{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HGONQVKEGOP76ZASLAJHNCAHU6","short_pith_number":"pith:HGONQVKE","canonical_record":{"source":{"id":"1706.00208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-01T08:47:43Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"d099b84dfed85651bfaff70004f6e97422fabf94ceb3347bf200b4c2465ee373","abstract_canon_sha256":"155198a27b26410b88b3d3d0f6dc19f593c89dced5303904cd2eea4793454ad2"},"schema_version":"1.0"},"canonical_sha256":"399cd85544339fff64125812768807a7b62e33ae058ba2e84d33bd0d98dd745a","source":{"kind":"arxiv","id":"1706.00208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00208","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00208v1","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00208","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"pith_short_12","alias_value":"HGONQVKEGOP7","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HGONQVKEGOP76ZAS","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HGONQVKE","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HGONQVKEGOP76ZASLAJHNCAHU6","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-01T08:47:43Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"d099b84dfed85651bfaff70004f6e97422fabf94ceb3347bf200b4c2465ee373","abstract_canon_sha256":"155198a27b26410b88b3d3d0f6dc19f593c89dced5303904cd2eea4793454ad2"},"schema_version":"1.0"},"canonical_sha256":"399cd85544339fff64125812768807a7b62e33ae058ba2e84d33bd0d98dd745a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:28.225278Z","signature_b64":"gf4hDmhknO4787TJb8qRIsbUXH3x6Jz7BJBAmEbFFYw4YBM0ixtUHchlE4KCSy3Ouj/9n7+4UFlHEV0/QnXdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"399cd85544339fff64125812768807a7b62e33ae058ba2e84d33bd0d98dd745a","last_reissued_at":"2026-05-18T00:30:28.224706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:28.224706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00208","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":"2026-05-18T00:30:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6YqaeTtLtP1G34gCZYrPx8MFQVcfcJ3DbSHhMt6zHJHiWJOkZlVcqiBoGeD/+PeCOvD69EZqTKYrOO8jAR9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:14:06.475502Z"},"content_sha256":"349c97ce067afc41090763aef08f8ad6f839f01ae6bfcab74d7cfd2a2a59f8b6","schema_version":"1.0","event_id":"sha256:349c97ce067afc41090763aef08f8ad6f839f01ae6bfcab74d7cfd2a2a59f8b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HGONQVKEGOP76ZASLAJHNCAHU6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Excellent rings in transchromatic homotopy theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AT","authors_text":"Nathaniel Stapleton, Tobias Barthel","submitted_at":"2017-06-01T08:47:43Z","abstract_excerpt":"The purpose of this note is to verify that several basic rings appearing in transchromatic homotopy theory are Noetherian excellent normal domains and thus amenable to standard techniques from commutative algebra. In particular, we show that the coefficients of iterated localizations of Morava $E$-theory at the Morava $K$-theories are normal domains and also that the coefficients in the transchromatic character map for a fixed group form a normal domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00208","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":"2026-05-18T00:30:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uv1ixpkgJ3zs6xDFoLoOZN9uF5meFuIIw9W0M9NhE9ZWP+Cw54KDJuVrf/zcrW51IEw6ipqgMBNFEb8PXdq1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:14:06.476242Z"},"content_sha256":"7000e47a764798c5634edb9873513769aaf3300be716621de5fa2978827a092f","schema_version":"1.0","event_id":"sha256:7000e47a764798c5634edb9873513769aaf3300be716621de5fa2978827a092f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HGONQVKEGOP76ZASLAJHNCAHU6/bundle.json","state_url":"https://pith.science/pith/HGONQVKEGOP76ZASLAJHNCAHU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HGONQVKEGOP76ZASLAJHNCAHU6/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":"2026-06-05T05:14:06Z","links":{"resolver":"https://pith.science/pith/HGONQVKEGOP76ZASLAJHNCAHU6","bundle":"https://pith.science/pith/HGONQVKEGOP76ZASLAJHNCAHU6/bundle.json","state":"https://pith.science/pith/HGONQVKEGOP76ZASLAJHNCAHU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HGONQVKEGOP76ZASLAJHNCAHU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HGONQVKEGOP76ZASLAJHNCAHU6","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":"155198a27b26410b88b3d3d0f6dc19f593c89dced5303904cd2eea4793454ad2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-01T08:47:43Z","title_canon_sha256":"d099b84dfed85651bfaff70004f6e97422fabf94ceb3347bf200b4c2465ee373"},"schema_version":"1.0","source":{"id":"1706.00208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00208","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00208v1","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00208","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"pith_short_12","alias_value":"HGONQVKEGOP7","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HGONQVKEGOP76ZAS","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HGONQVKE","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:7000e47a764798c5634edb9873513769aaf3300be716621de5fa2978827a092f","target":"graph","created_at":"2026-05-18T00:30:28Z","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":"The purpose of this note is to verify that several basic rings appearing in transchromatic homotopy theory are Noetherian excellent normal domains and thus amenable to standard techniques from commutative algebra. In particular, we show that the coefficients of iterated localizations of Morava $E$-theory at the Morava $K$-theories are normal domains and also that the coefficients in the transchromatic character map for a fixed group form a normal domain.","authors_text":"Nathaniel Stapleton, Tobias Barthel","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-01T08:47:43Z","title":"Excellent rings in transchromatic homotopy theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00208","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":"sha256:349c97ce067afc41090763aef08f8ad6f839f01ae6bfcab74d7cfd2a2a59f8b6","target":"record","created_at":"2026-05-18T00:30:28Z","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":"155198a27b26410b88b3d3d0f6dc19f593c89dced5303904cd2eea4793454ad2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-01T08:47:43Z","title_canon_sha256":"d099b84dfed85651bfaff70004f6e97422fabf94ceb3347bf200b4c2465ee373"},"schema_version":"1.0","source":{"id":"1706.00208","kind":"arxiv","version":1}},"canonical_sha256":"399cd85544339fff64125812768807a7b62e33ae058ba2e84d33bd0d98dd745a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"399cd85544339fff64125812768807a7b62e33ae058ba2e84d33bd0d98dd745a","first_computed_at":"2026-05-18T00:30:28.224706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:28.224706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gf4hDmhknO4787TJb8qRIsbUXH3x6Jz7BJBAmEbFFYw4YBM0ixtUHchlE4KCSy3Ouj/9n7+4UFlHEV0/QnXdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:28.225278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:349c97ce067afc41090763aef08f8ad6f839f01ae6bfcab74d7cfd2a2a59f8b6","sha256:7000e47a764798c5634edb9873513769aaf3300be716621de5fa2978827a092f"],"state_sha256":"aa0ee02a99684a735721c843310c4c669326e291b54b3a624d85e8d41b85845b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZQKY65EiahfWWkK0ZQBle8LSU115Ogp1EM5sChPgCffQJQOXxi0jpn1PNB21Zc+mFxt2NRA02w+CajXd5jpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:14:06.496079Z","bundle_sha256":"5d232868aab6c21a03f77b97ecd58be666409d26768f1cb812ad72c1ca9af87b"}}