{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7V427RAWDZZPPNGHOAMVIHXTBF","short_pith_number":"pith:7V427RAW","canonical_record":{"source":{"id":"1810.12339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-29T18:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"7501fb31af7fea5cd9f86300a965f3caa199b42cf46b5ded5cca2baf83567975","abstract_canon_sha256":"79940415eb4ee0379a12506da69e6b5ab8ebe22c4f271be4f98a9000c534f327"},"schema_version":"1.0"},"canonical_sha256":"fd79afc4161e72f7b4c77019541ef30973babddf3a6d9097616087071688cd27","source":{"kind":"arxiv","id":"1810.12339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12339","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12339v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12339","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"7V427RAWDZZP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7V427RAWDZZPPNGH","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7V427RAW","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7V427RAWDZZPPNGHOAMVIHXTBF","target":"record","payload":{"canonical_record":{"source":{"id":"1810.12339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-29T18:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"7501fb31af7fea5cd9f86300a965f3caa199b42cf46b5ded5cca2baf83567975","abstract_canon_sha256":"79940415eb4ee0379a12506da69e6b5ab8ebe22c4f271be4f98a9000c534f327"},"schema_version":"1.0"},"canonical_sha256":"fd79afc4161e72f7b4c77019541ef30973babddf3a6d9097616087071688cd27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.974911Z","signature_b64":"4E6SPxL/ZVSG6IPahlBsmjbJxF63T0vo9U83h7CJdQb6A3/vtzViuhAwiMFdWrmv4oI6qYYYEcSWPzNI5wD9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd79afc4161e72f7b4c77019541ef30973babddf3a6d9097616087071688cd27","last_reissued_at":"2026-05-18T00:02:02.974183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.974183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.12339","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":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIAfM7ltb6MZiCkzm0/cGYYLaYdtgJK01f7b+DD52gUptuobZ/fl/YiYbA7Kzxu7yUp9wVxqu6ds4zeUaHvVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:15:06.236041Z"},"content_sha256":"9e730cdbc63daa955867e00760758ff8fe833ca07eb613e2eb216bd719b4a842","schema_version":"1.0","event_id":"sha256:9e730cdbc63daa955867e00760758ff8fe833ca07eb613e2eb216bd719b4a842"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7V427RAWDZZPPNGHOAMVIHXTBF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lubin-Tate theory, character theory, and power operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nathaniel Stapleton","submitted_at":"2018-10-29T18:34:05Z","abstract_excerpt":"This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their symmetries. These symmetries are then used in conjunction with the Hopkins-Kuhn-Ravenel character theory to provide formulas for the power operations and the stabilizer group action on the E-cohomology of a finite group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12339","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":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dydU/K8NprUt4uRPBOKSongyptO6JtCnCzSQIvGZ9LmtA9MNF3b+6PxMKiebRXKvYc7+A9q+bkgFPiHROXUkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:15:06.236398Z"},"content_sha256":"71cdf590b2acd02a50db5459ee1c3a52ff4b041c620038fa8d8f67cdac9438ae","schema_version":"1.0","event_id":"sha256:71cdf590b2acd02a50db5459ee1c3a52ff4b041c620038fa8d8f67cdac9438ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7V427RAWDZZPPNGHOAMVIHXTBF/bundle.json","state_url":"https://pith.science/pith/7V427RAWDZZPPNGHOAMVIHXTBF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7V427RAWDZZPPNGHOAMVIHXTBF/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":"2026-07-02T19:15:06Z","links":{"resolver":"https://pith.science/pith/7V427RAWDZZPPNGHOAMVIHXTBF","bundle":"https://pith.science/pith/7V427RAWDZZPPNGHOAMVIHXTBF/bundle.json","state":"https://pith.science/pith/7V427RAWDZZPPNGHOAMVIHXTBF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7V427RAWDZZPPNGHOAMVIHXTBF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7V427RAWDZZPPNGHOAMVIHXTBF","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":"79940415eb4ee0379a12506da69e6b5ab8ebe22c4f271be4f98a9000c534f327","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-29T18:34:05Z","title_canon_sha256":"7501fb31af7fea5cd9f86300a965f3caa199b42cf46b5ded5cca2baf83567975"},"schema_version":"1.0","source":{"id":"1810.12339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12339","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12339v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12339","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"7V427RAWDZZP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7V427RAWDZZPPNGH","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7V427RAW","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:71cdf590b2acd02a50db5459ee1c3a52ff4b041c620038fa8d8f67cdac9438ae","target":"graph","created_at":"2026-05-18T00:02:02Z","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":"This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their symmetries. These symmetries are then used in conjunction with the Hopkins-Kuhn-Ravenel character theory to provide formulas for the power operations and the stabilizer group action on the E-cohomology of a finite group.","authors_text":"Nathaniel Stapleton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-29T18:34:05Z","title":"Lubin-Tate theory, character theory, and power operations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12339","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":"sha256:9e730cdbc63daa955867e00760758ff8fe833ca07eb613e2eb216bd719b4a842","target":"record","created_at":"2026-05-18T00:02:02Z","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":"79940415eb4ee0379a12506da69e6b5ab8ebe22c4f271be4f98a9000c534f327","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-29T18:34:05Z","title_canon_sha256":"7501fb31af7fea5cd9f86300a965f3caa199b42cf46b5ded5cca2baf83567975"},"schema_version":"1.0","source":{"id":"1810.12339","kind":"arxiv","version":1}},"canonical_sha256":"fd79afc4161e72f7b4c77019541ef30973babddf3a6d9097616087071688cd27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd79afc4161e72f7b4c77019541ef30973babddf3a6d9097616087071688cd27","first_computed_at":"2026-05-18T00:02:02.974183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:02.974183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4E6SPxL/ZVSG6IPahlBsmjbJxF63T0vo9U83h7CJdQb6A3/vtzViuhAwiMFdWrmv4oI6qYYYEcSWPzNI5wD9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:02.974911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e730cdbc63daa955867e00760758ff8fe833ca07eb613e2eb216bd719b4a842","sha256:71cdf590b2acd02a50db5459ee1c3a52ff4b041c620038fa8d8f67cdac9438ae"],"state_sha256":"f840dade5bf062366e6978a5013d53bffe42a8683407414532595ecf4a638dd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVQcrnmYGri8jQpMC7DZjY9i8jDRfXsa/l63MNepK8QTPFi/ybU/xojEw8q7hCHPdE4IQhxV57vuswtM8yExBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T19:15:06.238374Z","bundle_sha256":"70c88533d367a6377cde312c65584403ed696df109d65e519aba7b9c821a0f19"}}