{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M4PCK6HCXKX4YOY7ZCZCPHEOYE","short_pith_number":"pith:M4PCK6HC","canonical_record":{"source":{"id":"1508.05112","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-20T20:24:21Z","cross_cats_sorted":[],"title_canon_sha256":"bb00ade2a56df430ab492034ab63b7ad3eefa098aaf8374015e2ddba817af333","abstract_canon_sha256":"744228a4fdf0f9f4cf69f69272586078d6f123af604c082803ecefe2ee401b69"},"schema_version":"1.0"},"canonical_sha256":"671e2578e2baafcc3b1fc8b2279c8ec1266e1ba5c7fe9a0cb2f7d553d7b1abb4","source":{"kind":"arxiv","id":"1508.05112","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05112","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05112v7","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05112","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"M4PCK6HCXKX4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M4PCK6HCXKX4YOY7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M4PCK6HC","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M4PCK6HCXKX4YOY7ZCZCPHEOYE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.05112","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-20T20:24:21Z","cross_cats_sorted":[],"title_canon_sha256":"bb00ade2a56df430ab492034ab63b7ad3eefa098aaf8374015e2ddba817af333","abstract_canon_sha256":"744228a4fdf0f9f4cf69f69272586078d6f123af604c082803ecefe2ee401b69"},"schema_version":"1.0"},"canonical_sha256":"671e2578e2baafcc3b1fc8b2279c8ec1266e1ba5c7fe9a0cb2f7d553d7b1abb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:36.858444Z","signature_b64":"dJjMo/o7hOBuvqaacPq4n4X7kDG+pDygjT+5XrOFM5xWOMnocbTZLd2gCaQ2vuqQkYXA52xOd/D7Gv91FQdoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"671e2578e2baafcc3b1fc8b2279c8ec1266e1ba5c7fe9a0cb2f7d553d7b1abb4","last_reissued_at":"2026-05-18T01:03:36.857763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:36.857763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.05112","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Yy4vhEQlVXEb1NIxmOW9udb/dZOf7MbRud8SjnH+dADtH7swgoZELSX44ZVgr5Ul/XStRbKJPrYS61KvNrHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:05:25.787417Z"},"content_sha256":"206df5bbdc426ca0c1b6a562184d7facad6834524011f99d459ec35b3ca7c4fc","schema_version":"1.0","event_id":"sha256:206df5bbdc426ca0c1b6a562184d7facad6834524011f99d459ec35b3ca7c4fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M4PCK6HCXKX4YOY7ZCZCPHEOYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Versions of Eberlein-\\v{S}mulian and Amir-Lindenstrauss theorems in the framework of conditional sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jos\\'e Miguel Zapata","submitted_at":"2015-08-20T20:24:21Z","abstract_excerpt":"Based on conditional set theory, we study conditional weak topologies, extending some well-known results to this framework and culminating with the proof of conditional versions of Eberlein-\\v{S}mulian and Amir-Lindenstrauss Theorems. In pursuing this aim, we prove conditional versions of Baire Category Theorem and Uniform Boundedness Principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05112","kind":"arxiv","version":7},"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":"2026-05-18T01:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PcK1gnzmxkbGdYqmwWCj536nFPRfh2NJFZM7FjoKp5ap2CG0EKbwxETNMUuL/kT7Wpu8a/SI7TSGSxJpX8UjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:05:25.788035Z"},"content_sha256":"9feecd7966358b8b61fe93c3640eb7aac1d079ea6a13dcca547b453695ce0956","schema_version":"1.0","event_id":"sha256:9feecd7966358b8b61fe93c3640eb7aac1d079ea6a13dcca547b453695ce0956"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M4PCK6HCXKX4YOY7ZCZCPHEOYE/bundle.json","state_url":"https://pith.science/pith/M4PCK6HCXKX4YOY7ZCZCPHEOYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M4PCK6HCXKX4YOY7ZCZCPHEOYE/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":"2026-05-27T08:05:25Z","links":{"resolver":"https://pith.science/pith/M4PCK6HCXKX4YOY7ZCZCPHEOYE","bundle":"https://pith.science/pith/M4PCK6HCXKX4YOY7ZCZCPHEOYE/bundle.json","state":"https://pith.science/pith/M4PCK6HCXKX4YOY7ZCZCPHEOYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M4PCK6HCXKX4YOY7ZCZCPHEOYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M4PCK6HCXKX4YOY7ZCZCPHEOYE","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":"744228a4fdf0f9f4cf69f69272586078d6f123af604c082803ecefe2ee401b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-20T20:24:21Z","title_canon_sha256":"bb00ade2a56df430ab492034ab63b7ad3eefa098aaf8374015e2ddba817af333"},"schema_version":"1.0","source":{"id":"1508.05112","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05112","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05112v7","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05112","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"M4PCK6HCXKX4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M4PCK6HCXKX4YOY7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M4PCK6HC","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:9feecd7966358b8b61fe93c3640eb7aac1d079ea6a13dcca547b453695ce0956","target":"graph","created_at":"2026-05-18T01:03:36Z","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":"Based on conditional set theory, we study conditional weak topologies, extending some well-known results to this framework and culminating with the proof of conditional versions of Eberlein-\\v{S}mulian and Amir-Lindenstrauss Theorems. In pursuing this aim, we prove conditional versions of Baire Category Theorem and Uniform Boundedness Principle.","authors_text":"Jos\\'e Miguel Zapata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-20T20:24:21Z","title":"Versions of Eberlein-\\v{S}mulian and Amir-Lindenstrauss theorems in the framework of conditional sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05112","kind":"arxiv","version":7},"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":"sha256:206df5bbdc426ca0c1b6a562184d7facad6834524011f99d459ec35b3ca7c4fc","target":"record","created_at":"2026-05-18T01:03:36Z","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":"744228a4fdf0f9f4cf69f69272586078d6f123af604c082803ecefe2ee401b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-20T20:24:21Z","title_canon_sha256":"bb00ade2a56df430ab492034ab63b7ad3eefa098aaf8374015e2ddba817af333"},"schema_version":"1.0","source":{"id":"1508.05112","kind":"arxiv","version":7}},"canonical_sha256":"671e2578e2baafcc3b1fc8b2279c8ec1266e1ba5c7fe9a0cb2f7d553d7b1abb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"671e2578e2baafcc3b1fc8b2279c8ec1266e1ba5c7fe9a0cb2f7d553d7b1abb4","first_computed_at":"2026-05-18T01:03:36.857763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:36.857763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dJjMo/o7hOBuvqaacPq4n4X7kDG+pDygjT+5XrOFM5xWOMnocbTZLd2gCaQ2vuqQkYXA52xOd/D7Gv91FQdoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:36.858444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05112","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:206df5bbdc426ca0c1b6a562184d7facad6834524011f99d459ec35b3ca7c4fc","sha256:9feecd7966358b8b61fe93c3640eb7aac1d079ea6a13dcca547b453695ce0956"],"state_sha256":"49cffe5efe83179468c80dec86d0075b66974f26ae80ae4ddb801cbd68548de2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PWUJ/h4X3CmGfatPtZgBnheLvWtkvodAplXepNrSMeiwh0UiiiNL1KvljOYeDCaAmyZP+SMehzUoPTcgAbDjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:05:25.791413Z","bundle_sha256":"4d83ecb504ab35813bbb0d95627bc8a55a54e467cf9e34488e94bdda7033b7f4"}}