{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ZK4WREY7PI5VHUTDYSY25UXCBE","short_pith_number":"pith:ZK4WREY7","schema_version":"1.0","canonical_sha256":"cab968931f7a3b53d263c4b1aed2e2093b5e10cd47af16840c58715560a7dcce","source":{"kind":"arxiv","id":"2507.19247","version":5},"attestation_state":"computed","paper":{"title":"A Markov Categorical Framework for Language Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Yifan Zhang","submitted_at":"2025-07-25T13:14:03Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.19247","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-25T13:14:03Z","cross_cats_sorted":["cs.AI","cs.CL"],"title_canon_sha256":"2ad4151697264bf5db969bde4cb8c0c72074b4455167bfac164bc660b8d13286","abstract_canon_sha256":"6f830309c325d95c459daa0fa9968f2f55b20c886675bb870ade22b38fa2a20d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:34.967460Z","signature_b64":"ytZCrgSJPn9CadfQ3R3H+l67YhiMFhFROsykgAG5NtzpcmD/EhKl3r6pJhXF3NFmE7FhHOFe+9uWJolipIZ9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cab968931f7a3b53d263c4b1aed2e2093b5e10cd47af16840c58715560a7dcce","last_reissued_at":"2026-05-18T03:09:34.966984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:34.966984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Markov Categorical Framework for Language Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Yifan Zhang","submitted_at":"2025-07-25T13:14:03Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19247","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.19247","created_at":"2026-05-18T03:09:34.967056+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.19247v5","created_at":"2026-05-18T03:09:34.967056+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19247","created_at":"2026-05-18T03:09:34.967056+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZK4WREY7PI5V","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZK4WREY7PI5VHUTD","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZK4WREY7","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE","json":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE.json","graph_json":"https://pith.science/api/pith-number/ZK4WREY7PI5VHUTDYSY25UXCBE/graph.json","events_json":"https://pith.science/api/pith-number/ZK4WREY7PI5VHUTDYSY25UXCBE/events.json","paper":"https://pith.science/paper/ZK4WREY7"},"agent_actions":{"view_html":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE","download_json":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE.json","view_paper":"https://pith.science/paper/ZK4WREY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.19247&json=true","fetch_graph":"https://pith.science/api/pith-number/ZK4WREY7PI5VHUTDYSY25UXCBE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZK4WREY7PI5VHUTDYSY25UXCBE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE/action/storage_attestation","attest_author":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE/action/author_attestation","sign_citation":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE/action/citation_signature","submit_replication":"https://pith.science/pith/ZK4WREY7PI5VHUTDYSY25UXCBE/action/replication_record"}},"created_at":"2026-05-18T03:09:34.967056+00:00","updated_at":"2026-05-18T03:09:34.967056+00:00"}