{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RU7EPES73B5FVTLIFYFZMLRYWX","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":"ef3ae4252d8c5c79c012df250cdf5e7f62c3e44eeb843b08dc9b482471626875","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-05-02T19:58:16Z","title_canon_sha256":"c56a25700ac276973a37a21c150e9a809c4e39e973bc3432fa2ad930ec74c10c"},"schema_version":"1.0","source":{"id":"1605.00641","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00641","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00641v4","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00641","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"RU7EPES73B5F","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RU7EPES73B5FVTLI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RU7EPES7","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:2826b5486cd12706cd7e324f943c673edbeb538b26eeb83922bd9c55ea740c91","target":"graph","created_at":"2026-05-17T23:47:40Z","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":"When $p$ is a computable real so that $p \\geq 1$, the isometry degree of a computable copy $\\mathcal{B}$ of $\\ell^p$ is defined to be the least powerful Turing degree that computes a linear isometry of $\\ell^p$ onto $\\mathcal{B}$. We show that this degree always exists and that when $p \\neq 2$ these degrees are precisely the c.e. degrees.","authors_text":"D.M. Stull, Timothy H. McNicholl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-05-02T19:58:16Z","title":"The isometry degree of a computable copy of $\\ell^p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00641","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:db8c677ac9d830c31af18bc829b749d894feeaae66824ac6779137691b3945c5","target":"record","created_at":"2026-05-17T23:47:40Z","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":"ef3ae4252d8c5c79c012df250cdf5e7f62c3e44eeb843b08dc9b482471626875","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-05-02T19:58:16Z","title_canon_sha256":"c56a25700ac276973a37a21c150e9a809c4e39e973bc3432fa2ad930ec74c10c"},"schema_version":"1.0","source":{"id":"1605.00641","kind":"arxiv","version":4}},"canonical_sha256":"8d3e47925fd87a5acd682e0b962e38b5dc4ef921ab1bf1d1caed82247af3fdef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d3e47925fd87a5acd682e0b962e38b5dc4ef921ab1bf1d1caed82247af3fdef","first_computed_at":"2026-05-17T23:47:40.406935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:40.406935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jJ/qnuuq2h4aE8ijKSNl9kIjTvmHUO4P1WQbs6gUdUr0xQcRJA/gYIhbZ+e3eo9uGb1YXW5fAiEFS0FD9dLHCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:40.407548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00641","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db8c677ac9d830c31af18bc829b749d894feeaae66824ac6779137691b3945c5","sha256:2826b5486cd12706cd7e324f943c673edbeb538b26eeb83922bd9c55ea740c91"],"state_sha256":"203c3d25c3285a70fb31603b8718dd38eca50fe91199a5b5e5a69e4861e5119d"}