{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U3OZ35JNKMAZINVTG4K2VRK4PZ","short_pith_number":"pith:U3OZ35JN","canonical_record":{"source":{"id":"1811.02126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-06T02:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"1397ec65503fade18691b876139bd3ffd6bfddf2ddc84a61e59c1a567b232d6f","abstract_canon_sha256":"700c8b9a9b17664a825b6c294d7028dc00601cf939c7c646f21e077fef3349cd"},"schema_version":"1.0"},"canonical_sha256":"a6dd9df52d53019436b33715aac55c7e5afb4c24cd0cec521f5ed671e1ddd77e","source":{"kind":"arxiv","id":"1811.02126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02126","created_at":"2026-05-18T00:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02126v1","created_at":"2026-05-18T00:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02126","created_at":"2026-05-18T00:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"U3OZ35JNKMAZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U3OZ35JNKMAZINVT","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U3OZ35JN","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U3OZ35JNKMAZINVTG4K2VRK4PZ","target":"record","payload":{"canonical_record":{"source":{"id":"1811.02126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-06T02:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"1397ec65503fade18691b876139bd3ffd6bfddf2ddc84a61e59c1a567b232d6f","abstract_canon_sha256":"700c8b9a9b17664a825b6c294d7028dc00601cf939c7c646f21e077fef3349cd"},"schema_version":"1.0"},"canonical_sha256":"a6dd9df52d53019436b33715aac55c7e5afb4c24cd0cec521f5ed671e1ddd77e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:25.000492Z","signature_b64":"gCJxCb2GDDeiL+CFNjQnqmu4R3lOF0CqBH0wIWWXmYDRvyc91UEisQf8h+h/fMoOv3QwHqqD9zu190lpBstXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6dd9df52d53019436b33715aac55c7e5afb4c24cd0cec521f5ed671e1ddd77e","last_reissued_at":"2026-05-18T00:01:25.000107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:25.000107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.02126","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":"2026-05-18T00:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yyeRBAmuWfYnJyluckNvfa+WNybQeJzIrbH3KvkLfo38wiDBHAJ0c7NeWd/0AV9zJpKpwNMQ74X4pH2c7Uw8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:32:22.512955Z"},"content_sha256":"bd0d81256d693316ca3605afe9ee55852368fb7150b41c67da4a824950dce97b","schema_version":"1.0","event_id":"sha256:bd0d81256d693316ca3605afe9ee55852368fb7150b41c67da4a824950dce97b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U3OZ35JNKMAZINVTG4K2VRK4PZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recent progress in Rings and Subrings of Real Valued Measurable Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Joshua Sack, Sagarmoy Bag, Soumyadip Acharyya, Sudip Kumar Acharyya","submitted_at":"2018-11-06T02:07:59Z","abstract_excerpt":"Two separated realcompact measurable spaces $(X,\\mathcal{A})$ and $(Y,\\mathcal{B})$ are shown to be isomorphic if and only if the rings $\\mathcal{M}(X,\\mathcal{A})$ and $\\mathcal{M}(Y,\\mathcal{B})$ of all real valued measurable functions over these two spaces are isomorphic. It is furthermore shown that any such ring $\\mathcal{M}(X,\\mathcal{A})$, even without the realcompactness hypothesis on $X$, can be embedded monomorphically in a ring of the form $C(K)$, where $K$ is a zero dimensional Hausdorff topological space. It is also shown that given a measure $\\mu$ on $(X,\\mathcal{A})$, the $m_\\mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02126","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":"2026-05-18T00:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bE4hWh2r6V+CH3K2p67pj97KbD+g9PPok8f9CDZhVGjprp4ZWWA1CLlnEDCJk1DKFzIIIvYB0yG2ZRBzxoHcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:32:22.513649Z"},"content_sha256":"f825761f2d6eda1b341dfded7ef54e68a61d6524b9f5cf95c73b606760202d5f","schema_version":"1.0","event_id":"sha256:f825761f2d6eda1b341dfded7ef54e68a61d6524b9f5cf95c73b606760202d5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3OZ35JNKMAZINVTG4K2VRK4PZ/bundle.json","state_url":"https://pith.science/pith/U3OZ35JNKMAZINVTG4K2VRK4PZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3OZ35JNKMAZINVTG4K2VRK4PZ/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":"2026-06-10T22:32:22Z","links":{"resolver":"https://pith.science/pith/U3OZ35JNKMAZINVTG4K2VRK4PZ","bundle":"https://pith.science/pith/U3OZ35JNKMAZINVTG4K2VRK4PZ/bundle.json","state":"https://pith.science/pith/U3OZ35JNKMAZINVTG4K2VRK4PZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3OZ35JNKMAZINVTG4K2VRK4PZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U3OZ35JNKMAZINVTG4K2VRK4PZ","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":"700c8b9a9b17664a825b6c294d7028dc00601cf939c7c646f21e077fef3349cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-06T02:07:59Z","title_canon_sha256":"1397ec65503fade18691b876139bd3ffd6bfddf2ddc84a61e59c1a567b232d6f"},"schema_version":"1.0","source":{"id":"1811.02126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02126","created_at":"2026-05-18T00:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02126v1","created_at":"2026-05-18T00:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02126","created_at":"2026-05-18T00:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"U3OZ35JNKMAZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U3OZ35JNKMAZINVT","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U3OZ35JN","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:f825761f2d6eda1b341dfded7ef54e68a61d6524b9f5cf95c73b606760202d5f","target":"graph","created_at":"2026-05-18T00:01:25Z","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":"Two separated realcompact measurable spaces $(X,\\mathcal{A})$ and $(Y,\\mathcal{B})$ are shown to be isomorphic if and only if the rings $\\mathcal{M}(X,\\mathcal{A})$ and $\\mathcal{M}(Y,\\mathcal{B})$ of all real valued measurable functions over these two spaces are isomorphic. It is furthermore shown that any such ring $\\mathcal{M}(X,\\mathcal{A})$, even without the realcompactness hypothesis on $X$, can be embedded monomorphically in a ring of the form $C(K)$, where $K$ is a zero dimensional Hausdorff topological space. It is also shown that given a measure $\\mu$ on $(X,\\mathcal{A})$, the $m_\\mu","authors_text":"Joshua Sack, Sagarmoy Bag, Soumyadip Acharyya, Sudip Kumar Acharyya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-06T02:07:59Z","title":"Recent progress in Rings and Subrings of Real Valued Measurable Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02126","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:bd0d81256d693316ca3605afe9ee55852368fb7150b41c67da4a824950dce97b","target":"record","created_at":"2026-05-18T00:01:25Z","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":"700c8b9a9b17664a825b6c294d7028dc00601cf939c7c646f21e077fef3349cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-11-06T02:07:59Z","title_canon_sha256":"1397ec65503fade18691b876139bd3ffd6bfddf2ddc84a61e59c1a567b232d6f"},"schema_version":"1.0","source":{"id":"1811.02126","kind":"arxiv","version":1}},"canonical_sha256":"a6dd9df52d53019436b33715aac55c7e5afb4c24cd0cec521f5ed671e1ddd77e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6dd9df52d53019436b33715aac55c7e5afb4c24cd0cec521f5ed671e1ddd77e","first_computed_at":"2026-05-18T00:01:25.000107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:25.000107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCJxCb2GDDeiL+CFNjQnqmu4R3lOF0CqBH0wIWWXmYDRvyc91UEisQf8h+h/fMoOv3QwHqqD9zu190lpBstXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:25.000492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd0d81256d693316ca3605afe9ee55852368fb7150b41c67da4a824950dce97b","sha256:f825761f2d6eda1b341dfded7ef54e68a61d6524b9f5cf95c73b606760202d5f"],"state_sha256":"a2336880c7a181b791845825f4dd96ac6e625f5287c0671a8cacbc1b5d17dd31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Plzj6RkXJMR1VUQLRnJO5y5kJPpe60t2YfHhWu17H0oenoHVmHE8weG/pXso/6GbV+m44PhwuAM/TSiLhySYDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:32:22.517921Z","bundle_sha256":"0d82f3e7aabd8eb0dead13f2ec34ffec34d3885101457d9930a8e7981e9ad17a"}}