{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:AXLXT5HA25L7FPZMMUDPL6TUA2","short_pith_number":"pith:AXLXT5HA","schema_version":"1.0","canonical_sha256":"05d779f4e0d757f2bf2c6506f5fa740687778befe42e2ca382057aec742cfa06","source":{"kind":"arxiv","id":"0902.2499","version":2},"attestation_state":"computed","paper":{"title":"The congruence criterion for power operations in Morava E-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Charles Rezk","submitted_at":"2009-02-14T22:24:53Z","abstract_excerpt":"We prove a congruence criterion for the algebraic theory of power operations in Morava E-theory, analogous to Wilkerson's congruence criterion for torsion free lambda-rings. In addition, we provide a geometric description of this congruence criterion, in terms of sheaves on the moduli problem of deformations of formal groups and Frobenius isogenies."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0902.2499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-02-14T22:24:53Z","cross_cats_sorted":[],"title_canon_sha256":"7aa810c4de0c22356e1ccd23246ae509b158f199ef66a4f30eab8cb3a1aa6be4","abstract_canon_sha256":"74a607ded01c5bd9f3acfb6f8a62e5b64bcce08eb491967eef62734dd012faf6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:17:04.804086Z","signature_b64":"ITySa9ywpVsJ9dqx2BzC+g2zPDqc/d0SgwH9pP31nOwSh0SA6PjNq0kgyWY9r7G1MMS4N4thc/mJjHGmma5pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05d779f4e0d757f2bf2c6506f5fa740687778befe42e2ca382057aec742cfa06","last_reissued_at":"2026-07-04T17:17:04.803693Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:17:04.803693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The congruence criterion for power operations in Morava E-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Charles Rezk","submitted_at":"2009-02-14T22:24:53Z","abstract_excerpt":"We prove a congruence criterion for the algebraic theory of power operations in Morava E-theory, analogous to Wilkerson's congruence criterion for torsion free lambda-rings. In addition, we provide a geometric description of this congruence criterion, in terms of sheaves on the moduli problem of deformations of formal groups and Frobenius isogenies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2499","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0902.2499/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0902.2499","created_at":"2026-07-04T17:17:04.803754+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.2499v2","created_at":"2026-07-04T17:17:04.803754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2499","created_at":"2026-07-04T17:17:04.803754+00:00"},{"alias_kind":"pith_short_12","alias_value":"AXLXT5HA25L7","created_at":"2026-07-04T17:17:04.803754+00:00"},{"alias_kind":"pith_short_16","alias_value":"AXLXT5HA25L7FPZM","created_at":"2026-07-04T17:17:04.803754+00:00"},{"alias_kind":"pith_short_8","alias_value":"AXLXT5HA","created_at":"2026-07-04T17:17:04.803754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2","json":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2.json","graph_json":"https://pith.science/api/pith-number/AXLXT5HA25L7FPZMMUDPL6TUA2/graph.json","events_json":"https://pith.science/api/pith-number/AXLXT5HA25L7FPZMMUDPL6TUA2/events.json","paper":"https://pith.science/paper/AXLXT5HA"},"agent_actions":{"view_html":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2","download_json":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2.json","view_paper":"https://pith.science/paper/AXLXT5HA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.2499&json=true","fetch_graph":"https://pith.science/api/pith-number/AXLXT5HA25L7FPZMMUDPL6TUA2/graph.json","fetch_events":"https://pith.science/api/pith-number/AXLXT5HA25L7FPZMMUDPL6TUA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2/action/storage_attestation","attest_author":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2/action/author_attestation","sign_citation":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2/action/citation_signature","submit_replication":"https://pith.science/pith/AXLXT5HA25L7FPZMMUDPL6TUA2/action/replication_record"}},"created_at":"2026-07-04T17:17:04.803754+00:00","updated_at":"2026-07-04T17:17:04.803754+00:00"}