{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EN7EAQVLZBKCFMMUN2BBN53L2Z","short_pith_number":"pith:EN7EAQVL","canonical_record":{"source":{"id":"2608.08145","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-08-08T14:08:14Z","cross_cats_sorted":[],"title_canon_sha256":"68e87b355f296b47ba8b07b360822f15e6f61d12a3adec27bd1d3795dfc5cf25","abstract_canon_sha256":"19d25183d52adbe960a77fea50d7d106122c5784dd4432d380be0a192ccce692"},"schema_version":"1.0"},"canonical_sha256":"237e4042abc85422b1946e8216f76bd655adc1b8f7ceac95f86740c04c9380a3","source":{"kind":"arxiv","id":"2608.08145","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08145","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08145v1","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08145","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"pith_short_12","alias_value":"EN7EAQVLZBKC","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"pith_short_16","alias_value":"EN7EAQVLZBKCFMMU","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"pith_short_8","alias_value":"EN7EAQVL","created_at":"2026-08-11T01:21:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EN7EAQVLZBKCFMMUN2BBN53L2Z","target":"record","payload":{"canonical_record":{"source":{"id":"2608.08145","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-08-08T14:08:14Z","cross_cats_sorted":[],"title_canon_sha256":"68e87b355f296b47ba8b07b360822f15e6f61d12a3adec27bd1d3795dfc5cf25","abstract_canon_sha256":"19d25183d52adbe960a77fea50d7d106122c5784dd4432d380be0a192ccce692"},"schema_version":"1.0"},"canonical_sha256":"237e4042abc85422b1946e8216f76bd655adc1b8f7ceac95f86740c04c9380a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:21:48.829422Z","signature_b64":"/BGOQA0cN2fbhf1m/GohW7CZrXfarlvlB0bbqiGYP7H0jLdvEaF/9HWwRGp0nEWYpVyc8H7I9b13wGcmkVEqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"237e4042abc85422b1946e8216f76bd655adc1b8f7ceac95f86740c04c9380a3","last_reissued_at":"2026-08-11T01:21:48.827084Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:21:48.827084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.08145","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":"2026-08-11T01:21:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nF1xeKhDFitohORmeCSN1m/WB+m1bRyfIIb2eDDT1FPuosx+qxbeDc5qxbBkzhSAUAkzmYRZHl1uXUgZeEtkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T15:20:02.412736Z"},"content_sha256":"25cb16f726e36810919ff9b97a519f37be590bf0ea8d7d654e1a0319c706dc92","schema_version":"1.0","event_id":"sha256:25cb16f726e36810919ff9b97a519f37be590bf0ea8d7d654e1a0319c706dc92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EN7EAQVLZBKCFMMUN2BBN53L2Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the (Intuitionistic) Logic of Next-Token Prediction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Paul Tarau (University of North Texas)","submitted_at":"2026-08-08T14:08:14Z","abstract_excerpt":"We model in intuitionistic implicational logic the key enabler of today's GenerativeAI: the next-token prediction in autoregressive causal neural networks.\n  In our framework, next-token prediction corresponds to modus ponens, and sequence processing becomes constructive proof extension under the Curry-Howard correspondence. Our Prolog-based specialized theorem provers validate fundamental properties of the neural models, among which relations between commutative vs. non-commutative sequencing  and single-token vs. multi-token prediction choices.\n  We derive a neural architecture equivalent to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08145","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/2608.08145/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":"2026-08-11T01:21:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P05hz4BwdKKcrhDQIEa0UVDhgghe86+MOpu2FAoTHqveoqvrpKyDKqgBqT01C3i5328WfMHd+LdwzcLW5rE5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T15:20:02.413361Z"},"content_sha256":"59a496f41af3e304995c004fbf9b25e8cdc8b191bb5f166fcb0252542e038e07","schema_version":"1.0","event_id":"sha256:59a496f41af3e304995c004fbf9b25e8cdc8b191bb5f166fcb0252542e038e07"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:EN7EAQVLZBKCFMMUN2BBN53L2Z","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.18653/v1/2023.emnlp-main.313) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Theo Olausson, Alex Gu, Ben Lipkin, Cedegao Zhang, Armando Solar-Lezama, Joshua Tenenbaum & Roger Levy (2023): LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers. In: Proceedings","arxiv_id":"2608.08145","detector":"doi_compliance","evidence":{"ref_index":4,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.18653/v1/2023.emnlp-","reconstructed_doi":"10.18653/v1/2023.emnlp-main.313"},"severity":"advisory","ref_index":4,"audited_at":"2026-08-12T00:29:26.465602Z","event_type":"pith.integrity.v1","detected_doi":"10.18653/v1/2023.emnlp-main.313","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"167e0cfe1e158079dfa9d95e290c2bd941dd19089625301589efdb7b00606d30","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":19210,"payload_sha256":"f4785a36fa7bddae441916d9e7c8c4985014636f25e4c6de70557e44efc4cae4","signature_b64":"YijYBlXT9Fi30JH/+tzfCniNwfOO2b51GSbwQs2mb6ULlxZejWKRLdnY+tjTYoKIGmpFazy7hCbIlDFeldqiBQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-12T00:33:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iko4AgZ6wH3u1M1jkMKAVAReEfmA04nCB0M7wNmMGyQz9vnpiWLbaycGCQFj9vN1QvB4RU+dr27Yr8quayLfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T15:20:02.415925Z"},"content_sha256":"5620bbcf798ccd7215d08aa046049df60c49aa1f757e8354cfb1148b68390fe0","schema_version":"1.0","event_id":"sha256:5620bbcf798ccd7215d08aa046049df60c49aa1f757e8354cfb1148b68390fe0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EN7EAQVLZBKCFMMUN2BBN53L2Z/bundle.json","state_url":"https://pith.science/pith/EN7EAQVLZBKCFMMUN2BBN53L2Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EN7EAQVLZBKCFMMUN2BBN53L2Z/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":"2026-08-19T15:20:02Z","links":{"resolver":"https://pith.science/pith/EN7EAQVLZBKCFMMUN2BBN53L2Z","bundle":"https://pith.science/pith/EN7EAQVLZBKCFMMUN2BBN53L2Z/bundle.json","state":"https://pith.science/pith/EN7EAQVLZBKCFMMUN2BBN53L2Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EN7EAQVLZBKCFMMUN2BBN53L2Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EN7EAQVLZBKCFMMUN2BBN53L2Z","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"19d25183d52adbe960a77fea50d7d106122c5784dd4432d380be0a192ccce692","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-08-08T14:08:14Z","title_canon_sha256":"68e87b355f296b47ba8b07b360822f15e6f61d12a3adec27bd1d3795dfc5cf25"},"schema_version":"1.0","source":{"id":"2608.08145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08145","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08145v1","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08145","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"pith_short_12","alias_value":"EN7EAQVLZBKC","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"pith_short_16","alias_value":"EN7EAQVLZBKCFMMU","created_at":"2026-08-11T01:21:48Z"},{"alias_kind":"pith_short_8","alias_value":"EN7EAQVL","created_at":"2026-08-11T01:21:48Z"}],"graph_snapshots":[{"event_id":"sha256:59a496f41af3e304995c004fbf9b25e8cdc8b191bb5f166fcb0252542e038e07","target":"graph","created_at":"2026-08-11T01:21:48Z","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/2608.08145/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We model in intuitionistic implicational logic the key enabler of today's GenerativeAI: the next-token prediction in autoregressive causal neural networks.\n  In our framework, next-token prediction corresponds to modus ponens, and sequence processing becomes constructive proof extension under the Curry-Howard correspondence. Our Prolog-based specialized theorem provers validate fundamental properties of the neural models, among which relations between commutative vs. non-commutative sequencing  and single-token vs. multi-token prediction choices.\n  We derive a neural architecture equivalent to","authors_text":"Paul Tarau (University of North Texas)","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-08-08T14:08:14Z","title":"On the (Intuitionistic) Logic of Next-Token Prediction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08145","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":"sha256:25cb16f726e36810919ff9b97a519f37be590bf0ea8d7d654e1a0319c706dc92","target":"record","created_at":"2026-08-11T01:21:48Z","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":"19d25183d52adbe960a77fea50d7d106122c5784dd4432d380be0a192ccce692","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-08-08T14:08:14Z","title_canon_sha256":"68e87b355f296b47ba8b07b360822f15e6f61d12a3adec27bd1d3795dfc5cf25"},"schema_version":"1.0","source":{"id":"2608.08145","kind":"arxiv","version":1}},"canonical_sha256":"237e4042abc85422b1946e8216f76bd655adc1b8f7ceac95f86740c04c9380a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"237e4042abc85422b1946e8216f76bd655adc1b8f7ceac95f86740c04c9380a3","first_computed_at":"2026-08-11T01:21:48.827084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:21:48.827084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/BGOQA0cN2fbhf1m/GohW7CZrXfarlvlB0bbqiGYP7H0jLdvEaF/9HWwRGp0nEWYpVyc8H7I9b13wGcmkVEqCw==","signature_status":"signed_v1","signed_at":"2026-08-11T01:21:48.829422Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.08145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25cb16f726e36810919ff9b97a519f37be590bf0ea8d7d654e1a0319c706dc92","sha256:59a496f41af3e304995c004fbf9b25e8cdc8b191bb5f166fcb0252542e038e07","sha256:5620bbcf798ccd7215d08aa046049df60c49aa1f757e8354cfb1148b68390fe0"],"state_sha256":"9782dbe67aa1342677a7dc6e3a71b8f7c05aac130bc5479f6cf3d47a5346cd33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQyG4Cm6eFCXVaWAy6q8/XF+jReuDvnZxyO0UbL3GuQwEjIlrtysLPf/vvdmw2nyC3Rlx/cI/RlNBLU3ecEYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T15:20:02.418336Z","bundle_sha256":"72ef250b4208e20aa4baca692d3f40c86d977bdff93cc8d135174be5aa7895b4"}}