{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YN7FTRXTSPIOLFC6KW6AG7C3B6","short_pith_number":"pith:YN7FTRXT","schema_version":"1.0","canonical_sha256":"c37e59c6f393d0e5945e55bc037c5b0fa2e931e6c1aa442f8a9032941fa84c3d","source":{"kind":"arxiv","id":"2608.09726","version":1},"attestation_state":"computed","paper":{"title":"Abstract Six-Functor Formalisms: Extension to Ind- and Pro- Categories and Functorial Cohomological Purity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Chirantan Chowdhury","submitted_at":"2026-08-10T15:26:09Z","abstract_excerpt":"In this article, we study two consequences of abstract six-functor formalisms. Firstly, we show that an abstract six-functor formalism can be extended to specific Ind- and Pro- categories of geometric setups. As an application, we can define the motivic stable homotopy theory for ind-pro-algebraic stacks such as the Hecke stack. Secondly, we also show that Cohomological Purity is functorial using the multisimplicial language developed by Liu-Zheng."},"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":"2608.09726","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-08-10T15:26:09Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"bed832e5adb5275bb0335a8636aaf3d1ed0fecbdfcf966f850311f3b6622c944","abstract_canon_sha256":"1b1f8dff471cea6a635bdc8941b33de060a36082414e1c987982ca00d21a7432"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T02:24:53.586464Z","signature_b64":"0he4QvUD0MkwqhG1agBpBH5sidnLcnuM78omZlo/dugXSWmkYXKD3jMzoNfJD9VkxU5RyW8ZfotY9zZTtVjACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c37e59c6f393d0e5945e55bc037c5b0fa2e931e6c1aa442f8a9032941fa84c3d","last_reissued_at":"2026-08-11T02:24:53.584821Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T02:24:53.584821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Abstract Six-Functor Formalisms: Extension to Ind- and Pro- Categories and Functorial Cohomological Purity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Chirantan Chowdhury","submitted_at":"2026-08-10T15:26:09Z","abstract_excerpt":"In this article, we study two consequences of abstract six-functor formalisms. Firstly, we show that an abstract six-functor formalism can be extended to specific Ind- and Pro- categories of geometric setups. As an application, we can define the motivic stable homotopy theory for ind-pro-algebraic stacks such as the Hecke stack. Secondly, we also show that Cohomological Purity is functorial using the multisimplicial language developed by Liu-Zheng."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09726","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/2608.09726/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":"2608.09726","created_at":"2026-08-11T02:24:53.585474+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.09726v1","created_at":"2026-08-11T02:24:53.585474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09726","created_at":"2026-08-11T02:24:53.585474+00:00"},{"alias_kind":"pith_short_12","alias_value":"YN7FTRXTSPIO","created_at":"2026-08-11T02:24:53.585474+00:00"},{"alias_kind":"pith_short_16","alias_value":"YN7FTRXTSPIOLFC6","created_at":"2026-08-11T02:24:53.585474+00:00"},{"alias_kind":"pith_short_8","alias_value":"YN7FTRXT","created_at":"2026-08-11T02:24:53.585474+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/YN7FTRXTSPIOLFC6KW6AG7C3B6","json":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6.json","graph_json":"https://pith.science/api/pith-number/YN7FTRXTSPIOLFC6KW6AG7C3B6/graph.json","events_json":"https://pith.science/api/pith-number/YN7FTRXTSPIOLFC6KW6AG7C3B6/events.json","paper":"https://pith.science/paper/YN7FTRXT"},"agent_actions":{"view_html":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6","download_json":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6.json","view_paper":"https://pith.science/paper/YN7FTRXT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.09726&json=true","fetch_graph":"https://pith.science/api/pith-number/YN7FTRXTSPIOLFC6KW6AG7C3B6/graph.json","fetch_events":"https://pith.science/api/pith-number/YN7FTRXTSPIOLFC6KW6AG7C3B6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6/action/storage_attestation","attest_author":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6/action/author_attestation","sign_citation":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6/action/citation_signature","submit_replication":"https://pith.science/pith/YN7FTRXTSPIOLFC6KW6AG7C3B6/action/replication_record"}},"created_at":"2026-08-11T02:24:53.585474+00:00","updated_at":"2026-08-11T02:24:53.585474+00:00"}