{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:E3XNB76RH4N4XLNPSK6CIRZKJV","short_pith_number":"pith:E3XNB76R","canonical_record":{"source":{"id":"1208.4609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T20:02:25Z","cross_cats_sorted":[],"title_canon_sha256":"a232bfb7dbe57c3c5550b845dcbcea80013590275cfaa012097c967e2f2edb81","abstract_canon_sha256":"946f19dd1262a26cbf5f889c6877f8ef60f5b6661b40e2c332715facf5f839dc"},"schema_version":"1.0"},"canonical_sha256":"26eed0ffd13f1bcbadaf92bc24472a4d4c2951d33664e8e20740542795fd52e7","source":{"kind":"arxiv","id":"1208.4609","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4609","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4609v1","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4609","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"E3XNB76RH4N4","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3XNB76RH4N4XLNP","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3XNB76R","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:E3XNB76RH4N4XLNPSK6CIRZKJV","target":"record","payload":{"canonical_record":{"source":{"id":"1208.4609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T20:02:25Z","cross_cats_sorted":[],"title_canon_sha256":"a232bfb7dbe57c3c5550b845dcbcea80013590275cfaa012097c967e2f2edb81","abstract_canon_sha256":"946f19dd1262a26cbf5f889c6877f8ef60f5b6661b40e2c332715facf5f839dc"},"schema_version":"1.0"},"canonical_sha256":"26eed0ffd13f1bcbadaf92bc24472a4d4c2951d33664e8e20740542795fd52e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:13.012237Z","signature_b64":"0MlTS/3zEqSdzn+Cd6MW7AGE1Q22s5m1qJDYoBS8JqDCsHRzmFZWypBt1zGUdjg625sWDWWheQ6+7I4Nw0VdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26eed0ffd13f1bcbadaf92bc24472a4d4c2951d33664e8e20740542795fd52e7","last_reissued_at":"2026-05-18T03:48:13.011522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:13.011522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.4609","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":"2026-05-18T03:48:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Om4rwcmatM6SKa9RJrlzfV1FRMBpQkftcVi5rVye59f8e3ZadOWoiG8+tXspUnb08NUNqdklV+pkSxDYB81Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:01:53.743354Z"},"content_sha256":"f591683711cee0f3185da0f4442cc70c6356b8a4c3ea4c6436496a7c7d3edce5","schema_version":"1.0","event_id":"sha256:f591683711cee0f3185da0f4442cc70c6356b8a4c3ea4c6436496a7c7d3edce5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:E3XNB76RH4N4XLNPSK6CIRZKJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological radicals, V. From algebra to spectral theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Victor S. Shulman, Yuri V. Turovskii","submitted_at":"2012-08-22T20:02:25Z","abstract_excerpt":"We introduce and study procedures and constructions in the theory of the joint spectral radius that are related to the spectral theory. In particular we devlop the theory of the scattered radical. Among applications we find some sufficient conditions of continuity of the spectrum and spectral radii of various types, and prove that in GCR C*-algebras the joint spectral radius is continuous on precompact subsets and coincides with the Berger-Wang radius."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4609","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":"2026-05-18T03:48:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CiWmgoh2c9gKEdihIDrfs0CapPAKuWREAztnpNWN9A9YY1J3Urmkodc1Xc3PcgI1qBOAp2Q/65GH9AaLnBQBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:01:53.744007Z"},"content_sha256":"fca8e33b96486b0baf206f05f8241c8796e9030b8ffc83703a981e73ad4d8f16","schema_version":"1.0","event_id":"sha256:fca8e33b96486b0baf206f05f8241c8796e9030b8ffc83703a981e73ad4d8f16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3XNB76RH4N4XLNPSK6CIRZKJV/bundle.json","state_url":"https://pith.science/pith/E3XNB76RH4N4XLNPSK6CIRZKJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3XNB76RH4N4XLNPSK6CIRZKJV/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":"2026-06-07T18:01:53Z","links":{"resolver":"https://pith.science/pith/E3XNB76RH4N4XLNPSK6CIRZKJV","bundle":"https://pith.science/pith/E3XNB76RH4N4XLNPSK6CIRZKJV/bundle.json","state":"https://pith.science/pith/E3XNB76RH4N4XLNPSK6CIRZKJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3XNB76RH4N4XLNPSK6CIRZKJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E3XNB76RH4N4XLNPSK6CIRZKJV","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":"946f19dd1262a26cbf5f889c6877f8ef60f5b6661b40e2c332715facf5f839dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T20:02:25Z","title_canon_sha256":"a232bfb7dbe57c3c5550b845dcbcea80013590275cfaa012097c967e2f2edb81"},"schema_version":"1.0","source":{"id":"1208.4609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4609","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4609v1","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4609","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"E3XNB76RH4N4","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3XNB76RH4N4XLNP","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3XNB76R","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:fca8e33b96486b0baf206f05f8241c8796e9030b8ffc83703a981e73ad4d8f16","target":"graph","created_at":"2026-05-18T03:48:13Z","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 introduce and study procedures and constructions in the theory of the joint spectral radius that are related to the spectral theory. In particular we devlop the theory of the scattered radical. Among applications we find some sufficient conditions of continuity of the spectrum and spectral radii of various types, and prove that in GCR C*-algebras the joint spectral radius is continuous on precompact subsets and coincides with the Berger-Wang radius.","authors_text":"Victor S. Shulman, Yuri V. Turovskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T20:02:25Z","title":"Topological radicals, V. From algebra to spectral theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4609","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:f591683711cee0f3185da0f4442cc70c6356b8a4c3ea4c6436496a7c7d3edce5","target":"record","created_at":"2026-05-18T03:48:13Z","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":"946f19dd1262a26cbf5f889c6877f8ef60f5b6661b40e2c332715facf5f839dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-22T20:02:25Z","title_canon_sha256":"a232bfb7dbe57c3c5550b845dcbcea80013590275cfaa012097c967e2f2edb81"},"schema_version":"1.0","source":{"id":"1208.4609","kind":"arxiv","version":1}},"canonical_sha256":"26eed0ffd13f1bcbadaf92bc24472a4d4c2951d33664e8e20740542795fd52e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26eed0ffd13f1bcbadaf92bc24472a4d4c2951d33664e8e20740542795fd52e7","first_computed_at":"2026-05-18T03:48:13.011522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:13.011522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0MlTS/3zEqSdzn+Cd6MW7AGE1Q22s5m1qJDYoBS8JqDCsHRzmFZWypBt1zGUdjg625sWDWWheQ6+7I4Nw0VdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:13.012237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f591683711cee0f3185da0f4442cc70c6356b8a4c3ea4c6436496a7c7d3edce5","sha256:fca8e33b96486b0baf206f05f8241c8796e9030b8ffc83703a981e73ad4d8f16"],"state_sha256":"0f67f9ed7439fcac01d59de7d91abd1ae1201a77274052a9fdf9d81a3b7b9f2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNb40514VsCkRHL0CVX5ecps1dHrRF3Dflh21Lis8XiSSlF/OBuvXVcuUmGTPxUrloLD3/wXZ9xj+AMCta3PCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:01:53.747299Z","bundle_sha256":"ae84f962a37273c1a296d2e95759b1c6f39b3d372bdc05832c487cca75cbb391"}}