{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TAHEFZXRSDURE4C77GVVO4UVJ7","short_pith_number":"pith:TAHEFZXR","canonical_record":{"source":{"id":"1007.2520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-07-15T10:02:56Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"8962fc4d2a8045631814e4eb007a59be8417153c36e3eb9e557499aabbc25d6a","abstract_canon_sha256":"dfd425ba0f463c7f04a06f9a804858e53b412541bc0af5d4bd1e8c8ed8f139a4"},"schema_version":"1.0"},"canonical_sha256":"980e42e6f190e912705ff9ab5772954fd1e619b4a7c7829920fd4eac1db29be6","source":{"kind":"arxiv","id":"1007.2520","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2520","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2520v2","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2520","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"TAHEFZXRSDUR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TAHEFZXRSDURE4C7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TAHEFZXR","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TAHEFZXRSDURE4C77GVVO4UVJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1007.2520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-07-15T10:02:56Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"8962fc4d2a8045631814e4eb007a59be8417153c36e3eb9e557499aabbc25d6a","abstract_canon_sha256":"dfd425ba0f463c7f04a06f9a804858e53b412541bc0af5d4bd1e8c8ed8f139a4"},"schema_version":"1.0"},"canonical_sha256":"980e42e6f190e912705ff9ab5772954fd1e619b4a7c7829920fd4eac1db29be6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:59.988257Z","signature_b64":"UkBO70elxu4zxw4uS66gaBSRVivgemmptyXFKQU+I6V7yeK2XuKM4dEpSv0DeTvu0O648Nspiw0L8hfKlHm5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"980e42e6f190e912705ff9ab5772954fd1e619b4a7c7829920fd4eac1db29be6","last_reissued_at":"2026-05-18T03:49:59.987404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:59.987404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.2520","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hJCHF7/gNF0PMO2lu8V0nMm34Uf33snwV8sRzGOd3IRVOh+vEgWMUWN916YTK+CH7sA5FafuWY7QXHxkhuwkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:06:50.557764Z"},"content_sha256":"ffc0bac3ec771d2401309eacab9df8d4624889d196b2988c4ddf27663767a5de","schema_version":"1.0","event_id":"sha256:ffc0bac3ec771d2401309eacab9df8d4624889d196b2988c4ddf27663767a5de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TAHEFZXRSDURE4C77GVVO4UVJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On universal covers for four-dimensional sets of a given diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Zsolt Langi","submitted_at":"2010-07-15T10:02:56Z","abstract_excerpt":"Makeev proved that among centrally symmetric four-dimensional polytopes, with more than twenty facets and circumscribed about the Euclidean ball of diameter one, there is no universal cover for the family of unit diameter sets. In this paper we examine the converse problem, and prove that each centrally symmetric polytope, with at most fourteen facets and circumscribed about the Euclidean ball of diameter one, is a universal cover for the family of unit diameter sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2520","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":""},"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":"2026-05-18T03:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CrSlPMJdEoNhIV4kE7uJlzcnGMLyZz6Gg/cqVMhRmJsdfFmhaRatBlkv1cPRy+jgi6MjxMdNacP9IdV1m8r4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:06:50.558110Z"},"content_sha256":"97bb29e67d1a2b5657986c88419af075ff2b886aa5117cabf4683c22f52a9681","schema_version":"1.0","event_id":"sha256:97bb29e67d1a2b5657986c88419af075ff2b886aa5117cabf4683c22f52a9681"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAHEFZXRSDURE4C77GVVO4UVJ7/bundle.json","state_url":"https://pith.science/pith/TAHEFZXRSDURE4C77GVVO4UVJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAHEFZXRSDURE4C77GVVO4UVJ7/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":"2026-06-26T07:06:50Z","links":{"resolver":"https://pith.science/pith/TAHEFZXRSDURE4C77GVVO4UVJ7","bundle":"https://pith.science/pith/TAHEFZXRSDURE4C77GVVO4UVJ7/bundle.json","state":"https://pith.science/pith/TAHEFZXRSDURE4C77GVVO4UVJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAHEFZXRSDURE4C77GVVO4UVJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TAHEFZXRSDURE4C77GVVO4UVJ7","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":"dfd425ba0f463c7f04a06f9a804858e53b412541bc0af5d4bd1e8c8ed8f139a4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-07-15T10:02:56Z","title_canon_sha256":"8962fc4d2a8045631814e4eb007a59be8417153c36e3eb9e557499aabbc25d6a"},"schema_version":"1.0","source":{"id":"1007.2520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2520","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2520v2","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2520","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"TAHEFZXRSDUR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TAHEFZXRSDURE4C7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TAHEFZXR","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:97bb29e67d1a2b5657986c88419af075ff2b886aa5117cabf4683c22f52a9681","target":"graph","created_at":"2026-05-18T03:49:59Z","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":"Makeev proved that among centrally symmetric four-dimensional polytopes, with more than twenty facets and circumscribed about the Euclidean ball of diameter one, there is no universal cover for the family of unit diameter sets. In this paper we examine the converse problem, and prove that each centrally symmetric polytope, with at most fourteen facets and circumscribed about the Euclidean ball of diameter one, is a universal cover for the family of unit diameter sets.","authors_text":"Zsolt Langi","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-07-15T10:02:56Z","title":"On universal covers for four-dimensional sets of a given diameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2520","kind":"arxiv","version":2},"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:ffc0bac3ec771d2401309eacab9df8d4624889d196b2988c4ddf27663767a5de","target":"record","created_at":"2026-05-18T03:49:59Z","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":"dfd425ba0f463c7f04a06f9a804858e53b412541bc0af5d4bd1e8c8ed8f139a4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-07-15T10:02:56Z","title_canon_sha256":"8962fc4d2a8045631814e4eb007a59be8417153c36e3eb9e557499aabbc25d6a"},"schema_version":"1.0","source":{"id":"1007.2520","kind":"arxiv","version":2}},"canonical_sha256":"980e42e6f190e912705ff9ab5772954fd1e619b4a7c7829920fd4eac1db29be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"980e42e6f190e912705ff9ab5772954fd1e619b4a7c7829920fd4eac1db29be6","first_computed_at":"2026-05-18T03:49:59.987404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:59.987404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UkBO70elxu4zxw4uS66gaBSRVivgemmptyXFKQU+I6V7yeK2XuKM4dEpSv0DeTvu0O648Nspiw0L8hfKlHm5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:59.988257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffc0bac3ec771d2401309eacab9df8d4624889d196b2988c4ddf27663767a5de","sha256:97bb29e67d1a2b5657986c88419af075ff2b886aa5117cabf4683c22f52a9681"],"state_sha256":"6ea64d8bd0fbeab42b7344d1b77c46b870b5390e2d77a5c6e4801e740757e806"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6uFe+k+XuEaGWn3g//vUOHAWXYaOdD6QLASM0njS65WO9CACpEBI41LR6h82EAKPxfIMtAxZ0X3TtYjhfa9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:06:50.560364Z","bundle_sha256":"5fea86156c665e1b654a27508ede1c0b798fc11ba52515ac0f24dbedc04e1a92"}}