{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:T2JBDBDHMUKAFBPJKMUMZ2U7OB","short_pith_number":"pith:T2JBDBDH","canonical_record":{"source":{"id":"1212.5361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-12-21T08:53:08Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"17342ddfd05df7c9422173fb1196fb473d7bc42d4ad6bb499e662746d071c0e1","abstract_canon_sha256":"097e4b47e2fdd5a455f45072121a523eb0d4759b2dfac838c4494ad022d2d6c0"},"schema_version":"1.0"},"canonical_sha256":"9e9211846765140285e95328ccea9f707e5e0d61413b394d7d2ad3096c065e2c","source":{"kind":"arxiv","id":"1212.5361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5361","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5361v1","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5361","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"pith_short_12","alias_value":"T2JBDBDHMUKA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T2JBDBDHMUKAFBPJ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T2JBDBDH","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:T2JBDBDHMUKAFBPJKMUMZ2U7OB","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-12-21T08:53:08Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"17342ddfd05df7c9422173fb1196fb473d7bc42d4ad6bb499e662746d071c0e1","abstract_canon_sha256":"097e4b47e2fdd5a455f45072121a523eb0d4759b2dfac838c4494ad022d2d6c0"},"schema_version":"1.0"},"canonical_sha256":"9e9211846765140285e95328ccea9f707e5e0d61413b394d7d2ad3096c065e2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:02.097095Z","signature_b64":"0tm/Pyf/ubYjXmjEfwS8WqIEvYSPhh90RXga+UZhsNMQMXEcIHGndhpkkqZIxVcBcU3C/SXqj2dzAhyh573uDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e9211846765140285e95328ccea9f707e5e0d61413b394d7d2ad3096c065e2c","last_reissued_at":"2026-05-18T03:38:02.096493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:02.096493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5361","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":"2026-05-18T03:38:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+Au+i4eMLbv0J3qwSZs4Ov8ICR36NQrNrVmDFMc844iJ63nwXW19iMp1ucHeo1ev1T/5JeaD/k0amWeNEQjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T00:15:54.727800Z"},"content_sha256":"4eee7e123a86bcd24559c9d5705ff96bea93de94873845166609a263aec024d9","schema_version":"1.0","event_id":"sha256:4eee7e123a86bcd24559c9d5705ff96bea93de94873845166609a263aec024d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:T2JBDBDHMUKAFBPJKMUMZ2U7OB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distinguishing properties of weak slice conditions II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Alexander Stanoyevitch, Andre Diatta, Stephen M. Buckley","submitted_at":"2012-12-21T08:53:08Z","abstract_excerpt":"The slice condition and the more general weak slice conditions are geometric conditions on Euclidean space domains which have evolved over the last several years as a tool in various areas of analysis. This paper examines some of their finer distinctive properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5361","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":"2026-05-18T03:38:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t1pV98BLf9wZ2se2foALsGuyZ/ur98lWXFmlT52pTc2YIiBFt/WEUmj+UTlAcRVSGZpXrL9Ie9daW1ucVkGrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T00:15:54.728155Z"},"content_sha256":"db8abe737538cc5c25ca8c3752a8bc508cac2e58f6e0ab93a05bdbc1df5212fe","schema_version":"1.0","event_id":"sha256:db8abe737538cc5c25ca8c3752a8bc508cac2e58f6e0ab93a05bdbc1df5212fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T2JBDBDHMUKAFBPJKMUMZ2U7OB/bundle.json","state_url":"https://pith.science/pith/T2JBDBDHMUKAFBPJKMUMZ2U7OB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T2JBDBDHMUKAFBPJKMUMZ2U7OB/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":"2026-06-24T00:15:54Z","links":{"resolver":"https://pith.science/pith/T2JBDBDHMUKAFBPJKMUMZ2U7OB","bundle":"https://pith.science/pith/T2JBDBDHMUKAFBPJKMUMZ2U7OB/bundle.json","state":"https://pith.science/pith/T2JBDBDHMUKAFBPJKMUMZ2U7OB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T2JBDBDHMUKAFBPJKMUMZ2U7OB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:T2JBDBDHMUKAFBPJKMUMZ2U7OB","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":"097e4b47e2fdd5a455f45072121a523eb0d4759b2dfac838c4494ad022d2d6c0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-12-21T08:53:08Z","title_canon_sha256":"17342ddfd05df7c9422173fb1196fb473d7bc42d4ad6bb499e662746d071c0e1"},"schema_version":"1.0","source":{"id":"1212.5361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5361","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5361v1","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5361","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"pith_short_12","alias_value":"T2JBDBDHMUKA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T2JBDBDHMUKAFBPJ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T2JBDBDH","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:db8abe737538cc5c25ca8c3752a8bc508cac2e58f6e0ab93a05bdbc1df5212fe","target":"graph","created_at":"2026-05-18T03:38:02Z","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":"The slice condition and the more general weak slice conditions are geometric conditions on Euclidean space domains which have evolved over the last several years as a tool in various areas of analysis. This paper examines some of their finer distinctive properties.","authors_text":"Alexander Stanoyevitch, Andre Diatta, Stephen M. Buckley","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-12-21T08:53:08Z","title":"Distinguishing properties of weak slice conditions II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5361","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":"sha256:4eee7e123a86bcd24559c9d5705ff96bea93de94873845166609a263aec024d9","target":"record","created_at":"2026-05-18T03:38:02Z","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":"097e4b47e2fdd5a455f45072121a523eb0d4759b2dfac838c4494ad022d2d6c0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-12-21T08:53:08Z","title_canon_sha256":"17342ddfd05df7c9422173fb1196fb473d7bc42d4ad6bb499e662746d071c0e1"},"schema_version":"1.0","source":{"id":"1212.5361","kind":"arxiv","version":1}},"canonical_sha256":"9e9211846765140285e95328ccea9f707e5e0d61413b394d7d2ad3096c065e2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e9211846765140285e95328ccea9f707e5e0d61413b394d7d2ad3096c065e2c","first_computed_at":"2026-05-18T03:38:02.096493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:02.096493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tm/Pyf/ubYjXmjEfwS8WqIEvYSPhh90RXga+UZhsNMQMXEcIHGndhpkkqZIxVcBcU3C/SXqj2dzAhyh573uDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:02.097095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eee7e123a86bcd24559c9d5705ff96bea93de94873845166609a263aec024d9","sha256:db8abe737538cc5c25ca8c3752a8bc508cac2e58f6e0ab93a05bdbc1df5212fe"],"state_sha256":"4808d841bb2c77c7dc993e702d615037d48893bce3d0e1f2bd89eef030e11ecf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDBjkjAlQcNP6RK7xZgaxwpFfNZraiDYd3Y52g0WvlBw9fKFABg6w/pux7FWLERwlbKVkRH294DLdajua8rWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T00:15:54.730142Z","bundle_sha256":"b36a51bb8c29463a5cd4a15132b9a9d4f375e57690c0e7b136a7cc733e6c0d3e"}}