{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AHQWSB7S7U3MEBIZ34JECEHWKV","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":"530ff0e3d34e7907b2c43b48ffb20199c3b458007c05d29840990e6ddce2c52a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-09-29T16:00:05Z","title_canon_sha256":"42b0d7490fcef3102c78f696a9ffde643741dadb233323d10580f896b9d224c0"},"schema_version":"1.0","source":{"id":"1509.08825","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08825","created_at":"2026-05-18T01:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08825v2","created_at":"2026-05-18T01:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08825","created_at":"2026-05-18T01:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"AHQWSB7S7U3M","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AHQWSB7S7U3MEBIZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AHQWSB7S","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:78c912beee01d3b5e2f0e65b3b7855a1fc9b6b3822b69e89e8b2cba08b6d2f54","target":"graph","created_at":"2026-05-18T01:16:17Z","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":"We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko's framework for polynomial space computability in $\\mathbb{R}^n$ to define \\textit{weakly pspace-random} points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem holds for every weakly pspace-random point.","authors_text":"D. M. Stull, Xiang Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-09-29T16:00:05Z","title":"Polynomial Space Randomness in Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08825","kind":"arxiv","version":2},"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":"sha256:632929ec02dd32ccdb3843efa53287b0033f4e40c5c17ee29e3fce8c9ea684ce","target":"record","created_at":"2026-05-18T01:16:17Z","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":"530ff0e3d34e7907b2c43b48ffb20199c3b458007c05d29840990e6ddce2c52a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-09-29T16:00:05Z","title_canon_sha256":"42b0d7490fcef3102c78f696a9ffde643741dadb233323d10580f896b9d224c0"},"schema_version":"1.0","source":{"id":"1509.08825","kind":"arxiv","version":2}},"canonical_sha256":"01e16907f2fd36c20519df124110f655679e3755897322c3d27486b8c30ecada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01e16907f2fd36c20519df124110f655679e3755897322c3d27486b8c30ecada","first_computed_at":"2026-05-18T01:16:17.787377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:17.787377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uckEZcrDhUiWoTaF2t/dB5t/dQ6ccfPTHF//nDVhmng70MmEZHeSY95j6ZQ2ADSuYX5ujCC+QoIsiA8Xm9WbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:17.787976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08825","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:632929ec02dd32ccdb3843efa53287b0033f4e40c5c17ee29e3fce8c9ea684ce","sha256:78c912beee01d3b5e2f0e65b3b7855a1fc9b6b3822b69e89e8b2cba08b6d2f54"],"state_sha256":"761742e7e6ee2311eddef36b790bb76003994764bd23fffd43b1467952cf504f"}