{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PSKFQ6CPR5KXZYYRZ6VDAL6QJ7","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":"159d62a3b11b2f1baf17e0c13a3dccf0c1602f0614dfd9142b798cf2afce2b7d","cross_cats_sorted":["cs.PL","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-04T11:15:10Z","title_canon_sha256":"a759cde9821d73c376388e8c53890cbc6f24b4705f73a0db94b36255814de4fb"},"schema_version":"1.0","source":{"id":"2403.01939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.01939","created_at":"2026-07-05T07:51:54Z"},{"alias_kind":"arxiv_version","alias_value":"2403.01939v1","created_at":"2026-07-05T07:51:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.01939","created_at":"2026-07-05T07:51:54Z"},{"alias_kind":"pith_short_12","alias_value":"PSKFQ6CPR5KX","created_at":"2026-07-05T07:51:54Z"},{"alias_kind":"pith_short_16","alias_value":"PSKFQ6CPR5KXZYYR","created_at":"2026-07-05T07:51:54Z"},{"alias_kind":"pith_short_8","alias_value":"PSKFQ6CP","created_at":"2026-07-05T07:51:54Z"}],"graph_snapshots":[{"event_id":"sha256:c174d7aad55579cee2cebed7216d947583edfc178c23a13a1dfd5cb45533baea","target":"graph","created_at":"2026-07-05T07:51:54Z","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/2403.01939/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an extension of Martin-L\\\"of Type Theory that contains a tiny object; a type for which there is a right adjoint to the formation of function types as well as the expected left adjoint. We demonstrate the practicality of this type theory by proving various properties related to tininess internally and suggest a few potential applications.","authors_text":"Mitchell Riley","cross_cats":["cs.PL","math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-04T11:15:10Z","title":"A Type Theory with a Tiny Object"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.01939","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:a489803d8e5647fe1bb72ffb35ce1bc3c9f03553ab8f7932e6e340b70ef3d9fb","target":"record","created_at":"2026-07-05T07:51:54Z","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":"159d62a3b11b2f1baf17e0c13a3dccf0c1602f0614dfd9142b798cf2afce2b7d","cross_cats_sorted":["cs.PL","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-04T11:15:10Z","title_canon_sha256":"a759cde9821d73c376388e8c53890cbc6f24b4705f73a0db94b36255814de4fb"},"schema_version":"1.0","source":{"id":"2403.01939","kind":"arxiv","version":1}},"canonical_sha256":"7c9458784f8f557ce311cfaa302fd04fd21aca41db22eb5c6e7004351fe70027","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c9458784f8f557ce311cfaa302fd04fd21aca41db22eb5c6e7004351fe70027","first_computed_at":"2026-07-05T07:51:54.368880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:51:54.368880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bAQwY4ikAUGjBGarqfgz3qbxheMbV2Jrq+obFidULz0DrrU7CfwNk8HAS/aDZZGk2hQRdhwME+lwBNIQz8kuCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:51:54.369357Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.01939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a489803d8e5647fe1bb72ffb35ce1bc3c9f03553ab8f7932e6e340b70ef3d9fb","sha256:c174d7aad55579cee2cebed7216d947583edfc178c23a13a1dfd5cb45533baea"],"state_sha256":"69f5839c50b4ab07e05db0ac6c4c604228cdbc26a3c0715ee510fb9649c3f6de"}