{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:QMIOPOIYFQHLMCZXSD24MU7M7K","short_pith_number":"pith:QMIOPOIY","schema_version":"1.0","canonical_sha256":"8310e7b9182c0eb60b3790f5c653ecfa8367a3db38ef9a9e58db293117693057","source":{"kind":"arxiv","id":"cs/0701076","version":2},"attestation_state":"computed","paper":{"title":"Time-complexity semantics for feasible affine recursions (extended abstract)","license":"","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"James S. Royer, Norman Danner","submitted_at":"2007-01-11T16:22:11Z","abstract_excerpt":"The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursions. Here we extend ATR so that a broad range of affine recursions are directly expressible. In particular, the revised ATR can fairly naturally express the classic insertion- and selection-sort algorit"},"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":"cs/0701076","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.LO","submitted_at":"2007-01-11T16:22:11Z","cross_cats_sorted":[],"title_canon_sha256":"759165763f66c062f798ff25842a771182e0b287e9c45cecb47d8194c03e5d61","abstract_canon_sha256":"479c6a80c2cef0af24106e5682ce70557fd46df51e7375e1477cd9cfe4c3c38d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:00:15.665861Z","signature_b64":"1fRn5cw9YbSOZ+7XDYnrJ8FUqeKlI1nIvZtRsWkFYlMz6L9vu71fHTdki3ay6dxBD5gy8VEcrkwDicmN/555Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8310e7b9182c0eb60b3790f5c653ecfa8367a3db38ef9a9e58db293117693057","last_reissued_at":"2026-07-04T15:00:15.665460Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:00:15.665460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time-complexity semantics for feasible affine recursions (extended abstract)","license":"","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"James S. Royer, Norman Danner","submitted_at":"2007-01-11T16:22:11Z","abstract_excerpt":"The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursions. Here we extend ATR so that a broad range of affine recursions are directly expressible. In particular, the revised ATR can fairly naturally express the classic insertion- and selection-sort algorit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0701076","kind":"arxiv","version":2},"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/cs/0701076/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":"cs/0701076","created_at":"2026-07-04T15:00:15.665520+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0701076v2","created_at":"2026-07-04T15:00:15.665520+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0701076","created_at":"2026-07-04T15:00:15.665520+00:00"},{"alias_kind":"pith_short_12","alias_value":"QMIOPOIYFQHL","created_at":"2026-07-04T15:00:15.665520+00:00"},{"alias_kind":"pith_short_16","alias_value":"QMIOPOIYFQHLMCZX","created_at":"2026-07-04T15:00:15.665520+00:00"},{"alias_kind":"pith_short_8","alias_value":"QMIOPOIY","created_at":"2026-07-04T15:00:15.665520+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/QMIOPOIYFQHLMCZXSD24MU7M7K","json":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K.json","graph_json":"https://pith.science/api/pith-number/QMIOPOIYFQHLMCZXSD24MU7M7K/graph.json","events_json":"https://pith.science/api/pith-number/QMIOPOIYFQHLMCZXSD24MU7M7K/events.json","paper":"https://pith.science/paper/QMIOPOIY"},"agent_actions":{"view_html":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K","download_json":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K.json","view_paper":"https://pith.science/paper/QMIOPOIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0701076&json=true","fetch_graph":"https://pith.science/api/pith-number/QMIOPOIYFQHLMCZXSD24MU7M7K/graph.json","fetch_events":"https://pith.science/api/pith-number/QMIOPOIYFQHLMCZXSD24MU7M7K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K/action/storage_attestation","attest_author":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K/action/author_attestation","sign_citation":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K/action/citation_signature","submit_replication":"https://pith.science/pith/QMIOPOIYFQHLMCZXSD24MU7M7K/action/replication_record"}},"created_at":"2026-07-04T15:00:15.665520+00:00","updated_at":"2026-07-04T15:00:15.665520+00:00"}