{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:DYYDGZUBXKUUCTSK343KGKTS55","short_pith_number":"pith:DYYDGZUB","canonical_record":{"source":{"id":"math/9412219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-12-22T21:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"ee947ffc27d271164ac2ad106b62bf225f73f5d9fce51af49ef1cb8dfe73453c","abstract_canon_sha256":"225db0c6fff916b16cd1aa3443a4d660bfe2ff91024174f8f76af8327d3b1b63"},"schema_version":"1.0"},"canonical_sha256":"1e30336681baa9414e4adf36a32a72ef7ca97860870b041b0db925a0f0cfc217","source":{"kind":"arxiv","id":"math/9412219","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9412219","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9412219v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9412219","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"DYYDGZUBXKUU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"DYYDGZUBXKUUCTSK","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"DYYDGZUB","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:DYYDGZUBXKUUCTSK343KGKTS55","target":"record","payload":{"canonical_record":{"source":{"id":"math/9412219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-12-22T21:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"ee947ffc27d271164ac2ad106b62bf225f73f5d9fce51af49ef1cb8dfe73453c","abstract_canon_sha256":"225db0c6fff916b16cd1aa3443a4d660bfe2ff91024174f8f76af8327d3b1b63"},"schema_version":"1.0"},"canonical_sha256":"1e30336681baa9414e4adf36a32a72ef7ca97860870b041b0db925a0f0cfc217","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:50.748709Z","signature_b64":"ilMPwRyZarJg00L8XVWJQMnkhJVFmGTzr26XH+5wNvByg+Jpbbkxv4wDfN7kPvWrMLnMuy5E+r2frrcqI89GCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e30336681baa9414e4adf36a32a72ef7ca97860870b041b0db925a0f0cfc217","last_reissued_at":"2026-05-18T01:05:50.748161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:50.748161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9412219","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":"2026-05-18T01:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aCxVHeV/CVZdPsozn4vpjKDrzjig88YDNwCrs9Pylw1VGYVtIrUb/cUIkk7nwBVeEepcmkn4CTrt/mARlhcOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:22:12.602247Z"},"content_sha256":"85b9fb8f91bb5ba5d89c7ec0bf6d6ecc05fa2a3b92b46725bdaa2537f4db9905","schema_version":"1.0","event_id":"sha256:85b9fb8f91bb5ba5d89c7ec0bf6d6ecc05fa2a3b92b46725bdaa2537f4db9905"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:DYYDGZUBXKUUCTSK343KGKTS55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Mazur Intersection Property and Farthest Points","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pradipta Bandyopadhyay","submitted_at":"1994-12-22T21:39:41Z","abstract_excerpt":"K.\\ S.\\ Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points.\n  In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9412219","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":"2026-05-18T01:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wmTH4XmB45SCGU0Kq6Vp89wsfV2NIJQHPZu3xNXqux8BGClwNETFE7HSUNehi690ImJxJ+s4bQV+p6JlcBoVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:22:12.602599Z"},"content_sha256":"3f092a099b3846d35a216d98ab4139594e33ad205bc7613e9f8515ffecefd10a","schema_version":"1.0","event_id":"sha256:3f092a099b3846d35a216d98ab4139594e33ad205bc7613e9f8515ffecefd10a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYYDGZUBXKUUCTSK343KGKTS55/bundle.json","state_url":"https://pith.science/pith/DYYDGZUBXKUUCTSK343KGKTS55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYYDGZUBXKUUCTSK343KGKTS55/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":"2026-06-12T05:22:12Z","links":{"resolver":"https://pith.science/pith/DYYDGZUBXKUUCTSK343KGKTS55","bundle":"https://pith.science/pith/DYYDGZUBXKUUCTSK343KGKTS55/bundle.json","state":"https://pith.science/pith/DYYDGZUBXKUUCTSK343KGKTS55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYYDGZUBXKUUCTSK343KGKTS55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:DYYDGZUBXKUUCTSK343KGKTS55","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":"225db0c6fff916b16cd1aa3443a4d660bfe2ff91024174f8f76af8327d3b1b63","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1994-12-22T21:39:41Z","title_canon_sha256":"ee947ffc27d271164ac2ad106b62bf225f73f5d9fce51af49ef1cb8dfe73453c"},"schema_version":"1.0","source":{"id":"math/9412219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9412219","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9412219v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9412219","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"DYYDGZUBXKUU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"DYYDGZUBXKUUCTSK","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"DYYDGZUB","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:3f092a099b3846d35a216d98ab4139594e33ad205bc7613e9f8515ffecefd10a","target":"graph","created_at":"2026-05-18T01:05:50Z","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":"K.\\ S.\\ Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points.\n  In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.","authors_text":"Pradipta Bandyopadhyay","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1994-12-22T21:39:41Z","title":"The Mazur Intersection Property and Farthest Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9412219","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":"sha256:85b9fb8f91bb5ba5d89c7ec0bf6d6ecc05fa2a3b92b46725bdaa2537f4db9905","target":"record","created_at":"2026-05-18T01:05:50Z","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":"225db0c6fff916b16cd1aa3443a4d660bfe2ff91024174f8f76af8327d3b1b63","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1994-12-22T21:39:41Z","title_canon_sha256":"ee947ffc27d271164ac2ad106b62bf225f73f5d9fce51af49ef1cb8dfe73453c"},"schema_version":"1.0","source":{"id":"math/9412219","kind":"arxiv","version":1}},"canonical_sha256":"1e30336681baa9414e4adf36a32a72ef7ca97860870b041b0db925a0f0cfc217","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e30336681baa9414e4adf36a32a72ef7ca97860870b041b0db925a0f0cfc217","first_computed_at":"2026-05-18T01:05:50.748161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.748161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ilMPwRyZarJg00L8XVWJQMnkhJVFmGTzr26XH+5wNvByg+Jpbbkxv4wDfN7kPvWrMLnMuy5E+r2frrcqI89GCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.748709Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9412219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85b9fb8f91bb5ba5d89c7ec0bf6d6ecc05fa2a3b92b46725bdaa2537f4db9905","sha256:3f092a099b3846d35a216d98ab4139594e33ad205bc7613e9f8515ffecefd10a"],"state_sha256":"6906433a60b2532c5de1600478ab9271fff78f1bef2371985012780ad3245382"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tE12bGeP24Ya69gcV5LAgu1syZGd7Yv/vQLQi0In72JjZ16g/lGxtiknd8hOolXqRfWfwwmDp/LUigaKB0UYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:22:12.604467Z","bundle_sha256":"089c1415beb90f05b5ce6e57d9e85b78094748a5147798c2fdc14fa97ee34d9f"}}