{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:D2RBDMU26L6V5VDSSSLZS5HLK2","short_pith_number":"pith:D2RBDMU2","canonical_record":{"source":{"id":"1906.12209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-28T13:31:24Z","cross_cats_sorted":[],"title_canon_sha256":"f6e3911b5bbfac7b9fc92d48a578be9ee3d7ed883f9242612191e4ad192b3ef4","abstract_canon_sha256":"e8da2ba7011fd2ac08ae39826093db4ace75f154c792c20ec125aa4b7849c0fe"},"schema_version":"1.0"},"canonical_sha256":"1ea211b29af2fd5ed47294979974eb56b9256034cb3658c93e61839ad23dd1e4","source":{"kind":"arxiv","id":"1906.12209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.12209","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1906.12209v1","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.12209","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"D2RBDMU26L6V","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"D2RBDMU26L6V5VDS","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"D2RBDMU2","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:D2RBDMU26L6V5VDSSSLZS5HLK2","target":"record","payload":{"canonical_record":{"source":{"id":"1906.12209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-28T13:31:24Z","cross_cats_sorted":[],"title_canon_sha256":"f6e3911b5bbfac7b9fc92d48a578be9ee3d7ed883f9242612191e4ad192b3ef4","abstract_canon_sha256":"e8da2ba7011fd2ac08ae39826093db4ace75f154c792c20ec125aa4b7849c0fe"},"schema_version":"1.0"},"canonical_sha256":"1ea211b29af2fd5ed47294979974eb56b9256034cb3658c93e61839ad23dd1e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:58.999419Z","signature_b64":"60GaUgL3cHsSaqAwUw3SHQ615AQd0+XDOYUL2Prw4X15U4kP44NEZUjz7sZF5FpCPzmcJWAHdjHEDijA+QpjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ea211b29af2fd5ed47294979974eb56b9256034cb3658c93e61839ad23dd1e4","last_reissued_at":"2026-05-17T23:41:58.998950Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:58.998950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.12209","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":"2026-05-17T23:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BlsJ0tmPgxj1KusXjOJhZoAB+rzjxJCGdiYk1lPDu6NvnP62tnXfxip0HWoEGnJaE8UBMFzs276WW4ZSR7MoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:49:52.378233Z"},"content_sha256":"2b0efc68b2a255056e243216cb2cd0da96ad5d53da7676c92b413d3b10bd6445","schema_version":"1.0","event_id":"sha256:2b0efc68b2a255056e243216cb2cd0da96ad5d53da7676c92b413d3b10bd6445"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:D2RBDMU26L6V5VDSSSLZS5HLK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complexity of classifying Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alexander G. Melnikov, Timothy H. McNicholl, Tyler Brown","submitted_at":"2019-06-28T13:31:24Z","abstract_excerpt":"Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12209","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":"2026-05-17T23:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p5uYsoBzR/RweEeX6r6ZHa0vfvwcHixbH8LDDq+BDlI6U88S4SU475pEWLM3nThKWmS5ZclJ0P2fBqSlpCfjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:49:52.378639Z"},"content_sha256":"6b19b078a0636ecd43d6f915f47835161a3b8bcf05316d092d2efaaf0c745f57","schema_version":"1.0","event_id":"sha256:6b19b078a0636ecd43d6f915f47835161a3b8bcf05316d092d2efaaf0c745f57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2RBDMU26L6V5VDSSSLZS5HLK2/bundle.json","state_url":"https://pith.science/pith/D2RBDMU26L6V5VDSSSLZS5HLK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2RBDMU26L6V5VDSSSLZS5HLK2/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":"2026-06-12T06:49:52Z","links":{"resolver":"https://pith.science/pith/D2RBDMU26L6V5VDSSSLZS5HLK2","bundle":"https://pith.science/pith/D2RBDMU26L6V5VDSSSLZS5HLK2/bundle.json","state":"https://pith.science/pith/D2RBDMU26L6V5VDSSSLZS5HLK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2RBDMU26L6V5VDSSSLZS5HLK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:D2RBDMU26L6V5VDSSSLZS5HLK2","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":"e8da2ba7011fd2ac08ae39826093db4ace75f154c792c20ec125aa4b7849c0fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-28T13:31:24Z","title_canon_sha256":"f6e3911b5bbfac7b9fc92d48a578be9ee3d7ed883f9242612191e4ad192b3ef4"},"schema_version":"1.0","source":{"id":"1906.12209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.12209","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1906.12209v1","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.12209","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"D2RBDMU26L6V","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"D2RBDMU26L6V5VDS","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"D2RBDMU2","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:6b19b078a0636ecd43d6f915f47835161a3b8bcf05316d092d2efaaf0c745f57","target":"graph","created_at":"2026-05-17T23:41:58Z","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":"Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.","authors_text":"Alexander G. Melnikov, Timothy H. McNicholl, Tyler Brown","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-28T13:31:24Z","title":"On the complexity of classifying Lebesgue spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12209","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":"sha256:2b0efc68b2a255056e243216cb2cd0da96ad5d53da7676c92b413d3b10bd6445","target":"record","created_at":"2026-05-17T23:41:58Z","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":"e8da2ba7011fd2ac08ae39826093db4ace75f154c792c20ec125aa4b7849c0fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-28T13:31:24Z","title_canon_sha256":"f6e3911b5bbfac7b9fc92d48a578be9ee3d7ed883f9242612191e4ad192b3ef4"},"schema_version":"1.0","source":{"id":"1906.12209","kind":"arxiv","version":1}},"canonical_sha256":"1ea211b29af2fd5ed47294979974eb56b9256034cb3658c93e61839ad23dd1e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ea211b29af2fd5ed47294979974eb56b9256034cb3658c93e61839ad23dd1e4","first_computed_at":"2026-05-17T23:41:58.998950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:58.998950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"60GaUgL3cHsSaqAwUw3SHQ615AQd0+XDOYUL2Prw4X15U4kP44NEZUjz7sZF5FpCPzmcJWAHdjHEDijA+QpjAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:58.999419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.12209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b0efc68b2a255056e243216cb2cd0da96ad5d53da7676c92b413d3b10bd6445","sha256:6b19b078a0636ecd43d6f915f47835161a3b8bcf05316d092d2efaaf0c745f57"],"state_sha256":"9b17c7d4941202bb76f87f91bfd320e3064b274476be7a1d1c6c7994b13fb559"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+Pa9McRsiCBvlPP6kaI8wxgIuSZCNTSSe4EEPa/yGl5zrrNGiLpfuDewByPzBinjqZSNigzLntwRbScNbdCBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:49:52.380652Z","bundle_sha256":"b1bbd313370049636ea86a22a004b5e5d06a2633a6053eb6903a700151829723"}}