{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:N4TLROJY7NAD3QRD4U6J7MKWIT","short_pith_number":"pith:N4TLROJY","schema_version":"1.0","canonical_sha256":"6f26b8b938fb403dc223e53c9fb15644d601e914af946fd8aefed4e274f3ed4a","source":{"kind":"arxiv","id":"2504.07005","version":2},"attestation_state":"computed","paper":{"title":"A stacky approach to prismatic crystals via $q$-prism charts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Zeyu Liu","submitted_at":"2025-04-09T16:24:51Z","abstract_excerpt":"Let $Y$ be a locally complete intersection over $\\mathcal{O}_K$ containing a $p$-power root of unity $\\zeta_p$. We classify the derived category of prismatic crystals on the absolute prismatic site of $Y$ by studying quasi-coherent complexes on the prismatization of $Y$ via $q$-prism charts. We also develop a Galois descent mechanism to remove the assumption on $\\mathcal{O}_K$. As an application, we classify quasi-coherent complexes on the Cartier-Witt stack and give a purely algebraic calculation of the cohomology of the structure sheaf on the absolute prismatic site of $\\mathbb{Z}_p$. Along "},"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":"2504.07005","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-04-09T16:24:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fc2436f89133b7636f08176cfaa947bb5388f3855a242c9b83ffe162d2feaa5e","abstract_canon_sha256":"4c4bf0acbe896dad4d0a6fc3aad433c9a984e743170585495f1505e748ecc295"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:30.911519Z","signature_b64":"U82hQAZilkjj9bnV6iEXpgH7VQer4w69R13/U12COrHGV5reENOzHy2tqg1dLbqlaghsmoPVB+ekLUBN+oClCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f26b8b938fb403dc223e53c9fb15644d601e914af946fd8aefed4e274f3ed4a","last_reissued_at":"2026-07-05T10:48:30.911099Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:30.911099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stacky approach to prismatic crystals via $q$-prism charts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Zeyu Liu","submitted_at":"2025-04-09T16:24:51Z","abstract_excerpt":"Let $Y$ be a locally complete intersection over $\\mathcal{O}_K$ containing a $p$-power root of unity $\\zeta_p$. We classify the derived category of prismatic crystals on the absolute prismatic site of $Y$ by studying quasi-coherent complexes on the prismatization of $Y$ via $q$-prism charts. We also develop a Galois descent mechanism to remove the assumption on $\\mathcal{O}_K$. As an application, we classify quasi-coherent complexes on the Cartier-Witt stack and give a purely algebraic calculation of the cohomology of the structure sheaf on the absolute prismatic site of $\\mathbb{Z}_p$. Along "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07005","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/2504.07005/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":"2504.07005","created_at":"2026-07-05T10:48:30.911157+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.07005v2","created_at":"2026-07-05T10:48:30.911157+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.07005","created_at":"2026-07-05T10:48:30.911157+00:00"},{"alias_kind":"pith_short_12","alias_value":"N4TLROJY7NAD","created_at":"2026-07-05T10:48:30.911157+00:00"},{"alias_kind":"pith_short_16","alias_value":"N4TLROJY7NAD3QRD","created_at":"2026-07-05T10:48:30.911157+00:00"},{"alias_kind":"pith_short_8","alias_value":"N4TLROJY","created_at":"2026-07-05T10:48:30.911157+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2510.16961","citing_title":"Syntomification and crystalline local systems","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT","json":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT.json","graph_json":"https://pith.science/api/pith-number/N4TLROJY7NAD3QRD4U6J7MKWIT/graph.json","events_json":"https://pith.science/api/pith-number/N4TLROJY7NAD3QRD4U6J7MKWIT/events.json","paper":"https://pith.science/paper/N4TLROJY"},"agent_actions":{"view_html":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT","download_json":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT.json","view_paper":"https://pith.science/paper/N4TLROJY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.07005&json=true","fetch_graph":"https://pith.science/api/pith-number/N4TLROJY7NAD3QRD4U6J7MKWIT/graph.json","fetch_events":"https://pith.science/api/pith-number/N4TLROJY7NAD3QRD4U6J7MKWIT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT/action/storage_attestation","attest_author":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT/action/author_attestation","sign_citation":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT/action/citation_signature","submit_replication":"https://pith.science/pith/N4TLROJY7NAD3QRD4U6J7MKWIT/action/replication_record"}},"created_at":"2026-07-05T10:48:30.911157+00:00","updated_at":"2026-07-05T10:48:30.911157+00:00"}