{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:AO7L3G5LX5IIPWENZFZB3XIZIP","short_pith_number":"pith:AO7L3G5L","schema_version":"1.0","canonical_sha256":"03bebd9babbf5087d88dc9721ddd1943d987ce42f923fbb6809c10f20ca8eb92","source":{"kind":"arxiv","id":"2608.00999","version":1},"attestation_state":"computed","paper":{"title":"Tannakian reconstruction in derived algebraic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Joshua Mundinger, Shubhankar Sahai","submitted_at":"2026-08-02T04:59:20Z","abstract_excerpt":"We prove analogues of Tannakian reconstruction theorems of Lurie and Bhatt--Halpern-Leistner in \\emph{derived} algebraic geometry, where the basic geometric objects are spectra of animated rings rather than $\\mathbb{E}_\\infty$-rings. In this setting, symmetric monoidal $\\infty$-categories are replaced by the $\\Theta$-categories of Nuiten--To\\\"en. These are enhancements of symmetric monoidal $\\infty$-categories which capture the strict commutativity structure on animated rings."},"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":"2608.00999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-02T04:59:20Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"a9ccb6b26672c20392533ba81ab4f720cddb95f83d4b6cc19cb4074c5c7455d5","abstract_canon_sha256":"7b7c335b403ec2a25f0252c7d5b0ff133a22aba586025c8d231b27d21f95a912"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T01:56:11.465130Z","signature_b64":"sPWM8hBk0DwCtb4se6W5P9yFmyC6jTbFPljU4OvdNDPEwOtesoeJZHINKvuyv9w1Esp2DYjKXUEWOXGuZ1xyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03bebd9babbf5087d88dc9721ddd1943d987ce42f923fbb6809c10f20ca8eb92","last_reissued_at":"2026-08-04T01:56:11.463582Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T01:56:11.463582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tannakian reconstruction in derived algebraic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Joshua Mundinger, Shubhankar Sahai","submitted_at":"2026-08-02T04:59:20Z","abstract_excerpt":"We prove analogues of Tannakian reconstruction theorems of Lurie and Bhatt--Halpern-Leistner in \\emph{derived} algebraic geometry, where the basic geometric objects are spectra of animated rings rather than $\\mathbb{E}_\\infty$-rings. In this setting, symmetric monoidal $\\infty$-categories are replaced by the $\\Theta$-categories of Nuiten--To\\\"en. These are enhancements of symmetric monoidal $\\infty$-categories which capture the strict commutativity structure on animated rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00999","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/2608.00999/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":"2608.00999","created_at":"2026-08-04T01:56:11.464946+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.00999v1","created_at":"2026-08-04T01:56:11.464946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00999","created_at":"2026-08-04T01:56:11.464946+00:00"},{"alias_kind":"pith_short_12","alias_value":"AO7L3G5LX5II","created_at":"2026-08-04T01:56:11.464946+00:00"},{"alias_kind":"pith_short_16","alias_value":"AO7L3G5LX5IIPWEN","created_at":"2026-08-04T01:56:11.464946+00:00"},{"alias_kind":"pith_short_8","alias_value":"AO7L3G5L","created_at":"2026-08-04T01:56:11.464946+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/AO7L3G5LX5IIPWENZFZB3XIZIP","json":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP.json","graph_json":"https://pith.science/api/pith-number/AO7L3G5LX5IIPWENZFZB3XIZIP/graph.json","events_json":"https://pith.science/api/pith-number/AO7L3G5LX5IIPWENZFZB3XIZIP/events.json","paper":"https://pith.science/paper/AO7L3G5L"},"agent_actions":{"view_html":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP","download_json":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP.json","view_paper":"https://pith.science/paper/AO7L3G5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.00999&json=true","fetch_graph":"https://pith.science/api/pith-number/AO7L3G5LX5IIPWENZFZB3XIZIP/graph.json","fetch_events":"https://pith.science/api/pith-number/AO7L3G5LX5IIPWENZFZB3XIZIP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP/action/storage_attestation","attest_author":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP/action/author_attestation","sign_citation":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP/action/citation_signature","submit_replication":"https://pith.science/pith/AO7L3G5LX5IIPWENZFZB3XIZIP/action/replication_record"}},"created_at":"2026-08-04T01:56:11.464946+00:00","updated_at":"2026-08-04T01:56:11.464946+00:00"}