{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:G7SBKQOGXQ75R6JN6YHKWMRF4Y","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":"056d7c96229d255985daab546a9aa99081f2dd880c6c384b32b0319913fe4716","cross_cats_sorted":["cs.CL","cs.LG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.CC","submitted_at":"2025-04-20T22:35:53Z","title_canon_sha256":"58477d15ea26c4151017b7aef4c8e30b3f720650697380da208a34a287f7264d"},"schema_version":"1.0","source":{"id":"2507.12469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12469","created_at":"2026-07-05T11:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12469v1","created_at":"2026-07-05T11:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12469","created_at":"2026-07-05T11:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"G7SBKQOGXQ75","created_at":"2026-07-05T11:38:32Z"},{"alias_kind":"pith_short_16","alias_value":"G7SBKQOGXQ75R6JN","created_at":"2026-07-05T11:38:32Z"},{"alias_kind":"pith_short_8","alias_value":"G7SBKQOG","created_at":"2026-07-05T11:38:32Z"}],"graph_snapshots":[{"event_id":"sha256:b7833cb70b4fe7a790374b237d8229ade85e39272ee172e0bdd9f642d33174d8","target":"graph","created_at":"2026-07-05T11:38:32Z","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/2507.12469/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper explores the computational complexity of diffusion-based language modeling. We prove a dichotomy based on the quality of the score-matching network in a diffusion model. In one direction, a network that exactly computes the score function of some initial distribution can only perform language modeling within the $\\mathsf{TC}^0$ complexity class, reflecting limitations tied to rapid convergence. In the other direction, we show that if there is no requirement for the network to match any score function, then diffusion modeling can simulate any Turing machine in a certain sense. This d","authors_text":"Yuxi Liu","cross_cats":["cs.CL","cs.LG"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.CC","submitted_at":"2025-04-20T22:35:53Z","title":"Perfect diffusion is $\\mathsf{TC}^0$ -- Bad diffusion is Turing-complete"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12469","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:c47dba3e9c612b136489339dac995faa4e98816b99ab5922b2949d895074db83","target":"record","created_at":"2026-07-05T11:38:32Z","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":"056d7c96229d255985daab546a9aa99081f2dd880c6c384b32b0319913fe4716","cross_cats_sorted":["cs.CL","cs.LG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.CC","submitted_at":"2025-04-20T22:35:53Z","title_canon_sha256":"58477d15ea26c4151017b7aef4c8e30b3f720650697380da208a34a287f7264d"},"schema_version":"1.0","source":{"id":"2507.12469","kind":"arxiv","version":1}},"canonical_sha256":"37e41541c6bc3fd8f92df60eab3225e639e8088e64c5def08445677d00e27bb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37e41541c6bc3fd8f92df60eab3225e639e8088e64c5def08445677d00e27bb7","first_computed_at":"2026-07-05T11:38:32.453180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:32.453180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5qCTOt4nmg78jOEIephN01MXUcbwx4TRs5Q10eSsuyW8ESToJyjbtObblFHAIZKEM+sMBuWEPuMDDRDujx/BBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:32.453761Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.12469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c47dba3e9c612b136489339dac995faa4e98816b99ab5922b2949d895074db83","sha256:b7833cb70b4fe7a790374b237d8229ade85e39272ee172e0bdd9f642d33174d8"],"state_sha256":"8db5075dd13b944fe47078406c8ea6330d87f0dcd56a969dfcd737c1e9bf1c9c"}