{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:BG7HSKGUCKMSV5XKG3VQVWDMCA","short_pith_number":"pith:BG7HSKGU","canonical_record":{"source":{"id":"math/9709208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"e9b59b487ed1e167520f65724cb47d7897ae4ccff23a00867680bf16acf76fc2","abstract_canon_sha256":"c900a542430e1f770ba7ff0f9c57d3ef2c1e9de521e3098bdf4401d92c9d81b3"},"schema_version":"1.0"},"canonical_sha256":"09be7928d412992af6ea36eb0ad86c10399f65d113a78e83b91a9e0fd6824978","source":{"kind":"arxiv","id":"math/9709208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9709208","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9709208v1","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9709208","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"BG7HSKGUCKMS","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"BG7HSKGUCKMSV5XK","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"BG7HSKGU","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:BG7HSKGUCKMSV5XKG3VQVWDMCA","target":"record","payload":{"canonical_record":{"source":{"id":"math/9709208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"e9b59b487ed1e167520f65724cb47d7897ae4ccff23a00867680bf16acf76fc2","abstract_canon_sha256":"c900a542430e1f770ba7ff0f9c57d3ef2c1e9de521e3098bdf4401d92c9d81b3"},"schema_version":"1.0"},"canonical_sha256":"09be7928d412992af6ea36eb0ad86c10399f65d113a78e83b91a9e0fd6824978","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:34.872604Z","signature_b64":"YBo7zh0RPUdlsMLI/z/PLvcCMZWMplrFJ6BDaA8Vy7ylegIkG8FXQW7nMwFqyWCzdGX7989H/J/MXxP2YztrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09be7928d412992af6ea36eb0ad86c10399f65d113a78e83b91a9e0fd6824978","last_reissued_at":"2026-05-18T01:05:34.871819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:34.871819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9709208","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":"2026-05-18T01:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NwVQT1pNybxqIW0s1HvHt+iMAkGMTYQCdt/wzLN2iEdN0u1XdoOjXfvau40ZOM9nhyP89e+mI5f/V0wPTno7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:51:03.246947Z"},"content_sha256":"bfef9fe627176cf98f3d970d40631b353e42c2c74ce6b2c3ec0ec624f64531f8","schema_version":"1.0","event_id":"sha256:bfef9fe627176cf98f3d970d40631b353e42c2c74ce6b2c3ec0ec624f64531f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:BG7HSKGUCKMSV5XKG3VQVWDMCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral characterization of sums of commutators II","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kenneth J. Dykema, Nigel J. Kalton","submitted_at":"1997-09-08T00:00:00Z","abstract_excerpt":"For countably generated ideals, $\\Jc$, of $B(\\Hil)$, geometric stability is necessary for the canonical spectral characterization of sums of $(\\Jc,B(\\Hil))$--commutators to hold. This answers a question raised by Dykema, Figiel, Weiss and Wodzicki. There are some ideals, $\\Jc$, having quasi--nilpotent elements that are not sums of $(\\Jc,B(\\Hil))$--commutators. Also, every trace on every geometrically stable ideal is a spectral trace."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9709208","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":"2026-05-18T01:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2M+GY+Mf7PeAqyLukBMM6EwLygsweCxwcGIswZtduUdKI+B9TDk6UAElFmKuU/uij4YjTlJJ4v+3UuSB+YRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:51:03.247671Z"},"content_sha256":"e7d3bd4e4a0557511afe035cb63975a0c296898b564e5d0fba4b8987d1539910","schema_version":"1.0","event_id":"sha256:e7d3bd4e4a0557511afe035cb63975a0c296898b564e5d0fba4b8987d1539910"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BG7HSKGUCKMSV5XKG3VQVWDMCA/bundle.json","state_url":"https://pith.science/pith/BG7HSKGUCKMSV5XKG3VQVWDMCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BG7HSKGUCKMSV5XKG3VQVWDMCA/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":"2026-05-25T22:51:03Z","links":{"resolver":"https://pith.science/pith/BG7HSKGUCKMSV5XKG3VQVWDMCA","bundle":"https://pith.science/pith/BG7HSKGUCKMSV5XKG3VQVWDMCA/bundle.json","state":"https://pith.science/pith/BG7HSKGUCKMSV5XKG3VQVWDMCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BG7HSKGUCKMSV5XKG3VQVWDMCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:BG7HSKGUCKMSV5XKG3VQVWDMCA","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":"c900a542430e1f770ba7ff0f9c57d3ef2c1e9de521e3098bdf4401d92c9d81b3","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","title_canon_sha256":"e9b59b487ed1e167520f65724cb47d7897ae4ccff23a00867680bf16acf76fc2"},"schema_version":"1.0","source":{"id":"math/9709208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9709208","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9709208v1","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9709208","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"BG7HSKGUCKMS","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"BG7HSKGUCKMSV5XK","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"BG7HSKGU","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:e7d3bd4e4a0557511afe035cb63975a0c296898b564e5d0fba4b8987d1539910","target":"graph","created_at":"2026-05-18T01:05:34Z","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":"For countably generated ideals, $\\Jc$, of $B(\\Hil)$, geometric stability is necessary for the canonical spectral characterization of sums of $(\\Jc,B(\\Hil))$--commutators to hold. This answers a question raised by Dykema, Figiel, Weiss and Wodzicki. There are some ideals, $\\Jc$, having quasi--nilpotent elements that are not sums of $(\\Jc,B(\\Hil))$--commutators. Also, every trace on every geometrically stable ideal is a spectral trace.","authors_text":"Kenneth J. Dykema, Nigel J. Kalton","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","title":"Spectral characterization of sums of commutators II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9709208","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:bfef9fe627176cf98f3d970d40631b353e42c2c74ce6b2c3ec0ec624f64531f8","target":"record","created_at":"2026-05-18T01:05:34Z","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":"c900a542430e1f770ba7ff0f9c57d3ef2c1e9de521e3098bdf4401d92c9d81b3","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","title_canon_sha256":"e9b59b487ed1e167520f65724cb47d7897ae4ccff23a00867680bf16acf76fc2"},"schema_version":"1.0","source":{"id":"math/9709208","kind":"arxiv","version":1}},"canonical_sha256":"09be7928d412992af6ea36eb0ad86c10399f65d113a78e83b91a9e0fd6824978","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09be7928d412992af6ea36eb0ad86c10399f65d113a78e83b91a9e0fd6824978","first_computed_at":"2026-05-18T01:05:34.871819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:34.871819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YBo7zh0RPUdlsMLI/z/PLvcCMZWMplrFJ6BDaA8Vy7ylegIkG8FXQW7nMwFqyWCzdGX7989H/J/MXxP2YztrCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:34.872604Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9709208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfef9fe627176cf98f3d970d40631b353e42c2c74ce6b2c3ec0ec624f64531f8","sha256:e7d3bd4e4a0557511afe035cb63975a0c296898b564e5d0fba4b8987d1539910"],"state_sha256":"d01a5c0e281130158b6c32fc8590100f3ab7ac7cb7aa7830a69c83f88fcf50f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dg9X0R/3DPCGJBQBkf4rgiJmzqkzhfz+rMUV7m+TR3YW/4jUDrmzWU/HCoVNs7kyGX8GbPb0eXv+M+LgMnXhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:51:03.251626Z","bundle_sha256":"47af351b53d3c78889420f0f4f0f300ad677af15d52881aabe7ef01e038b4bc5"}}