{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UGETYKD7M45OZ4J4GW54VCEYJ3","short_pith_number":"pith:UGETYKD7","canonical_record":{"source":{"id":"1802.10439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T14:43:31Z","cross_cats_sorted":[],"title_canon_sha256":"1c455e973c16df55c8467c73dd4f39e22ad7e1075fbbf898029377139e76437f","abstract_canon_sha256":"40ed5c8e9426a8c765b9f3d8ed0fb2b835fc4d913d36d1810c44942c0ae047e0"},"schema_version":"1.0"},"canonical_sha256":"a1893c287f673aecf13c35bbca88984ed4db6f0d356f66d2ea5ea5cf89369fc4","source":{"kind":"arxiv","id":"1802.10439","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10439","created_at":"2026-05-18T00:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10439v2","created_at":"2026-05-18T00:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10439","created_at":"2026-05-18T00:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"UGETYKD7M45O","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UGETYKD7M45OZ4J4","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UGETYKD7","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UGETYKD7M45OZ4J4GW54VCEYJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1802.10439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T14:43:31Z","cross_cats_sorted":[],"title_canon_sha256":"1c455e973c16df55c8467c73dd4f39e22ad7e1075fbbf898029377139e76437f","abstract_canon_sha256":"40ed5c8e9426a8c765b9f3d8ed0fb2b835fc4d913d36d1810c44942c0ae047e0"},"schema_version":"1.0"},"canonical_sha256":"a1893c287f673aecf13c35bbca88984ed4db6f0d356f66d2ea5ea5cf89369fc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:51.636605Z","signature_b64":"CUQRGNz2Z0dHQrVNcllAT7XeFB+/es3To8lFzDVR5w2F8vCY3uf62GAiyLKnJ1z9siN7XfDsNsFZHAGWx9aVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1893c287f673aecf13c35bbca88984ed4db6f0d356f66d2ea5ea5cf89369fc4","last_reissued_at":"2026-05-18T00:20:51.636092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:51.636092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.10439","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":"2026-05-18T00:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzELUeprUoqy3mFWZS2WhW+dotU/g4P+MUoQBV/LGnJA7B5C4W6tuFKjjDRUXBhttcitG+xIHLb4y8LJLOJVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:56:03.098441Z"},"content_sha256":"40c20c3060c604d931e0f4b7c43bf2e70d685b750835d49360599acb9a35a8ad","schema_version":"1.0","event_id":"sha256:40c20c3060c604d931e0f4b7c43bf2e70d685b750835d49360599acb9a35a8ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UGETYKD7M45OZ4J4GW54VCEYJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the norm attainment set of a bounded linear operator and semi-inner-products in normed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Debmalya Sain","submitted_at":"2018-02-28T14:43:31Z","abstract_excerpt":"We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of semi-inner-products to obtain a complete characterization of the norm attainment set of a bounded linear operator between any two real normed spaces. In particular, this answers an open question raised recently in [Sain, D., \\textit{On the norm attainment set of a bounded linear operator}, J. Math. Anal. Appl., \\textbf{457} (2018), 67-76.]. Our results illustrate the ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10439","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":"2026-05-18T00:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zWECchSY5e0kkupLUUZOHTcv81q2c5kClaTLOuhBqddv+3sR9ha2QQU+GRanZmIdNuhu6L8J1sG0W4LHH+UDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:56:03.098809Z"},"content_sha256":"5538bf1da55e505b0c4583267693c6a4f8730a8d40b1b3b4032aa7fe86fb1a5b","schema_version":"1.0","event_id":"sha256:5538bf1da55e505b0c4583267693c6a4f8730a8d40b1b3b4032aa7fe86fb1a5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UGETYKD7M45OZ4J4GW54VCEYJ3/bundle.json","state_url":"https://pith.science/pith/UGETYKD7M45OZ4J4GW54VCEYJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UGETYKD7M45OZ4J4GW54VCEYJ3/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":"2026-06-12T06:56:03Z","links":{"resolver":"https://pith.science/pith/UGETYKD7M45OZ4J4GW54VCEYJ3","bundle":"https://pith.science/pith/UGETYKD7M45OZ4J4GW54VCEYJ3/bundle.json","state":"https://pith.science/pith/UGETYKD7M45OZ4J4GW54VCEYJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UGETYKD7M45OZ4J4GW54VCEYJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UGETYKD7M45OZ4J4GW54VCEYJ3","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":"40ed5c8e9426a8c765b9f3d8ed0fb2b835fc4d913d36d1810c44942c0ae047e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T14:43:31Z","title_canon_sha256":"1c455e973c16df55c8467c73dd4f39e22ad7e1075fbbf898029377139e76437f"},"schema_version":"1.0","source":{"id":"1802.10439","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10439","created_at":"2026-05-18T00:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10439v2","created_at":"2026-05-18T00:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10439","created_at":"2026-05-18T00:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"UGETYKD7M45O","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UGETYKD7M45OZ4J4","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UGETYKD7","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:5538bf1da55e505b0c4583267693c6a4f8730a8d40b1b3b4032aa7fe86fb1a5b","target":"graph","created_at":"2026-05-18T00:20:51Z","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 obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of semi-inner-products to obtain a complete characterization of the norm attainment set of a bounded linear operator between any two real normed spaces. In particular, this answers an open question raised recently in [Sain, D., \\textit{On the norm attainment set of a bounded linear operator}, J. Math. Anal. Appl., \\textbf{457} (2018), 67-76.]. Our results illustrate the ap","authors_text":"Debmalya Sain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T14:43:31Z","title":"On the norm attainment set of a bounded linear operator and semi-inner-products in normed spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10439","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":"sha256:40c20c3060c604d931e0f4b7c43bf2e70d685b750835d49360599acb9a35a8ad","target":"record","created_at":"2026-05-18T00:20:51Z","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":"40ed5c8e9426a8c765b9f3d8ed0fb2b835fc4d913d36d1810c44942c0ae047e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T14:43:31Z","title_canon_sha256":"1c455e973c16df55c8467c73dd4f39e22ad7e1075fbbf898029377139e76437f"},"schema_version":"1.0","source":{"id":"1802.10439","kind":"arxiv","version":2}},"canonical_sha256":"a1893c287f673aecf13c35bbca88984ed4db6f0d356f66d2ea5ea5cf89369fc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1893c287f673aecf13c35bbca88984ed4db6f0d356f66d2ea5ea5cf89369fc4","first_computed_at":"2026-05-18T00:20:51.636092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:51.636092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUQRGNz2Z0dHQrVNcllAT7XeFB+/es3To8lFzDVR5w2F8vCY3uf62GAiyLKnJ1z9siN7XfDsNsFZHAGWx9aVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:51.636605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.10439","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40c20c3060c604d931e0f4b7c43bf2e70d685b750835d49360599acb9a35a8ad","sha256:5538bf1da55e505b0c4583267693c6a4f8730a8d40b1b3b4032aa7fe86fb1a5b"],"state_sha256":"70811219753513fdc67ca71587e22c54c029099464247e27f69df12dfbc57f14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDE/oC7wMQn7I1oSyDpUpxCiVerByr6ovJYCUReOmyAcw/lQfa0/11BmnZY0HJlahAfsTyOnyj7ZD79fzh9ABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:56:03.101270Z","bundle_sha256":"66601847de08c98b87629deb07c7a0790e549869fcab02c358b58f6676984617"}}