{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZK4WREY7PI5VHUTDYSY25UXCBE","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":"6f830309c325d95c459daa0fa9968f2f55b20c886675bb870ade22b38fa2a20d","cross_cats_sorted":["cs.AI","cs.CL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-25T13:14:03Z","title_canon_sha256":"2ad4151697264bf5db969bde4cb8c0c72074b4455167bfac164bc660b8d13286"},"schema_version":"1.0","source":{"id":"2507.19247","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19247","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19247v5","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19247","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZK4WREY7PI5V","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZK4WREY7PI5VHUTD","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZK4WREY7","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:308f92123622122e5bea1fb563b97daf61d0e45a0b45703becda4e87872de6e7","target":"graph","created_at":"2026-05-18T03:09:34Z","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"},"paper":{"abstract_excerpt":"Autoregressive language models achieve remarkable performance, yet a unified theory explaining their internal mechanisms, how training shapes representations, and why these representations support complex behavior remains incomplete. We introduce an analytical framework that models the single-step generation process as a composition of information-processing stages using the language of Markov categories. This compositional perspective connects three aspects of language modeling that are often studied separately: the training objective, the geometry of the learned representation space, and pra","authors_text":"Yifan Zhang","cross_cats":["cs.AI","cs.CL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-25T13:14:03Z","title":"A Markov Categorical Framework for Language Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19247","kind":"arxiv","version":5},"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:be20c3672fd0e969d3f8b0fcc9025bf94f471430ea510ecd6008aec4cde25f00","target":"record","created_at":"2026-05-18T03:09:34Z","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":"6f830309c325d95c459daa0fa9968f2f55b20c886675bb870ade22b38fa2a20d","cross_cats_sorted":["cs.AI","cs.CL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-25T13:14:03Z","title_canon_sha256":"2ad4151697264bf5db969bde4cb8c0c72074b4455167bfac164bc660b8d13286"},"schema_version":"1.0","source":{"id":"2507.19247","kind":"arxiv","version":5}},"canonical_sha256":"cab968931f7a3b53d263c4b1aed2e2093b5e10cd47af16840c58715560a7dcce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cab968931f7a3b53d263c4b1aed2e2093b5e10cd47af16840c58715560a7dcce","first_computed_at":"2026-05-18T03:09:34.966984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:34.966984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ytZCrgSJPn9CadfQ3R3H+l67YhiMFhFROsykgAG5NtzpcmD/EhKl3r6pJhXF3NFmE7FhHOFe+9uWJolipIZ9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:34.967460Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.19247","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be20c3672fd0e969d3f8b0fcc9025bf94f471430ea510ecd6008aec4cde25f00","sha256:308f92123622122e5bea1fb563b97daf61d0e45a0b45703becda4e87872de6e7"],"state_sha256":"696506baa33aa77b75801cfd3d649ae53171c08217aef7935fd80037cf4e32ec"}