{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:KSI45UPVINYNIBJYQ3BQILLUHQ","short_pith_number":"pith:KSI45UPV","schema_version":"1.0","canonical_sha256":"5491ced1f54370d4053886c3042d743c347a932735140886f10fd0f6b8c0685a","source":{"kind":"arxiv","id":"2607.13662","version":1},"attestation_state":"computed","paper":{"title":"Definitional Inversion, Without Normalisation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Adrien Frabetti Mathieu, Mario Carneiro, Meven Lennon-Bertrand, Paul-Andr\\'e Melli\\`es, Stephanie Weirich, Thierry Coquand","submitted_at":"2026-07-15T10:06:45Z","abstract_excerpt":"We contribute a new proof technique, based on domain theory, to prove key meta-theoretic properties of dependent type systems: definitional inversion properties, i.e. injectivity and no-confusion of type constructors. This proof technique is independent of normalisation, and indeed applies even for the \"type-in-type\" rule of Martin-L\\\"of's original type theory. Our proof is the first to establish injectivity of type constructors for such a system in the presence of $\\eta$ laws. More generally, the technique is motivated by, and intended for, the metatheory of systems such as Idris, Lean, or de"},"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":"2607.13662","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-07-15T10:06:45Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"aaa1c1ffc5201611e080e6897936049440fcdf0409cc3cda9543ecf562f38a1a","abstract_canon_sha256":"3702ec3d65aa9a76ca93952943a2efba7425d39c3b4d52aee7c863fa87070bdd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:22:59.538739Z","signature_b64":"Sc/aoSixp/fPszSMagillApChn3UCXKcaG+20JeWDpNLM5Xdp6kusTGoAR2MOIB7ZwtZqgg/GyeaklQtGMhACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5491ced1f54370d4053886c3042d743c347a932735140886f10fd0f6b8c0685a","last_reissued_at":"2026-07-16T01:22:59.537863Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:22:59.537863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Definitional Inversion, Without Normalisation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Adrien Frabetti Mathieu, Mario Carneiro, Meven Lennon-Bertrand, Paul-Andr\\'e Melli\\`es, Stephanie Weirich, Thierry Coquand","submitted_at":"2026-07-15T10:06:45Z","abstract_excerpt":"We contribute a new proof technique, based on domain theory, to prove key meta-theoretic properties of dependent type systems: definitional inversion properties, i.e. injectivity and no-confusion of type constructors. This proof technique is independent of normalisation, and indeed applies even for the \"type-in-type\" rule of Martin-L\\\"of's original type theory. Our proof is the first to establish injectivity of type constructors for such a system in the presence of $\\eta$ laws. More generally, the technique is motivated by, and intended for, the metatheory of systems such as Idris, Lean, or de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13662","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/2607.13662/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.13662","created_at":"2026-07-16T01:22:59.538337+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13662v1","created_at":"2026-07-16T01:22:59.538337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13662","created_at":"2026-07-16T01:22:59.538337+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSI45UPVINYN","created_at":"2026-07-16T01:22:59.538337+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSI45UPVINYNIBJY","created_at":"2026-07-16T01:22:59.538337+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSI45UPV","created_at":"2026-07-16T01:22:59.538337+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/KSI45UPVINYNIBJYQ3BQILLUHQ","json":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ.json","graph_json":"https://pith.science/api/pith-number/KSI45UPVINYNIBJYQ3BQILLUHQ/graph.json","events_json":"https://pith.science/api/pith-number/KSI45UPVINYNIBJYQ3BQILLUHQ/events.json","paper":"https://pith.science/paper/KSI45UPV"},"agent_actions":{"view_html":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ","download_json":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ.json","view_paper":"https://pith.science/paper/KSI45UPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13662&json=true","fetch_graph":"https://pith.science/api/pith-number/KSI45UPVINYNIBJYQ3BQILLUHQ/graph.json","fetch_events":"https://pith.science/api/pith-number/KSI45UPVINYNIBJYQ3BQILLUHQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ/action/storage_attestation","attest_author":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ/action/author_attestation","sign_citation":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ/action/citation_signature","submit_replication":"https://pith.science/pith/KSI45UPVINYNIBJYQ3BQILLUHQ/action/replication_record"}},"created_at":"2026-07-16T01:22:59.538337+00:00","updated_at":"2026-07-16T01:22:59.538337+00:00"}