{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XPKKAVHZYSBFMVWWMOUKIZ5NIB","short_pith_number":"pith:XPKKAVHZ","canonical_record":{"source":{"id":"1409.4558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-09-16T09:58:24Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a4d8e15a04bb4550416d8cfc9bdbd8df363cd178a43e2f597fcb0888396a40c9","abstract_canon_sha256":"eb3f59fa0c84bbaa2b667e2dbf163430fad4edc6386f345f57e370270656cca1"},"schema_version":"1.0"},"canonical_sha256":"bbd4a054f9c4825656d663a8a467ad4047eec4852197ae7db1c4b680e75ade1e","source":{"kind":"arxiv","id":"1409.4558","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4558","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4558v1","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4558","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"XPKKAVHZYSBF","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XPKKAVHZYSBFMVWW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XPKKAVHZ","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XPKKAVHZYSBFMVWWMOUKIZ5NIB","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-09-16T09:58:24Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a4d8e15a04bb4550416d8cfc9bdbd8df363cd178a43e2f597fcb0888396a40c9","abstract_canon_sha256":"eb3f59fa0c84bbaa2b667e2dbf163430fad4edc6386f345f57e370270656cca1"},"schema_version":"1.0"},"canonical_sha256":"bbd4a054f9c4825656d663a8a467ad4047eec4852197ae7db1c4b680e75ade1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:49.214440Z","signature_b64":"6JTmRVAm0AsYRsuTKe0qp8Rj5jAvTsYC77CgXMO/hgCqsOmbU6hJCREHRu4xM6VobwR/ZoGxlMVfmVpF1Q3GBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbd4a054f9c4825656d663a8a467ad4047eec4852197ae7db1c4b680e75ade1e","last_reissued_at":"2026-05-18T01:30:49.213977Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:49.213977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4558","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":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzsEXs64q+XVAA/DpN/jZzbCsWhExhIUi3PerLUFNdN4ayH7Qv7T2wgRUiaIvKkoO7B9stPBgsmB4YLXdEB8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:27:46.453511Z"},"content_sha256":"89910ff21cdedd57c676d986420141ec585aabcfcfa60afaeaade349e181b5c2","schema_version":"1.0","event_id":"sha256:89910ff21cdedd57c676d986420141ec585aabcfcfa60afaeaade349e181b5c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XPKKAVHZYSBFMVWWMOUKIZ5NIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An observation concerning boundary points of the numerical range","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Marcel Hansmann","submitted_at":"2014-09-16T09:58:24Z","abstract_excerpt":"A theorem of H\\\"ubner states that non-round boundary points of the numerical range of a linear operator, i.e. points where the boundary has infinite curvature, are contained in the spectrum of the operator. In this note, answering a question of Salinas and Velasco, we will show that H\\\"ubner's result remains true under the weaker assumption that the boundary has infinite upper curvature. Our short and simple proof relies on some classical ideas of Berberian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4558","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":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KzulsaOVDghZOw7TXXkWtqO99kESb7SGtENfW40/ij0HcmBXVg8wbK8bFtXNhhKC86/FdYADymLlThtUQalxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:27:46.453858Z"},"content_sha256":"f187ba2d5e7cf4bb776b43d5384133ff9a0e55ca1d0abcf7850c41c2ed61e300","schema_version":"1.0","event_id":"sha256:f187ba2d5e7cf4bb776b43d5384133ff9a0e55ca1d0abcf7850c41c2ed61e300"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPKKAVHZYSBFMVWWMOUKIZ5NIB/bundle.json","state_url":"https://pith.science/pith/XPKKAVHZYSBFMVWWMOUKIZ5NIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPKKAVHZYSBFMVWWMOUKIZ5NIB/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":"2026-06-02T20:27:46Z","links":{"resolver":"https://pith.science/pith/XPKKAVHZYSBFMVWWMOUKIZ5NIB","bundle":"https://pith.science/pith/XPKKAVHZYSBFMVWWMOUKIZ5NIB/bundle.json","state":"https://pith.science/pith/XPKKAVHZYSBFMVWWMOUKIZ5NIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPKKAVHZYSBFMVWWMOUKIZ5NIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XPKKAVHZYSBFMVWWMOUKIZ5NIB","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":"eb3f59fa0c84bbaa2b667e2dbf163430fad4edc6386f345f57e370270656cca1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-09-16T09:58:24Z","title_canon_sha256":"a4d8e15a04bb4550416d8cfc9bdbd8df363cd178a43e2f597fcb0888396a40c9"},"schema_version":"1.0","source":{"id":"1409.4558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4558","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4558v1","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4558","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"XPKKAVHZYSBF","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XPKKAVHZYSBFMVWW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XPKKAVHZ","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:f187ba2d5e7cf4bb776b43d5384133ff9a0e55ca1d0abcf7850c41c2ed61e300","target":"graph","created_at":"2026-05-18T01:30:49Z","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":"A theorem of H\\\"ubner states that non-round boundary points of the numerical range of a linear operator, i.e. points where the boundary has infinite curvature, are contained in the spectrum of the operator. In this note, answering a question of Salinas and Velasco, we will show that H\\\"ubner's result remains true under the weaker assumption that the boundary has infinite upper curvature. Our short and simple proof relies on some classical ideas of Berberian.","authors_text":"Marcel Hansmann","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-09-16T09:58:24Z","title":"An observation concerning boundary points of the numerical range"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4558","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":"sha256:89910ff21cdedd57c676d986420141ec585aabcfcfa60afaeaade349e181b5c2","target":"record","created_at":"2026-05-18T01:30:49Z","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":"eb3f59fa0c84bbaa2b667e2dbf163430fad4edc6386f345f57e370270656cca1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-09-16T09:58:24Z","title_canon_sha256":"a4d8e15a04bb4550416d8cfc9bdbd8df363cd178a43e2f597fcb0888396a40c9"},"schema_version":"1.0","source":{"id":"1409.4558","kind":"arxiv","version":1}},"canonical_sha256":"bbd4a054f9c4825656d663a8a467ad4047eec4852197ae7db1c4b680e75ade1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbd4a054f9c4825656d663a8a467ad4047eec4852197ae7db1c4b680e75ade1e","first_computed_at":"2026-05-18T01:30:49.213977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:49.213977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6JTmRVAm0AsYRsuTKe0qp8Rj5jAvTsYC77CgXMO/hgCqsOmbU6hJCREHRu4xM6VobwR/ZoGxlMVfmVpF1Q3GBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:49.214440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89910ff21cdedd57c676d986420141ec585aabcfcfa60afaeaade349e181b5c2","sha256:f187ba2d5e7cf4bb776b43d5384133ff9a0e55ca1d0abcf7850c41c2ed61e300"],"state_sha256":"7a9419352a7a2560fe1079bbbdf8cd07091e91682ce66135cf44fc59310a8bfd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5SIFWO7M5kWPt8G3OVoIPIon65xbwcqXfYAdYXQEDC3jjrLS8fyb6IXwwU86p4f+3uRo7HEiws4VYd9KGYBsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:27:46.455826Z","bundle_sha256":"7061fa726291b06083edb5ffc34f045a38bf9ce847139d43aead61df0952ad24"}}