{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JHDP76OOYJ5E2KSMYKNONKDAFV","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":"7b508587ba745d4b2069ce88be945c114199eff2a7ad8367a3e3ed0922ef2f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-09T13:24:37Z","title_canon_sha256":"9d523528f84829c3f8a2b596d1c15825d3e745c3950e5943a446d40932f79659"},"schema_version":"1.0","source":{"id":"1208.1901","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1901","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1901v4","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1901","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"JHDP76OOYJ5E","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JHDP76OOYJ5E2KSM","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JHDP76OO","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:287c6b7f33ee47330294ccfc56606d6c28449219d7169552d10ebab037f95e7a","target":"graph","created_at":"2026-05-18T03:42:44Z","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":"Infinite Time Register Machines ($ITRM$'s) are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. Koepke (2009), Koepke and Welch (2011) and Koepke and Miller (2008). We consider the notion of recognizability, which was first formulated for Infinite Time Turing Machines in Hamkins and Lewis (200) and applied to $ITRM$'s in Carl et al. (2010). A real $x$ is $ITRM$-recognizable iff there is an $ITRM$-program $P$ such that $P^{y}$ stops with output 1 iff $y=x$, and otherwise stops with output 0. In Carl et al. (20","authors_text":"Merlin Carl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-09T13:24:37Z","title":"The distribution of ITRM-recognizable reals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1901","kind":"arxiv","version":4},"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:fced0c27927a8547c8cba3450ecb32ad5f3ad2b48e2b70dc6d4b79cf98d17d84","target":"record","created_at":"2026-05-18T03:42:44Z","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":"7b508587ba745d4b2069ce88be945c114199eff2a7ad8367a3e3ed0922ef2f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-09T13:24:37Z","title_canon_sha256":"9d523528f84829c3f8a2b596d1c15825d3e745c3950e5943a446d40932f79659"},"schema_version":"1.0","source":{"id":"1208.1901","kind":"arxiv","version":4}},"canonical_sha256":"49c6fff9cec27a4d2a4cc29ae6a8602d4e5791b505bb47df06f6b0c2be53b9ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49c6fff9cec27a4d2a4cc29ae6a8602d4e5791b505bb47df06f6b0c2be53b9ed","first_computed_at":"2026-05-18T03:42:44.058434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:44.058434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LHymtugdktGR1zhUFRu/LLaRN8BpCrUxKW0BS5N8ap8epTHsBErUehgvuD5nhZyeVFZRKw8FH9I+rFBJxG4jAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:44.059741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1901","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fced0c27927a8547c8cba3450ecb32ad5f3ad2b48e2b70dc6d4b79cf98d17d84","sha256:287c6b7f33ee47330294ccfc56606d6c28449219d7169552d10ebab037f95e7a"],"state_sha256":"0218a81e6f076d009778a01df0e697fda608bb38a58dce65776e343b156d3e0b"}