{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:C6TYBUUUSCLRQTILHKMJ34QJLK","short_pith_number":"pith:C6TYBUUU","schema_version":"1.0","canonical_sha256":"17a780d2949097184d0b3a989df2095a8af4852fc57fd06dec0e988648b7b4c8","source":{"kind":"arxiv","id":"1508.06493","version":2},"attestation_state":"computed","paper":{"title":"Infinite Time Recognizability from Random Oracles and the Recognizable Jump Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Merlin Carl","submitted_at":"2015-08-26T13:46:29Z","abstract_excerpt":"By a theorem of Sacks, if a real $x$ is recursive relative to all elements of a set of positive Lebesgue measure, $x$ is recursive. This statement, and the analogous statement for non-meagerness instead of positive Lebesgue measure, have been shown to carry over to many models of transfinite computations. Here, we start exploring another analogue concerning recognizability rather than computability. We introduce a notion of relativized recognizability and show that, for Infinite Time Turing Machines (ITTMs), if a real $x$ is recognizable relative to all elements of a non-meager Borel set $Y$, "},"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":"1508.06493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-26T13:46:29Z","cross_cats_sorted":[],"title_canon_sha256":"9c9c7d519689cd5f8bb42e7e2a9a99d01db0f4637f15d16c7e213a3e39cce574","abstract_canon_sha256":"61d442c7dd5a1a0fc8d9968f0fed3b643b781a189a87e2c64e24ff7391ba463d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:33.564443Z","signature_b64":"jo8WGtn6CrYeeeqloSBx/CgKfR8OKObEBryU3EXRXA7UX/J/ImkKVVdJSQ9ySTvjEL2aRElo2Dy3xIIq8TV9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a780d2949097184d0b3a989df2095a8af4852fc57fd06dec0e988648b7b4c8","last_reissued_at":"2026-05-18T00:36:33.564037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:33.564037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite Time Recognizability from Random Oracles and the Recognizable Jump Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Merlin Carl","submitted_at":"2015-08-26T13:46:29Z","abstract_excerpt":"By a theorem of Sacks, if a real $x$ is recursive relative to all elements of a set of positive Lebesgue measure, $x$ is recursive. This statement, and the analogous statement for non-meagerness instead of positive Lebesgue measure, have been shown to carry over to many models of transfinite computations. Here, we start exploring another analogue concerning recognizability rather than computability. We introduce a notion of relativized recognizability and show that, for Infinite Time Turing Machines (ITTMs), if a real $x$ is recognizable relative to all elements of a non-meager Borel set $Y$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06493","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":""},"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":"1508.06493","created_at":"2026-05-18T00:36:33.564097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.06493v2","created_at":"2026-05-18T00:36:33.564097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06493","created_at":"2026-05-18T00:36:33.564097+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6TYBUUUSCLR","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6TYBUUUSCLRQTIL","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6TYBUUU","created_at":"2026-05-18T12:29:14.074870+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/C6TYBUUUSCLRQTILHKMJ34QJLK","json":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK.json","graph_json":"https://pith.science/api/pith-number/C6TYBUUUSCLRQTILHKMJ34QJLK/graph.json","events_json":"https://pith.science/api/pith-number/C6TYBUUUSCLRQTILHKMJ34QJLK/events.json","paper":"https://pith.science/paper/C6TYBUUU"},"agent_actions":{"view_html":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK","download_json":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK.json","view_paper":"https://pith.science/paper/C6TYBUUU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.06493&json=true","fetch_graph":"https://pith.science/api/pith-number/C6TYBUUUSCLRQTILHKMJ34QJLK/graph.json","fetch_events":"https://pith.science/api/pith-number/C6TYBUUUSCLRQTILHKMJ34QJLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK/action/storage_attestation","attest_author":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK/action/author_attestation","sign_citation":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK/action/citation_signature","submit_replication":"https://pith.science/pith/C6TYBUUUSCLRQTILHKMJ34QJLK/action/replication_record"}},"created_at":"2026-05-18T00:36:33.564097+00:00","updated_at":"2026-05-18T00:36:33.564097+00:00"}