{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:O2PKQR6GQ2FAPZA5OJQD7DVTX7","short_pith_number":"pith:O2PKQR6G","canonical_record":{"source":{"id":"2512.15391","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2025-12-17T12:41:27Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"e4211a5e8d0331ae90c281221f2922bcffa81eb3eda67d729750a0ef8e36e2b8","abstract_canon_sha256":"c175d17d70498bb5f0b181c0539e35f1e276fe10b9211ef259d33ff7434f9cde"},"schema_version":"1.0"},"canonical_sha256":"769ea847c6868a07e41d72603f8eb3bffa3b02488cc90a23433076d9e5bbe41a","source":{"kind":"arxiv","id":"2512.15391","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.15391","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2512.15391v3","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.15391","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"O2PKQR6GQ2FA","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"O2PKQR6GQ2FAPZA5","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"O2PKQR6G","created_at":"2026-06-09T01:04:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:O2PKQR6GQ2FAPZA5OJQD7DVTX7","target":"record","payload":{"canonical_record":{"source":{"id":"2512.15391","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2025-12-17T12:41:27Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"e4211a5e8d0331ae90c281221f2922bcffa81eb3eda67d729750a0ef8e36e2b8","abstract_canon_sha256":"c175d17d70498bb5f0b181c0539e35f1e276fe10b9211ef259d33ff7434f9cde"},"schema_version":"1.0"},"canonical_sha256":"769ea847c6868a07e41d72603f8eb3bffa3b02488cc90a23433076d9e5bbe41a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:40.466377Z","signature_b64":"z8DK1xt6bhhkBBhecOp6WIsKCEKBy1qiDt6M9WwCEOlqbVq2+yewWaIiYhXRCmfl4s1emNjZC5Z42aCLFK0vBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"769ea847c6868a07e41d72603f8eb3bffa3b02488cc90a23433076d9e5bbe41a","last_reissued_at":"2026-06-09T01:04:40.465904Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:40.465904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.15391","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YjLJKf4VEC80gmTbyqLJwxVZo1PHvWLOgt8cTd+Qa8OnJf2ZfkxDBpsati6t2toC62+krFJeUYNeGxsn32/NAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:41:13.271382Z"},"content_sha256":"730bc2d8ace0bfe6f8c9c324dd95e360073b31e3115e777f8f804a020839997c","schema_version":"1.0","event_id":"sha256:730bc2d8ace0bfe6f8c9c324dd95e360073b31e3115e777f8f804a020839997c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:O2PKQR6GQ2FAPZA5OJQD7DVTX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform Interpolation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Sam van Gool","submitted_at":"2025-12-17T12:41:27Z","abstract_excerpt":"Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic propositional logic. We outline how this theorem may be proved semantically via the definability of bisimulation quantifiers, and how it generalizes to an open mapping theorem between Esakia spaces. We also discuss connections between uniform interpolation and research in categorical logic, algebra, and model theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.15391","kind":"arxiv","version":3},"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/2512.15391/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":"2026-06-09T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6KBoH3/oELoIjWXFTgLH85sXVmPwnFF7PEcN3OEdyxscrTnV1ayfRT8ZFxzcSJmRvr1l9pih5Z6iAHwS3SQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:41:13.272004Z"},"content_sha256":"4915059e3359c7553f3b3adf6635b5af451eef49d5759cb9d0bb765923b3f65c","schema_version":"1.0","event_id":"sha256:4915059e3359c7553f3b3adf6635b5af451eef49d5759cb9d0bb765923b3f65c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2PKQR6GQ2FAPZA5OJQD7DVTX7/bundle.json","state_url":"https://pith.science/pith/O2PKQR6GQ2FAPZA5OJQD7DVTX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2PKQR6GQ2FAPZA5OJQD7DVTX7/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":"2026-06-24T07:41:13Z","links":{"resolver":"https://pith.science/pith/O2PKQR6GQ2FAPZA5OJQD7DVTX7","bundle":"https://pith.science/pith/O2PKQR6GQ2FAPZA5OJQD7DVTX7/bundle.json","state":"https://pith.science/pith/O2PKQR6GQ2FAPZA5OJQD7DVTX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2PKQR6GQ2FAPZA5OJQD7DVTX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:O2PKQR6GQ2FAPZA5OJQD7DVTX7","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":"c175d17d70498bb5f0b181c0539e35f1e276fe10b9211ef259d33ff7434f9cde","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2025-12-17T12:41:27Z","title_canon_sha256":"e4211a5e8d0331ae90c281221f2922bcffa81eb3eda67d729750a0ef8e36e2b8"},"schema_version":"1.0","source":{"id":"2512.15391","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.15391","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2512.15391v3","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.15391","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"O2PKQR6GQ2FA","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"O2PKQR6GQ2FAPZA5","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"O2PKQR6G","created_at":"2026-06-09T01:04:40Z"}],"graph_snapshots":[{"event_id":"sha256:4915059e3359c7553f3b3adf6635b5af451eef49d5759cb9d0bb765923b3f65c","target":"graph","created_at":"2026-06-09T01:04:40Z","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/2512.15391/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic propositional logic. We outline how this theorem may be proved semantically via the definability of bisimulation quantifiers, and how it generalizes to an open mapping theorem between Esakia spaces. We also discuss connections between uniform interpolation and research in categorical logic, algebra, and model theory.","authors_text":"Sam van Gool","cross_cats":["cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2025-12-17T12:41:27Z","title":"Uniform Interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.15391","kind":"arxiv","version":3},"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":"sha256:730bc2d8ace0bfe6f8c9c324dd95e360073b31e3115e777f8f804a020839997c","target":"record","created_at":"2026-06-09T01:04:40Z","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":"c175d17d70498bb5f0b181c0539e35f1e276fe10b9211ef259d33ff7434f9cde","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2025-12-17T12:41:27Z","title_canon_sha256":"e4211a5e8d0331ae90c281221f2922bcffa81eb3eda67d729750a0ef8e36e2b8"},"schema_version":"1.0","source":{"id":"2512.15391","kind":"arxiv","version":3}},"canonical_sha256":"769ea847c6868a07e41d72603f8eb3bffa3b02488cc90a23433076d9e5bbe41a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769ea847c6868a07e41d72603f8eb3bffa3b02488cc90a23433076d9e5bbe41a","first_computed_at":"2026-06-09T01:04:40.465904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:04:40.465904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z8DK1xt6bhhkBBhecOp6WIsKCEKBy1qiDt6M9WwCEOlqbVq2+yewWaIiYhXRCmfl4s1emNjZC5Z42aCLFK0vBA==","signature_status":"signed_v1","signed_at":"2026-06-09T01:04:40.466377Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.15391","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:730bc2d8ace0bfe6f8c9c324dd95e360073b31e3115e777f8f804a020839997c","sha256:4915059e3359c7553f3b3adf6635b5af451eef49d5759cb9d0bb765923b3f65c"],"state_sha256":"35e60fe7f00db65eb518f95cfea796bb58f7e08ebc8704124de1ed580ab85545"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4DfYRPBnIIClcI+JKqjBryIvVCpmuCvJCR1fIGqzLgwEPeKzle67YCWM/Z1dZjTjNNtF9RPWrPAHW+dCQEkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:41:13.274765Z","bundle_sha256":"0036e25de889da3d5dab188c9d260c45b82b305274606e79f6a021179edef484"}}