{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:N6443UVTIO4NYZO446LPW4ZQ4F","short_pith_number":"pith:N6443UVT","canonical_record":{"source":{"id":"1707.09257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-07-28T14:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"1c5c4d0a726ecca15dd07316549dc979f27abb839c533499174248d38578d083","abstract_canon_sha256":"72bba2978151e96c95e6f674c27992d1a390b72459702ee20f24994bb33edb8e"},"schema_version":"1.0"},"canonical_sha256":"6fb9cdd2b343b8dc65dce796fb7330e167b4d42f359d4ffdd1538ba0b9f81c53","source":{"kind":"arxiv","id":"1707.09257","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09257","created_at":"2026-05-18T00:33:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09257v2","created_at":"2026-05-18T00:33:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09257","created_at":"2026-05-18T00:33:31Z"},{"alias_kind":"pith_short_12","alias_value":"N6443UVTIO4N","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N6443UVTIO4NYZO4","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N6443UVT","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:N6443UVTIO4NYZO446LPW4ZQ4F","target":"record","payload":{"canonical_record":{"source":{"id":"1707.09257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-07-28T14:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"1c5c4d0a726ecca15dd07316549dc979f27abb839c533499174248d38578d083","abstract_canon_sha256":"72bba2978151e96c95e6f674c27992d1a390b72459702ee20f24994bb33edb8e"},"schema_version":"1.0"},"canonical_sha256":"6fb9cdd2b343b8dc65dce796fb7330e167b4d42f359d4ffdd1538ba0b9f81c53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:31.844477Z","signature_b64":"o589t3cS9gQ+PaqLTB08cpEvOd6HyZvbbHrRry6FacYqvMNNdOpOadZ1GafLiV2SwLkIjy8//rVJop3mLSBODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fb9cdd2b343b8dc65dce796fb7330e167b4d42f359d4ffdd1538ba0b9f81c53","last_reissued_at":"2026-05-18T00:33:31.843896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:31.843896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.09257","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G9J2onZP0y9bAyA7dMHSzHrSR+7zTNkT8mteDgHVnahoajWa5rGBCPrLQYNw6GpfKXJ8GEPv7KH7LQLWUo+NBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:49:49.850669Z"},"content_sha256":"8af853a182af41321945620244d819b04000bd7450eea61ee2865b16746e4ddb","schema_version":"1.0","event_id":"sha256:8af853a182af41321945620244d819b04000bd7450eea61ee2865b16746e4ddb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:N6443UVTIO4NYZO446LPW4ZQ4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of $L^p$ AF algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Maria Grazia Viola, N. Christopher Phillips","submitted_at":"2017-07-28T14:42:17Z","abstract_excerpt":"We define spatial $L^p$ AF algebras for $p \\in [1, \\infty) \\setminus \\{ 2 \\}$, and prove the following analog of the Elliott AF algebra classification theorem. If $A$ and $B$ are spatial $L^p$ AF algebras, then the following are equivalent: 1) $A$ and $B$ have isomorphic scaled preordered $K_0$-groups. 2) $A \\cong B$ as rings. 3) $A \\cong B$ (not necessarily isometrically) as Banach algebras. 4) $A$ is isometrically isomorphic to $B$ as Banach algebras. 5) $A$ is completely isometrically isomorphic to $B$ as matrix normed Banach algebra. As background, we develop the theory of matrix normed $L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09257","kind":"arxiv","version":2},"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":"2026-05-18T00:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGQkw3qmmbHtj7jwkZSw/LWYAAapnBk81Cpg/L7AfiIPCVEJYdU0x7FzP4taUytWxznI0OLT6oZ4UUQFCyIjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:49:49.851017Z"},"content_sha256":"41a5410bce1de2ee16515dec85bc1f949a0d4261814606d5e2277febd03e5f5a","schema_version":"1.0","event_id":"sha256:41a5410bce1de2ee16515dec85bc1f949a0d4261814606d5e2277febd03e5f5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6443UVTIO4NYZO446LPW4ZQ4F/bundle.json","state_url":"https://pith.science/pith/N6443UVTIO4NYZO446LPW4ZQ4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6443UVTIO4NYZO446LPW4ZQ4F/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":"2026-06-05T12:49:49Z","links":{"resolver":"https://pith.science/pith/N6443UVTIO4NYZO446LPW4ZQ4F","bundle":"https://pith.science/pith/N6443UVTIO4NYZO446LPW4ZQ4F/bundle.json","state":"https://pith.science/pith/N6443UVTIO4NYZO446LPW4ZQ4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6443UVTIO4NYZO446LPW4ZQ4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N6443UVTIO4NYZO446LPW4ZQ4F","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":"72bba2978151e96c95e6f674c27992d1a390b72459702ee20f24994bb33edb8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-07-28T14:42:17Z","title_canon_sha256":"1c5c4d0a726ecca15dd07316549dc979f27abb839c533499174248d38578d083"},"schema_version":"1.0","source":{"id":"1707.09257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09257","created_at":"2026-05-18T00:33:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09257v2","created_at":"2026-05-18T00:33:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09257","created_at":"2026-05-18T00:33:31Z"},{"alias_kind":"pith_short_12","alias_value":"N6443UVTIO4N","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N6443UVTIO4NYZO4","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N6443UVT","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:41a5410bce1de2ee16515dec85bc1f949a0d4261814606d5e2277febd03e5f5a","target":"graph","created_at":"2026-05-18T00:33:31Z","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 define spatial $L^p$ AF algebras for $p \\in [1, \\infty) \\setminus \\{ 2 \\}$, and prove the following analog of the Elliott AF algebra classification theorem. If $A$ and $B$ are spatial $L^p$ AF algebras, then the following are equivalent: 1) $A$ and $B$ have isomorphic scaled preordered $K_0$-groups. 2) $A \\cong B$ as rings. 3) $A \\cong B$ (not necessarily isometrically) as Banach algebras. 4) $A$ is isometrically isomorphic to $B$ as Banach algebras. 5) $A$ is completely isometrically isomorphic to $B$ as matrix normed Banach algebra. As background, we develop the theory of matrix normed $L","authors_text":"Maria Grazia Viola, N. Christopher Phillips","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-07-28T14:42:17Z","title":"Classification of $L^p$ AF algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09257","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":"sha256:8af853a182af41321945620244d819b04000bd7450eea61ee2865b16746e4ddb","target":"record","created_at":"2026-05-18T00:33:31Z","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":"72bba2978151e96c95e6f674c27992d1a390b72459702ee20f24994bb33edb8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-07-28T14:42:17Z","title_canon_sha256":"1c5c4d0a726ecca15dd07316549dc979f27abb839c533499174248d38578d083"},"schema_version":"1.0","source":{"id":"1707.09257","kind":"arxiv","version":2}},"canonical_sha256":"6fb9cdd2b343b8dc65dce796fb7330e167b4d42f359d4ffdd1538ba0b9f81c53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fb9cdd2b343b8dc65dce796fb7330e167b4d42f359d4ffdd1538ba0b9f81c53","first_computed_at":"2026-05-18T00:33:31.843896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:31.843896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o589t3cS9gQ+PaqLTB08cpEvOd6HyZvbbHrRry6FacYqvMNNdOpOadZ1GafLiV2SwLkIjy8//rVJop3mLSBODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:31.844477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.09257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8af853a182af41321945620244d819b04000bd7450eea61ee2865b16746e4ddb","sha256:41a5410bce1de2ee16515dec85bc1f949a0d4261814606d5e2277febd03e5f5a"],"state_sha256":"a083ba78407c0f6cba0e5ec01d46c119ac8652d8aa9b12271894c96410496da5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zd1ow7j2DCfYkiJbXiKoz7kIf6dPE6iyXEBW++BpiXFSoSRzsgaqEsFkpKICt+ovbKpy45WdetHg3aKRD6GxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:49:49.852977Z","bundle_sha256":"e03bd2201d5e25550b6b898d88d88137bb1b1dd411c13fc6b04e86b42e55609e"}}