{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:54MK23LS3D4TGWBEGWFU3LU6ZL","short_pith_number":"pith:54MK23LS","schema_version":"1.0","canonical_sha256":"ef18ad6d72d8f9335824358b4dae9ecac12e3b8e15f0bceea7405c81a5b24c50","source":{"kind":"arxiv","id":"2606.13294","version":1},"attestation_state":"computed","paper":{"title":"A small Banach space $C(K)$ without nice renormings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"math.FA","authors_text":"Damian Sobota, Lyubomyr Zdomskyy, Todor Manev","submitted_at":"2026-06-11T12:48:25Z","abstract_excerpt":"We prove that consistently $\\omega_1<\\mathfrak{c}$ and there exists a compact space $K$ whose Banach space $C(K)$ of continuous real-valued functions is Grothendieck, has density $\\omega_1$, and admits no renorming which is strictly convex or sequentially Kadets--Klee."},"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":"2606.13294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-11T12:48:25Z","cross_cats_sorted":["math.GN","math.LO"],"title_canon_sha256":"fbfe4e78404bd92fb021f51c057337d0269b90080bef0a58717cb22c73cb2cc6","abstract_canon_sha256":"3e6f038dadb779b93987d719b886ba5182dd3198978de86ade9ef6dc0af980e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:51.081957Z","signature_b64":"yFl0m+TVgesdgqURpVgCkDuF5FlMsdce4uOmt2vJBHWwNexOSwZbQdNhtLc3cWu7tp7XOpcqeCm0W4Kb/6yEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef18ad6d72d8f9335824358b4dae9ecac12e3b8e15f0bceea7405c81a5b24c50","last_reissued_at":"2026-06-12T01:09:51.081376Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:51.081376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A small Banach space $C(K)$ without nice renormings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"math.FA","authors_text":"Damian Sobota, Lyubomyr Zdomskyy, Todor Manev","submitted_at":"2026-06-11T12:48:25Z","abstract_excerpt":"We prove that consistently $\\omega_1<\\mathfrak{c}$ and there exists a compact space $K$ whose Banach space $C(K)$ of continuous real-valued functions is Grothendieck, has density $\\omega_1$, and admits no renorming which is strictly convex or sequentially Kadets--Klee."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13294","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/2606.13294/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":"2606.13294","created_at":"2026-06-12T01:09:51.081464+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.13294v1","created_at":"2026-06-12T01:09:51.081464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13294","created_at":"2026-06-12T01:09:51.081464+00:00"},{"alias_kind":"pith_short_12","alias_value":"54MK23LS3D4T","created_at":"2026-06-12T01:09:51.081464+00:00"},{"alias_kind":"pith_short_16","alias_value":"54MK23LS3D4TGWBE","created_at":"2026-06-12T01:09:51.081464+00:00"},{"alias_kind":"pith_short_8","alias_value":"54MK23LS","created_at":"2026-06-12T01:09:51.081464+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/54MK23LS3D4TGWBEGWFU3LU6ZL","json":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL.json","graph_json":"https://pith.science/api/pith-number/54MK23LS3D4TGWBEGWFU3LU6ZL/graph.json","events_json":"https://pith.science/api/pith-number/54MK23LS3D4TGWBEGWFU3LU6ZL/events.json","paper":"https://pith.science/paper/54MK23LS"},"agent_actions":{"view_html":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL","download_json":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL.json","view_paper":"https://pith.science/paper/54MK23LS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.13294&json=true","fetch_graph":"https://pith.science/api/pith-number/54MK23LS3D4TGWBEGWFU3LU6ZL/graph.json","fetch_events":"https://pith.science/api/pith-number/54MK23LS3D4TGWBEGWFU3LU6ZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL/action/storage_attestation","attest_author":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL/action/author_attestation","sign_citation":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL/action/citation_signature","submit_replication":"https://pith.science/pith/54MK23LS3D4TGWBEGWFU3LU6ZL/action/replication_record"}},"created_at":"2026-06-12T01:09:51.081464+00:00","updated_at":"2026-06-12T01:09:51.081464+00:00"}