTR35GMTEG3J6V","bundle":"https://pith.science/pith/X5TLISQWDRZCQTR35GMTEG3J6V/bundle.json","state":"https://pith.science/pith/X5TLISQWDRZCQTR35GMTEG3J6V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5TLISQWDRZCQTR35GMTEG3J6V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X5TLISQWDRZCQTR35GMTEG3J6V","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":"e7e16af3ffcab4b275a4c0fcf170c13bad9d6761367d2c22760dbe77532144b5","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-06-04T18:43:23Z","title_canon_sha256":"e5410164d72bb27c97f06d48155d7593095046a233e176d00f018109381f4a87"},"schema_version":"1.0","source":{"id":"2506.04374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04374","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04374v1","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04374","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"pith_short_12","alias_value":"X5TLISQWDRZC","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"pith_short_16","alias_value":"X5TLISQWDRZCQTR3","created_at":"2026-07-05T11:16:36Z"},{"alias_kind":"pith_short_8","alias_value":"X5TLISQW","created_at":"2026-07-05T11:16:36Z"}],"graph_snapshots":[{"event_id":"sha256:8fbc48cff3fac9ae5a7ecf32db7681589441997b5a18309cc45238754d1399b6","target":"graph","created_at":"2026-07-05T11:16:36Z","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/2506.04374/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transformer LMs show emergent reasoning that resists mechanistic understanding. We offer a statistical physics framework for continuous-time chain-of-thought reasoning dynamics. We model sentence-level hidden state trajectories as a stochastic dynamical system on a lower-dimensional manifold. This drift-diffusion system uses latent regime switching to capture diverse reasoning phases, including misaligned states or failures. Empirical trajectories (8 models, 7 benchmarks) show a rank-40 projection (balancing variance capture and feasibility) explains ~50% variance. We find four latent reasonin","authors_text":"Amir Reisizadeh, Jack David Carson","cross_cats":["cs.CL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-06-04T18:43:23Z","title":"A Statistical Physics of Language Model Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04374","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":"sha256:63c0a08cf7d29e877e284c40efe3e35322ed9874b662f493d2ad0e8755b49907","target":"record","created_at":"2026-07-05T11:16:36Z","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":"e7e16af3ffcab4b275a4c0fcf170c13bad9d6761367d2c22760dbe77532144b5","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-06-04T18:43:23Z","title_canon_sha256":"e5410164d72bb27c97f06d48155d7593095046a233e176d00f018109381f4a87"},"schema_version":"1.0","source":{"id":"2506.04374","kind":"arxiv","version":1}},"canonical_sha256":"bf66b44a161c72284e3be999321b69f5532b1f883de7de54ca6733ef6ce9f6c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf66b44a161c72284e3be999321b69f5532b1f883de7de54ca6733ef6ce9f6c1","first_computed_at":"2026-07-05T11:16:36.429305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:36.429305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y03msOrxJoIaPfKDh6cBhd7v2rPYP0KVjL6e8XrUK7DGd2wY1AU4ElUQRV0B691yfVauNO7XEKDHqchLZ2chAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:36.429894Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c0a08cf7d29e877e284c40efe3e35322ed9874b662f493d2ad0e8755b49907","sha256:8fbc48cff3fac9ae5a7ecf32db7681589441997b5a18309cc45238754d1399b6"],"state_sha256":"0173c0c7a275c7386bfc0a6cf41f24d709d7fb1525e11d1cc6080acd18dd878f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"waWjArfz1twIqalQZyTpOAexiFKhW5iD9qrXxUx6Mp6rlHTy2wo3jp6+lIJTqsEeugkvTWuFe3zFMa/ZdOpeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:24:54.948282Z","bundle_sha256":"d3836dd914e930b17352bdcb6fa75a680dff40c7e678eb897125f21ad6f7269a"}}