{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:MSQLZ7RZ64UUCBCJ7T2D3O725U","short_pith_number":"pith:MSQLZ7RZ","canonical_record":{"source":{"id":"math/0501184","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2005-01-12T13:03:44Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"b0e05a97c00cf0dc21d010ec165f9ad39ab1f47d581f55be709cb1312b8c2be9","abstract_canon_sha256":"648d02eefe3c72fafe238e61215857472c211addc927a7d2e197f2d700b75c06"},"schema_version":"1.0"},"canonical_sha256":"64a0bcfe39f729410449fcf43dbbfaed0ca7c347a0c555892df0b51dd6241536","source":{"kind":"arxiv","id":"math/0501184","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501184","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501184v2","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501184","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"MSQLZ7RZ64UU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MSQLZ7RZ64UUCBCJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MSQLZ7RZ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:MSQLZ7RZ64UUCBCJ7T2D3O725U","target":"record","payload":{"canonical_record":{"source":{"id":"math/0501184","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2005-01-12T13:03:44Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"b0e05a97c00cf0dc21d010ec165f9ad39ab1f47d581f55be709cb1312b8c2be9","abstract_canon_sha256":"648d02eefe3c72fafe238e61215857472c211addc927a7d2e197f2d700b75c06"},"schema_version":"1.0"},"canonical_sha256":"64a0bcfe39f729410449fcf43dbbfaed0ca7c347a0c555892df0b51dd6241536","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:16.957418Z","signature_b64":"+tJoTKcu5cxhqThJ9FPn5E0jL+0Mikrmfz1zLT/zdq7g5vsOYZaTUmG05DBhSc4fYPpjcfxqQs28jnpoob/GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64a0bcfe39f729410449fcf43dbbfaed0ca7c347a0c555892df0b51dd6241536","last_reissued_at":"2026-05-18T00:14:16.956864Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:16.956864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0501184","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":"2026-05-18T00:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lOANvdmvuNW71H/Iz/ibBZRdHpLwa6A3IvuIoUK3JK2QKBnRpDEzaVTjQtdtMdNhM55b2A6mf6x2c6ToUSo0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:17:22.103375Z"},"content_sha256":"4c4b2443fd3f4f9df603904d1deaddcb12395f2d9bc0f09623187f0379defde6","schema_version":"1.0","event_id":"sha256:4c4b2443fd3f4f9df603904d1deaddcb12395f2d9bc0f09623187f0379defde6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:MSQLZ7RZ64UUCBCJ7T2D3O725U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex domains and K-spectral sets","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Bernard Delyon, Catalin Badea, Michel Crouzeix","submitted_at":"2005-01-12T13:03:44Z","abstract_excerpt":"Let $\\Omega$ be an open convex domain of the complex plane. We study constants K such that $\\Omega$ is K-spectral or complete K-spectral for each continuous linear Hilbert space operator with numerical range included in $\\Omega$. Several approaches are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501184","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":"2026-05-18T00:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/hPy1FR8/CSjAxJfLjpMR+7SDa+j4nvdtgxEgdu08w/gw2nSpT86YVrXIgNepEhbxpN1MS2paAJKJjp8NsHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:17:22.103720Z"},"content_sha256":"7196a70e0fd1cabba1b01a8d68ffa7a33f96db9f321c15646668ba2a77abd2b6","schema_version":"1.0","event_id":"sha256:7196a70e0fd1cabba1b01a8d68ffa7a33f96db9f321c15646668ba2a77abd2b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSQLZ7RZ64UUCBCJ7T2D3O725U/bundle.json","state_url":"https://pith.science/pith/MSQLZ7RZ64UUCBCJ7T2D3O725U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSQLZ7RZ64UUCBCJ7T2D3O725U/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":"2026-06-23T21:17:22Z","links":{"resolver":"https://pith.science/pith/MSQLZ7RZ64UUCBCJ7T2D3O725U","bundle":"https://pith.science/pith/MSQLZ7RZ64UUCBCJ7T2D3O725U/bundle.json","state":"https://pith.science/pith/MSQLZ7RZ64UUCBCJ7T2D3O725U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSQLZ7RZ64UUCBCJ7T2D3O725U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:MSQLZ7RZ64UUCBCJ7T2D3O725U","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":"648d02eefe3c72fafe238e61215857472c211addc927a7d2e197f2d700b75c06","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"math.FA","submitted_at":"2005-01-12T13:03:44Z","title_canon_sha256":"b0e05a97c00cf0dc21d010ec165f9ad39ab1f47d581f55be709cb1312b8c2be9"},"schema_version":"1.0","source":{"id":"math/0501184","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501184","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501184v2","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501184","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"MSQLZ7RZ64UU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MSQLZ7RZ64UUCBCJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MSQLZ7RZ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7196a70e0fd1cabba1b01a8d68ffa7a33f96db9f321c15646668ba2a77abd2b6","target":"graph","created_at":"2026-05-18T00:14:16Z","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":"Let $\\Omega$ be an open convex domain of the complex plane. We study constants K such that $\\Omega$ is K-spectral or complete K-spectral for each continuous linear Hilbert space operator with numerical range included in $\\Omega$. Several approaches are discussed.","authors_text":"Bernard Delyon, Catalin Badea, Michel Crouzeix","cross_cats":["math.OA"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2005-01-12T13:03:44Z","title":"Convex domains and K-spectral sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501184","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":"sha256:4c4b2443fd3f4f9df603904d1deaddcb12395f2d9bc0f09623187f0379defde6","target":"record","created_at":"2026-05-18T00:14:16Z","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":"648d02eefe3c72fafe238e61215857472c211addc927a7d2e197f2d700b75c06","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"math.FA","submitted_at":"2005-01-12T13:03:44Z","title_canon_sha256":"b0e05a97c00cf0dc21d010ec165f9ad39ab1f47d581f55be709cb1312b8c2be9"},"schema_version":"1.0","source":{"id":"math/0501184","kind":"arxiv","version":2}},"canonical_sha256":"64a0bcfe39f729410449fcf43dbbfaed0ca7c347a0c555892df0b51dd6241536","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64a0bcfe39f729410449fcf43dbbfaed0ca7c347a0c555892df0b51dd6241536","first_computed_at":"2026-05-18T00:14:16.956864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:16.956864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+tJoTKcu5cxhqThJ9FPn5E0jL+0Mikrmfz1zLT/zdq7g5vsOYZaTUmG05DBhSc4fYPpjcfxqQs28jnpoob/GAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:16.957418Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c4b2443fd3f4f9df603904d1deaddcb12395f2d9bc0f09623187f0379defde6","sha256:7196a70e0fd1cabba1b01a8d68ffa7a33f96db9f321c15646668ba2a77abd2b6"],"state_sha256":"8b923e1a0b3399c6c6df3bef2d1fb6ca518d62dc5c176ec5fec636910da46b84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjtUDaHqRwVdBQ4QqEfEDwmaXwciYRQX7LFozsgF6jYCXLxSogAIBbQl424ClFRZY6T52qpP2Ebu8rkOGkD/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:17:22.105567Z","bundle_sha256":"898125f819afb838b9a9c1fc097a9e92a2b587b07fb46c8eabc3fef9f46ee3c4"}}