{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CES7BU3ZLSY3SMWJGEVHXTLCLX","short_pith_number":"pith:CES7BU3Z","canonical_record":{"source":{"id":"1306.5128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-06-21T13:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"5bda121361508dd0cf4d7a2319371c22cf9ed80d4803dcf5e1380ef76d152ab0","abstract_canon_sha256":"82e4b0913fec83a13b4a5ae332ad15e81e590fb51489661f93961127a0d678b8"},"schema_version":"1.0"},"canonical_sha256":"1125f0d3795cb1b932c9312a7bcd625ddd9fff3c5467aff6b8461506f2f9192d","source":{"kind":"arxiv","id":"1306.5128","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5128","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5128v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5128","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"CES7BU3ZLSY3","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CES7BU3ZLSY3SMWJ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CES7BU3Z","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CES7BU3ZLSY3SMWJGEVHXTLCLX","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-06-21T13:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"5bda121361508dd0cf4d7a2319371c22cf9ed80d4803dcf5e1380ef76d152ab0","abstract_canon_sha256":"82e4b0913fec83a13b4a5ae332ad15e81e590fb51489661f93961127a0d678b8"},"schema_version":"1.0"},"canonical_sha256":"1125f0d3795cb1b932c9312a7bcd625ddd9fff3c5467aff6b8461506f2f9192d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:19.655873Z","signature_b64":"XBxUcFscSfrp3AepaVikLidgb1v79GRr5Omxz7Hnkp+TSDLXSMCdXpFzHuao8lfzzE9b1/CFSUQqhwjvu8ufCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1125f0d3795cb1b932c9312a7bcd625ddd9fff3c5467aff6b8461506f2f9192d","last_reissued_at":"2026-05-18T03:20:19.655132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:19.655132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5128","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZV68QImVNF/HnKdRmb2xPe2Y6S85n6maAUuyd3z2FUE94G9lDH4+vCR/0rF7G6zp8PUpsLHT3Scrp7Kdo3FCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:34:01.323065Z"},"content_sha256":"54e1144c289d5502e1939054a85e140d38ec92fb98fc52a5f5bbc1308b10ca16","schema_version":"1.0","event_id":"sha256:54e1144c289d5502e1939054a85e140d38ec92fb98fc52a5f5bbc1308b10ca16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CES7BU3ZLSY3SMWJGEVHXTLCLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Results on ITRM-recognizability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Merlin Carl","submitted_at":"2013-06-21T13:19:17Z","abstract_excerpt":"Exploring further the properties of ITRM-recognizable reals, we provide a detailed analysis of recognizable reals and their distribution in G\\\"odels constructible universe L. In particular, we show that, for unresetting infinite time register machines, the recognizable reals coincide with the computable reals and that, for ITRMs, unrecognizables are generated at every index bigger than the first limit of admissibles. We show that a real r is recognizable iff it is $\\Sigma_{1}$-definable over $L_{\\omega_{\\omega}^{CK,r}}$, that $r\\in L_{\\omega_{\\omega}^{CK,r}}$ for every recognizable real $r$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5128","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":""},"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":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u96EVV3OxhhCgl0kiIdxWZuR2BSSOCJsLL/n5wUPvpdDLMmJdMKQ/TiManxYwpHryMX0vAYgyO3TNAkp9rSwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:34:01.323420Z"},"content_sha256":"526f751d771be78e9ebe8abd481c4e2c1a390a6f05d1ce4324b0d613a20448b7","schema_version":"1.0","event_id":"sha256:526f751d771be78e9ebe8abd481c4e2c1a390a6f05d1ce4324b0d613a20448b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CES7BU3ZLSY3SMWJGEVHXTLCLX/bundle.json","state_url":"https://pith.science/pith/CES7BU3ZLSY3SMWJGEVHXTLCLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CES7BU3ZLSY3SMWJGEVHXTLCLX/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":"2026-06-30T23:34:01Z","links":{"resolver":"https://pith.science/pith/CES7BU3ZLSY3SMWJGEVHXTLCLX","bundle":"https://pith.science/pith/CES7BU3ZLSY3SMWJGEVHXTLCLX/bundle.json","state":"https://pith.science/pith/CES7BU3ZLSY3SMWJGEVHXTLCLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CES7BU3ZLSY3SMWJGEVHXTLCLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CES7BU3ZLSY3SMWJGEVHXTLCLX","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":"82e4b0913fec83a13b4a5ae332ad15e81e590fb51489661f93961127a0d678b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-06-21T13:19:17Z","title_canon_sha256":"5bda121361508dd0cf4d7a2319371c22cf9ed80d4803dcf5e1380ef76d152ab0"},"schema_version":"1.0","source":{"id":"1306.5128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5128","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5128v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5128","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"CES7BU3ZLSY3","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CES7BU3ZLSY3SMWJ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CES7BU3Z","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:526f751d771be78e9ebe8abd481c4e2c1a390a6f05d1ce4324b0d613a20448b7","target":"graph","created_at":"2026-05-18T03:20:19Z","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"},"paper":{"abstract_excerpt":"Exploring further the properties of ITRM-recognizable reals, we provide a detailed analysis of recognizable reals and their distribution in G\\\"odels constructible universe L. In particular, we show that, for unresetting infinite time register machines, the recognizable reals coincide with the computable reals and that, for ITRMs, unrecognizables are generated at every index bigger than the first limit of admissibles. We show that a real r is recognizable iff it is $\\Sigma_{1}$-definable over $L_{\\omega_{\\omega}^{CK,r}}$, that $r\\in L_{\\omega_{\\omega}^{CK,r}}$ for every recognizable real $r$ an","authors_text":"Merlin Carl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-06-21T13:19:17Z","title":"Optimal Results on ITRM-recognizability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5128","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":"sha256:54e1144c289d5502e1939054a85e140d38ec92fb98fc52a5f5bbc1308b10ca16","target":"record","created_at":"2026-05-18T03:20:19Z","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":"82e4b0913fec83a13b4a5ae332ad15e81e590fb51489661f93961127a0d678b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-06-21T13:19:17Z","title_canon_sha256":"5bda121361508dd0cf4d7a2319371c22cf9ed80d4803dcf5e1380ef76d152ab0"},"schema_version":"1.0","source":{"id":"1306.5128","kind":"arxiv","version":1}},"canonical_sha256":"1125f0d3795cb1b932c9312a7bcd625ddd9fff3c5467aff6b8461506f2f9192d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1125f0d3795cb1b932c9312a7bcd625ddd9fff3c5467aff6b8461506f2f9192d","first_computed_at":"2026-05-18T03:20:19.655132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:19.655132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XBxUcFscSfrp3AepaVikLidgb1v79GRr5Omxz7Hnkp+TSDLXSMCdXpFzHuao8lfzzE9b1/CFSUQqhwjvu8ufCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:19.655873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54e1144c289d5502e1939054a85e140d38ec92fb98fc52a5f5bbc1308b10ca16","sha256:526f751d771be78e9ebe8abd481c4e2c1a390a6f05d1ce4324b0d613a20448b7"],"state_sha256":"6c4108fcc53e7de0c5638c1ae3dcc47d865bb09db75f81396c8b35e7123b11c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L5LXbM9xQMp7G67DaBtbK5y6GRYRwdFbWU0Qy8IolG4kkhJKnI+J2e83g4giEqo23suYn9ZAcDVfb7aqnFd8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:34:01.325444Z","bundle_sha256":"227ce9524c8986d3f39b04787cda06febe27ed0d72c29096d78bb2cd456b441c"}}