{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6XCZAWPD45QDLJ3LPAVZTCQF6X","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":"36ae7657710e1d1ffe03faf1c1ed444467942f1dcdd69ac7befc4bcd2826ad41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-16T15:14:55Z","title_canon_sha256":"584d413a94c321a96ff6585ab29d6cf15f0127d98269bc87226ae33665bed97d"},"schema_version":"1.0","source":{"id":"1905.06832","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06832","created_at":"2026-05-20T00:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06832v6","created_at":"2026-05-20T00:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06832","created_at":"2026-05-20T00:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"6XCZAWPD45QD","created_at":"2026-05-20T00:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"6XCZAWPD45QDLJ3L","created_at":"2026-05-20T00:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"6XCZAWPD","created_at":"2026-05-20T00:05:23Z"}],"graph_snapshots":[{"event_id":"sha256:8e5359263a42459896056fc0635a8a6ed6088342c5503f45fedfb38c771505de","target":"graph","created_at":"2026-05-20T00:05:23Z","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/1905.06832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider notions of space complexity for Infinite Time Turing Machines (ITTMs) that were introduced by B. L\\\"owe and studied further by J. Winter.\n  We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P$_{+}=$PSPACE$_{+}$ and P$_{++}=$PSPACE$_{++}$ holds for ITTMs (all three are false). We also show various separation results between space complexity classes for ITTMs. This considerably expands our earlier observations on the topic in section 7.2.2 of \\cite{Ca2}, w","authors_text":"Merlin Carl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-16T15:14:55Z","title":"Space and Time Complexity for Infinite Time Turing Machines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06832","kind":"arxiv","version":6},"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":"sha256:229dc52b775a0baf9283e611c7586898886e568257b2cd22b489406e1fb2903c","target":"record","created_at":"2026-05-20T00:05:23Z","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":"36ae7657710e1d1ffe03faf1c1ed444467942f1dcdd69ac7befc4bcd2826ad41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-16T15:14:55Z","title_canon_sha256":"584d413a94c321a96ff6585ab29d6cf15f0127d98269bc87226ae33665bed97d"},"schema_version":"1.0","source":{"id":"1905.06832","kind":"arxiv","version":6}},"canonical_sha256":"f5c59059e3e76035a76b782b998a05f5fdfead6b7d48b62b5249e165f9661c12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5c59059e3e76035a76b782b998a05f5fdfead6b7d48b62b5249e165f9661c12","first_computed_at":"2026-05-20T00:05:23.461743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:23.461743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MwoM7Ru7lsN1K2fi1nAPf0JzqcYMydVDxY4Ce5aZ0Q271xcBXh3ViMuCTD0H9RXD953SPPj2OHxEsX4f6dCqBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:23.462688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.06832","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:229dc52b775a0baf9283e611c7586898886e568257b2cd22b489406e1fb2903c","sha256:8e5359263a42459896056fc0635a8a6ed6088342c5503f45fedfb38c771505de"],"state_sha256":"ed51d2385e38325e5e92d256dfbb204065af91e3388b412050743f4057252b7d"}