{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BDM4HBUGKCQE6VSICK3RORTMZ7","short_pith_number":"pith:BDM4HBUG","canonical_record":{"source":{"id":"1009.4681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-23T18:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"8c05ca0c262f25030352bbb3ffabebdbdb466d0cbea5aee1ceefa6227805ba90","abstract_canon_sha256":"e58373975c71150af9dfc0d7222a8a722e5267fd4199bf43419afb6155cc3141"},"schema_version":"1.0"},"canonical_sha256":"08d9c3868650a04f564812b717466ccfd7e93042ede0d175da1709e7d9121ac9","source":{"kind":"arxiv","id":"1009.4681","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4681","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4681v1","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4681","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"BDM4HBUGKCQE","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BDM4HBUGKCQE6VSI","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BDM4HBUG","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BDM4HBUGKCQE6VSICK3RORTMZ7","target":"record","payload":{"canonical_record":{"source":{"id":"1009.4681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-23T18:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"8c05ca0c262f25030352bbb3ffabebdbdb466d0cbea5aee1ceefa6227805ba90","abstract_canon_sha256":"e58373975c71150af9dfc0d7222a8a722e5267fd4199bf43419afb6155cc3141"},"schema_version":"1.0"},"canonical_sha256":"08d9c3868650a04f564812b717466ccfd7e93042ede0d175da1709e7d9121ac9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:21.772567Z","signature_b64":"ipcyQ/2oDg89yisxbG1KQQW0MTAbdELn2i6fZTPQSmzzMD2cs7jfF9VXSnD7pDml8C/YFLgx6ir72fklouwoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08d9c3868650a04f564812b717466ccfd7e93042ede0d175da1709e7d9121ac9","last_reissued_at":"2026-05-18T02:45:21.771945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:21.771945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.4681","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UQaomNJlmGoaff5bwrRaPfTS3wlOH0TqpTJR7dVxZrEiX4C1kudj/UY5pTSJnq30rjrFVxa9qGuSKKcMAq+KCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:20:40.537974Z"},"content_sha256":"d290f3245491a649856a90c26aa8641d48f5e40c7e42475964f4dfd80d07248e","schema_version":"1.0","event_id":"sha256:d290f3245491a649856a90c26aa8641d48f5e40c7e42475964f4dfd80d07248e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BDM4HBUGKCQE6VSICK3RORTMZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a question by Corson about point-finite coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andrea Marchese, Clemente Zanco","submitted_at":"2010-09-23T18:42:32Z","abstract_excerpt":"We answer in the affirmative the following question raised by H. H. Corson in 1961: \"Is it possible to cover every Banach space X by bounded convex sets with nonempty interior in such a way that no point of X belongs to infinitely many of them?\" Actually we show the way to produce in every Banach space X a bounded convex tiling of order 2, i.e. a covering of X by bounded convex closed sets with nonempty interior (tiles) such that the interiors are pairwise disjoint and no point of X belongs to more than two tiles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4681","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7i6eT08t350zRs/xBYFFRTuL0Pcv0DKBixWZ/Npa0DBJIlhJDIPMmfhnPxxDI7BUTLDpcUlk6OTidBdkLMRvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:20:40.538330Z"},"content_sha256":"2c5450b9c94dbd0a19eb36435a9c81c37c6bceec624050130e44a56269fefcf2","schema_version":"1.0","event_id":"sha256:2c5450b9c94dbd0a19eb36435a9c81c37c6bceec624050130e44a56269fefcf2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDM4HBUGKCQE6VSICK3RORTMZ7/bundle.json","state_url":"https://pith.science/pith/BDM4HBUGKCQE6VSICK3RORTMZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDM4HBUGKCQE6VSICK3RORTMZ7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T22:20:40Z","links":{"resolver":"https://pith.science/pith/BDM4HBUGKCQE6VSICK3RORTMZ7","bundle":"https://pith.science/pith/BDM4HBUGKCQE6VSICK3RORTMZ7/bundle.json","state":"https://pith.science/pith/BDM4HBUGKCQE6VSICK3RORTMZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDM4HBUGKCQE6VSICK3RORTMZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BDM4HBUGKCQE6VSICK3RORTMZ7","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":"e58373975c71150af9dfc0d7222a8a722e5267fd4199bf43419afb6155cc3141","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-23T18:42:32Z","title_canon_sha256":"8c05ca0c262f25030352bbb3ffabebdbdb466d0cbea5aee1ceefa6227805ba90"},"schema_version":"1.0","source":{"id":"1009.4681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4681","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4681v1","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4681","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"BDM4HBUGKCQE","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BDM4HBUGKCQE6VSI","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BDM4HBUG","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:2c5450b9c94dbd0a19eb36435a9c81c37c6bceec624050130e44a56269fefcf2","target":"graph","created_at":"2026-05-18T02:45:21Z","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":"We answer in the affirmative the following question raised by H. H. Corson in 1961: \"Is it possible to cover every Banach space X by bounded convex sets with nonempty interior in such a way that no point of X belongs to infinitely many of them?\" Actually we show the way to produce in every Banach space X a bounded convex tiling of order 2, i.e. a covering of X by bounded convex closed sets with nonempty interior (tiles) such that the interiors are pairwise disjoint and no point of X belongs to more than two tiles.","authors_text":"Andrea Marchese, Clemente Zanco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-23T18:42:32Z","title":"On a question by Corson about point-finite coverings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4681","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:d290f3245491a649856a90c26aa8641d48f5e40c7e42475964f4dfd80d07248e","target":"record","created_at":"2026-05-18T02:45:21Z","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":"e58373975c71150af9dfc0d7222a8a722e5267fd4199bf43419afb6155cc3141","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-23T18:42:32Z","title_canon_sha256":"8c05ca0c262f25030352bbb3ffabebdbdb466d0cbea5aee1ceefa6227805ba90"},"schema_version":"1.0","source":{"id":"1009.4681","kind":"arxiv","version":1}},"canonical_sha256":"08d9c3868650a04f564812b717466ccfd7e93042ede0d175da1709e7d9121ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08d9c3868650a04f564812b717466ccfd7e93042ede0d175da1709e7d9121ac9","first_computed_at":"2026-05-18T02:45:21.771945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:21.771945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ipcyQ/2oDg89yisxbG1KQQW0MTAbdELn2i6fZTPQSmzzMD2cs7jfF9VXSnD7pDml8C/YFLgx6ir72fklouwoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:21.772567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d290f3245491a649856a90c26aa8641d48f5e40c7e42475964f4dfd80d07248e","sha256:2c5450b9c94dbd0a19eb36435a9c81c37c6bceec624050130e44a56269fefcf2"],"state_sha256":"129bfd4fe7c2aa3db0d49ecdaf50351571aee13665b6f5c55e50a52c454e0129"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JcQr1ccLVU5cvZlZoSRQbOlL2ZK28CG8ixx7MXd8j4caP+iW+zTkhKb6M+sOKpj9kp1c80HuFoUzVJf+/N8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:20:40.540308Z","bundle_sha256":"25f42ca44de29202f6cf663c4335cd6d0cd0fb7146a7dc68f061377e65116090"}}