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In this paper, for a semi-stable $p$-adic formal scheme $\\frakX$ over $\\calO_K$ with rigid generic fibre $X$ and canonical log structure $\\calM_{\\frakX} = \\calO_{\\frakX}\\cap\\calO_X^{\\times}$, we study Hodge--Tate crystals over the absolute logarithmic prismatic site $(\\frakX,\\calM_{\\frakX})_{\\Prism}$. As an application, we give an equivalence between the category of rational Hodge--Tate crystals on the absolute logarithmic prismatic site $(\\frakX,\\calM_{\\frakX})_{\\Prism}$ and the c"},"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":"2205.08895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-05-18T12:35:08Z","cross_cats_sorted":[],"title_canon_sha256":"93ae19ac2313b6e3bf786994b6b38b087334484ce63eaff80e997ed1add7af18","abstract_canon_sha256":"d6b4f1f7bced64b950ada27e531bde37b74e5f18715448ada32eca21176c656c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:28.384146Z","signature_b64":"1YPNlt8D9NF6txmrcSAtpsN7hgXCQTMm8XlDlEbk9ke8V/0gg9pz43zfn673MPCmxDiT8qIRwqOrXpijG3NIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87384915ed96bd20900c80b274a73b661fc5b0a1ea9a7f331f6fdc4477d55814","last_reissued_at":"2026-07-05T04:32:28.383676Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:28.383676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hodge--Tate crystals on the logarithmic prismatic sites of semi-stable formal schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yu Min, Yupeng Wang","submitted_at":"2022-05-18T12:35:08Z","abstract_excerpt":"Let $\\calO_K$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ with a perfect residue field. 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As an application, we give an equivalence between the category of rational Hodge--Tate crystals on the absolute logarithmic prismatic site $(\\frakX,\\calM_{\\frakX})_{\\Prism}$ and the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.08895","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/2205.08895/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":"2205.08895","created_at":"2026-07-05T04:32:28.383733+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.08895v2","created_at":"2026-07-05T04:32:28.383733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.08895","created_at":"2026-07-05T04:32:28.383733+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q44ESFPNS26S","created_at":"2026-07-05T04:32:28.383733+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q44ESFPNS26SBEAM","created_at":"2026-07-05T04:32:28.383733+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q44ESFPN","created_at":"2026-07-05T04:32:28.383733+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.08451","citing_title":"A prismatic-etale comparison theorem in the semistable case","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY","json":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY.json","graph_json":"https://pith.science/api/pith-number/Q44ESFPNS26SBEAMQCZHJJZ3MY/graph.json","events_json":"https://pith.science/api/pith-number/Q44ESFPNS26SBEAMQCZHJJZ3MY/events.json","paper":"https://pith.science/paper/Q44ESFPN"},"agent_actions":{"view_html":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY","download_json":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY.json","view_paper":"https://pith.science/paper/Q44ESFPN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.08895&json=true","fetch_graph":"https://pith.science/api/pith-number/Q44ESFPNS26SBEAMQCZHJJZ3MY/graph.json","fetch_events":"https://pith.science/api/pith-number/Q44ESFPNS26SBEAMQCZHJJZ3MY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY/action/storage_attestation","attest_author":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY/action/author_attestation","sign_citation":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY/action/citation_signature","submit_replication":"https://pith.science/pith/Q44ESFPNS26SBEAMQCZHJJZ3MY/action/replication_record"}},"created_at":"2026-07-05T04:32:28.383733+00:00","updated_at":"2026-07-05T04:32:28.383733+00:00"}