{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MOHTFRXSSWP3KWXMOT7X4AHARL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f8bef05382b80087a02a84f6fec1ceffceedb9d43fb1a3f188e265dd4f9c594b","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-06T17:50:47Z","title_canon_sha256":"8d78b3a1de7ca9c28934aa0afa57cac8393f354fa29915df40520e2e9dda913d"},"schema_version":"1.0","source":{"id":"1612.01924","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01924","created_at":"2026-05-18T00:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01924v1","created_at":"2026-05-18T00:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01924","created_at":"2026-05-18T00:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"MOHTFRXSSWP3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MOHTFRXSSWP3KWXM","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MOHTFRXS","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:d1d38f24bf8665747cdd373b0aaedacd8f49099f2d5c3a782b88cf229d44d2d8","target":"graph","created_at":"2026-05-18T00:17:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $K$ be a field of characteristic zero complete with respect to a non-trivial, non-Archimedean valuation. We relate the sheaf $\\widehat{\\mathcal{D}}$ of infinite order differential operators on smooth rigid $K$-analytic spaces to the algebra $\\mathcal{E}$ of bounded $K$-linear endomorphisms of the structure sheaf. In the case of complex manifolds, Ishimura proved that the analogous sheaves are isomorphic. In the rigid analytic situation, we prove that the natural map $\\widehat{\\mathcal{D}} \\to \\mathcal{E}$ is an isomorphism if and only if the ground field $K$ is algebraically closed and its","authors_text":"Konstantin Ardakov, Oren Ben-Bassat","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-06T17:50:47Z","title":"Bounded linear endomorphisms of rigid analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01924","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a4ed9a0d3537100a02aee94e311f31439988791fb62e9b3edbf349d248160aec","target":"record","created_at":"2026-05-18T00:17:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f8bef05382b80087a02a84f6fec1ceffceedb9d43fb1a3f188e265dd4f9c594b","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-06T17:50:47Z","title_canon_sha256":"8d78b3a1de7ca9c28934aa0afa57cac8393f354fa29915df40520e2e9dda913d"},"schema_version":"1.0","source":{"id":"1612.01924","kind":"arxiv","version":1}},"canonical_sha256":"638f32c6f2959fb55aec74ff7e00e08adafb9549029e11aa6391d54f4993a36b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"638f32c6f2959fb55aec74ff7e00e08adafb9549029e11aa6391d54f4993a36b","first_computed_at":"2026-05-18T00:17:44.243587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:44.243587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSXGECCqk007ZblFsjUnnEUgEYbibhWpl7uBTw7LrjltuDwFO1MvJvRZT0B8pPa6oGDxVF3ihGcsRJJ+EV7iCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:44.244223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01924","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4ed9a0d3537100a02aee94e311f31439988791fb62e9b3edbf349d248160aec","sha256:d1d38f24bf8665747cdd373b0aaedacd8f49099f2d5c3a782b88cf229d44d2d8"],"state_sha256":"6c12f18aeece69faee47c3a82063a7cecbb20327d5745de142e41e136eb1cbf1"}