{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:G6F7TBYGX7XRCOWJYTRWTLWVNE","short_pith_number":"pith:G6F7TBYG","schema_version":"1.0","canonical_sha256":"378bf98706bfef113ac9c4e369aed5691beb6d3753ca7d4a2d469f3360ee1ab3","source":{"kind":"arxiv","id":"2607.22680","version":1},"attestation_state":"computed","paper":{"title":"A rigidity theorem for $\\pi_*$-\\'etale $\\mathbb E_k$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"XianSheng Li","submitted_at":"2026-07-12T15:12:29Z","abstract_excerpt":"We prove a rigidity theorem for $\\pi_*$-\\'etale $\\mathbb E_k$-algebras over an $\\mathbb E_{k+1}$-ring spectrum: the category of $\\pi_*$-\\'etale extensions of an $\\mathbb E_k$-algebra is identified with the ordinary category of \\'etale Dirac algebras over its graded homotopy Dirac ring. The proof develops a relative Goerss-Hopkins type obstruction theory in synthetic spectra, including an $I$-complete version. As an application, the completed obstruction theory constructs the $I_n$-complete $\\mathbb E_3$-$MU_{(p)}$-algebra realization of the Lubin-Tate theory, hence an $\\mathbb E_4$-orientation"},"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":"2607.22680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-12T15:12:29Z","cross_cats_sorted":[],"title_canon_sha256":"65a8aa129600c8e3ced21a91f1789809b57b367fd557ec4d4ba0e58528eacbae","abstract_canon_sha256":"83fa815cf95e2bcaeef66ea6cebc0916b33b0c4b12dfc24d3cd16473ceeb9fb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T00:21:48.782954Z","signature_b64":"oCs7dLmki+xEFY7beC1U3VKu7peOBDwo7C4SK1FiAf/ZDxQcScaJwmmbHbSQFl+wfcyCythKWd/5wT6LBI7nCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"378bf98706bfef113ac9c4e369aed5691beb6d3753ca7d4a2d469f3360ee1ab3","last_reissued_at":"2026-07-28T00:21:48.782049Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T00:21:48.782049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rigidity theorem for $\\pi_*$-\\'etale $\\mathbb E_k$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"XianSheng Li","submitted_at":"2026-07-12T15:12:29Z","abstract_excerpt":"We prove a rigidity theorem for $\\pi_*$-\\'etale $\\mathbb E_k$-algebras over an $\\mathbb E_{k+1}$-ring spectrum: the category of $\\pi_*$-\\'etale extensions of an $\\mathbb E_k$-algebra is identified with the ordinary category of \\'etale Dirac algebras over its graded homotopy Dirac ring. The proof develops a relative Goerss-Hopkins type obstruction theory in synthetic spectra, including an $I$-complete version. As an application, the completed obstruction theory constructs the $I_n$-complete $\\mathbb E_3$-$MU_{(p)}$-algebra realization of the Lubin-Tate theory, hence an $\\mathbb E_4$-orientation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22680","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22680/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":"2607.22680","created_at":"2026-07-28T00:21:48.782479+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.22680v1","created_at":"2026-07-28T00:21:48.782479+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22680","created_at":"2026-07-28T00:21:48.782479+00:00"},{"alias_kind":"pith_short_12","alias_value":"G6F7TBYGX7XR","created_at":"2026-07-28T00:21:48.782479+00:00"},{"alias_kind":"pith_short_16","alias_value":"G6F7TBYGX7XRCOWJ","created_at":"2026-07-28T00:21:48.782479+00:00"},{"alias_kind":"pith_short_8","alias_value":"G6F7TBYG","created_at":"2026-07-28T00:21:48.782479+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/G6F7TBYGX7XRCOWJYTRWTLWVNE","json":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE.json","graph_json":"https://pith.science/api/pith-number/G6F7TBYGX7XRCOWJYTRWTLWVNE/graph.json","events_json":"https://pith.science/api/pith-number/G6F7TBYGX7XRCOWJYTRWTLWVNE/events.json","paper":"https://pith.science/paper/G6F7TBYG"},"agent_actions":{"view_html":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE","download_json":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE.json","view_paper":"https://pith.science/paper/G6F7TBYG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.22680&json=true","fetch_graph":"https://pith.science/api/pith-number/G6F7TBYGX7XRCOWJYTRWTLWVNE/graph.json","fetch_events":"https://pith.science/api/pith-number/G6F7TBYGX7XRCOWJYTRWTLWVNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE/action/storage_attestation","attest_author":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE/action/author_attestation","sign_citation":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE/action/citation_signature","submit_replication":"https://pith.science/pith/G6F7TBYGX7XRCOWJYTRWTLWVNE/action/replication_record"}},"created_at":"2026-07-28T00:21:48.782479+00:00","updated_at":"2026-07-28T00:21:48.782479+00:00"}