{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:PCAF2YTKWMTJAD5SFWLMMWJTO4","short_pith_number":"pith:PCAF2YTK","canonical_record":{"source":{"id":"math/0407222","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2004-07-13T17:34:43Z","cross_cats_sorted":[],"title_canon_sha256":"475360b15de7c38aadbd908ff0ad02bb5d0b3c3a968895d9598579f8b90f5c8b","abstract_canon_sha256":"7deb9faf2b30ba23a60dcf48e7a4529bcd574fbd73f1c0d79c0f6aba48a2aaad"},"schema_version":"1.0"},"canonical_sha256":"78805d626ab326900fb22d96c65933771ac38a514c44641dca3192d03e826d29","source":{"kind":"arxiv","id":"math/0407222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407222","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407222v1","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407222","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"PCAF2YTKWMTJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"PCAF2YTKWMTJAD5S","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"PCAF2YTK","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:PCAF2YTKWMTJAD5SFWLMMWJTO4","target":"record","payload":{"canonical_record":{"source":{"id":"math/0407222","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2004-07-13T17:34:43Z","cross_cats_sorted":[],"title_canon_sha256":"475360b15de7c38aadbd908ff0ad02bb5d0b3c3a968895d9598579f8b90f5c8b","abstract_canon_sha256":"7deb9faf2b30ba23a60dcf48e7a4529bcd574fbd73f1c0d79c0f6aba48a2aaad"},"schema_version":"1.0"},"canonical_sha256":"78805d626ab326900fb22d96c65933771ac38a514c44641dca3192d03e826d29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:34.328643Z","signature_b64":"C0jE2QdQuzydq7QriQJYLy2LKq1dTNE6e+LwU97itpl4xzK7ejS0LDrRM7ZrNPOQXDY49NTbA4ZVnj9neDGqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78805d626ab326900fb22d96c65933771ac38a514c44641dca3192d03e826d29","last_reissued_at":"2026-05-18T03:42:34.327913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:34.327913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0407222","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":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f4Z/Rx+jvEkKu41IrxLA5iTqpWsAE1eMzOglXwlPNoXjwbPYoF0DgdTwDX3TXAWMUtNrXdGq2j0Z4Da+c8ZGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:41:30.151965Z"},"content_sha256":"4eeb92df3f3f9727901cec22e94295cb810a4e503055a49c94edbb71ccf69bfc","schema_version":"1.0","event_id":"sha256:4eeb92df3f3f9727901cec22e94295cb810a4e503055a49c94edbb71ccf69bfc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:PCAF2YTKWMTJAD5SFWLMMWJTO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-Eberlein spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"A. Leiderman, W. Kubi\\'s","submitted_at":"2004-07-13T17:34:43Z","abstract_excerpt":"We investigate the class of compact spaces which are embeddable into a power of the real line $R^\\kappa$ in such a way that c_0(\\kappa) is dense in the image. We show that this is a proper subclass of the class of Valdivia, even when restricted to Corson compacta. We prove a preservation result concerning inverse sequences with semi-open retractions. As a corollary we obtain that retracts of Cantor or Tikhonov cubes belong to the above class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407222","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":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYz0+7O2ixv0ZGuZKnH8r1RYNpXHKgtNmURu2Mue0j/u8xnxgjLUtSb0/d3yyHykcBabcKuI9jTxIoL/KihzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:41:30.152307Z"},"content_sha256":"77be2de88342378693f0276a9938270a378cbe31e10fc4da0450c372016ba722","schema_version":"1.0","event_id":"sha256:77be2de88342378693f0276a9938270a378cbe31e10fc4da0450c372016ba722"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCAF2YTKWMTJAD5SFWLMMWJTO4/bundle.json","state_url":"https://pith.science/pith/PCAF2YTKWMTJAD5SFWLMMWJTO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCAF2YTKWMTJAD5SFWLMMWJTO4/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":"2026-06-28T16:41:30Z","links":{"resolver":"https://pith.science/pith/PCAF2YTKWMTJAD5SFWLMMWJTO4","bundle":"https://pith.science/pith/PCAF2YTKWMTJAD5SFWLMMWJTO4/bundle.json","state":"https://pith.science/pith/PCAF2YTKWMTJAD5SFWLMMWJTO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCAF2YTKWMTJAD5SFWLMMWJTO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:PCAF2YTKWMTJAD5SFWLMMWJTO4","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":"7deb9faf2b30ba23a60dcf48e7a4529bcd574fbd73f1c0d79c0f6aba48a2aaad","cross_cats_sorted":[],"license":"","primary_cat":"math.GN","submitted_at":"2004-07-13T17:34:43Z","title_canon_sha256":"475360b15de7c38aadbd908ff0ad02bb5d0b3c3a968895d9598579f8b90f5c8b"},"schema_version":"1.0","source":{"id":"math/0407222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407222","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407222v1","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407222","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"PCAF2YTKWMTJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"PCAF2YTKWMTJAD5S","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"PCAF2YTK","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:77be2de88342378693f0276a9938270a378cbe31e10fc4da0450c372016ba722","target":"graph","created_at":"2026-05-18T03:42:34Z","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 investigate the class of compact spaces which are embeddable into a power of the real line $R^\\kappa$ in such a way that c_0(\\kappa) is dense in the image. We show that this is a proper subclass of the class of Valdivia, even when restricted to Corson compacta. We prove a preservation result concerning inverse sequences with semi-open retractions. As a corollary we obtain that retracts of Cantor or Tikhonov cubes belong to the above class.","authors_text":"A. Leiderman, W. Kubi\\'s","cross_cats":[],"headline":"","license":"","primary_cat":"math.GN","submitted_at":"2004-07-13T17:34:43Z","title":"Semi-Eberlein spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407222","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":"sha256:4eeb92df3f3f9727901cec22e94295cb810a4e503055a49c94edbb71ccf69bfc","target":"record","created_at":"2026-05-18T03:42:34Z","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":"7deb9faf2b30ba23a60dcf48e7a4529bcd574fbd73f1c0d79c0f6aba48a2aaad","cross_cats_sorted":[],"license":"","primary_cat":"math.GN","submitted_at":"2004-07-13T17:34:43Z","title_canon_sha256":"475360b15de7c38aadbd908ff0ad02bb5d0b3c3a968895d9598579f8b90f5c8b"},"schema_version":"1.0","source":{"id":"math/0407222","kind":"arxiv","version":1}},"canonical_sha256":"78805d626ab326900fb22d96c65933771ac38a514c44641dca3192d03e826d29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78805d626ab326900fb22d96c65933771ac38a514c44641dca3192d03e826d29","first_computed_at":"2026-05-18T03:42:34.327913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:34.327913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C0jE2QdQuzydq7QriQJYLy2LKq1dTNE6e+LwU97itpl4xzK7ejS0LDrRM7ZrNPOQXDY49NTbA4ZVnj9neDGqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:34.328643Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0407222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eeb92df3f3f9727901cec22e94295cb810a4e503055a49c94edbb71ccf69bfc","sha256:77be2de88342378693f0276a9938270a378cbe31e10fc4da0450c372016ba722"],"state_sha256":"8944121277e4a83dba3ff63b3ea94dc29f129d5e3404ab0446d9dbc60c44e636"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMdZSynPufCjGf8HwpxzsEdSGezfRE5esydfIiOcXRe03/Jp4WKlcqsZZ6W0gnIYTgLRT8Bwra4MtSwnLktMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T16:41:30.154266Z","bundle_sha256":"d5f44bc81e44aede27a98a3d82b3245e0e0179b68bccf0ed5aeebb640eb8c7c4"}}