{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:64GYK3QWELGVUAKHOH2LV7QAF3","short_pith_number":"pith:64GYK3QW","canonical_record":{"source":{"id":"2607.28376","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-30T15:36:05Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"74fd4ee5f3971cf06c514123687bf6c54c409771e19fdede05c2e65356254295","abstract_canon_sha256":"6ff6154e4f69716eed996ebdd04d599a2928834c8119cd573d3a84a6cbc9847b"},"schema_version":"1.0"},"canonical_sha256":"f70d856e1622cd5a014771f4bafe002ee5bc1b43487324e84fc2b970435b2b7d","source":{"kind":"arxiv","id":"2607.28376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28376","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28376v1","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28376","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"64GYK3QWELGV","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"pith_short_16","alias_value":"64GYK3QWELGVUAKH","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"pith_short_8","alias_value":"64GYK3QW","created_at":"2026-07-31T01:37:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:64GYK3QWELGVUAKHOH2LV7QAF3","target":"record","payload":{"canonical_record":{"source":{"id":"2607.28376","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-30T15:36:05Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"74fd4ee5f3971cf06c514123687bf6c54c409771e19fdede05c2e65356254295","abstract_canon_sha256":"6ff6154e4f69716eed996ebdd04d599a2928834c8119cd573d3a84a6cbc9847b"},"schema_version":"1.0"},"canonical_sha256":"f70d856e1622cd5a014771f4bafe002ee5bc1b43487324e84fc2b970435b2b7d","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f70d856e1622cd5a014771f4bafe002ee5bc1b43487324e84fc2b970435b2b7d","last_reissued_at":"2026-07-31T01:37:28.778905Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:37:28.778905Z"},"source_kind":"arxiv","source_id":"2607.28376","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":"2026-07-31T01:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1gPGOgUD7Y2Bl+EonSlNXAu/ezmTPQzj27qvB+E0MW+Mww+P93Aw1aS1rkpkjA3rd0b2EEmBdPSarmqgHEhTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:22:19.357719Z"},"content_sha256":"8b7ae02fc7066ef5b8cfb819b1cf0204220f761775d95e4385e60b65b9b330a3","schema_version":"1.0","event_id":"sha256:8b7ae02fc7066ef5b8cfb819b1cf0204220f761775d95e4385e60b65b9b330a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:64GYK3QWELGVUAKHOH2LV7QAF3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The isoperimetric inequality for the Ky Fan norm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.FA","authors_text":"Lu\\'{\\i}s Daniel Abreu","submitted_at":"2026-07-30T15:36:05Z","abstract_excerpt":"We show that, among all measurable sets $\\Omega \\subset \\mathbb{C}$ with finite area $s$, the disc of area $s$ maximizes the Ky Fan norm, which is defined as the sum of the first $N$ eigenvalues of the Toeplitz operator with symbol $\\mathbf{1}_{\\Omega }$ on the Fock space. For $N=1$ this reduces to Nicola-Tilli's celebrated Faber--Krahn inequality and for general $N$ the result was conjectured by Nicola, Riccardi and Tilli, who proved it for radial sets. The proof combines Ky Fan's maximum principle with methods from quantum information theory based on Fock rearrangements of density operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28376","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28376/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-31T01:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8STmv4TwG8vxsV5D7m2ogXWEyN3V5XIAIM6zv/opFm25IQmbNpoK3GrD4mD0/K80bi+jttewA3tVgHiOTNRFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:22:19.358662Z"},"content_sha256":"6a53f7625971044d76fedbbd06b3bf2bd826afc97ed51bdb103a4d4afd309fc2","schema_version":"1.0","event_id":"sha256:6a53f7625971044d76fedbbd06b3bf2bd826afc97ed51bdb103a4d4afd309fc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64GYK3QWELGVUAKHOH2LV7QAF3/bundle.json","state_url":"https://pith.science/pith/64GYK3QWELGVUAKHOH2LV7QAF3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64GYK3QWELGVUAKHOH2LV7QAF3/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":"2026-08-19T22:22:19Z","links":{"resolver":"https://pith.science/pith/64GYK3QWELGVUAKHOH2LV7QAF3","bundle":"https://pith.science/pith/64GYK3QWELGVUAKHOH2LV7QAF3/bundle.json","state":"https://pith.science/pith/64GYK3QWELGVUAKHOH2LV7QAF3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64GYK3QWELGVUAKHOH2LV7QAF3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:64GYK3QWELGVUAKHOH2LV7QAF3","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":"6ff6154e4f69716eed996ebdd04d599a2928834c8119cd573d3a84a6cbc9847b","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-30T15:36:05Z","title_canon_sha256":"74fd4ee5f3971cf06c514123687bf6c54c409771e19fdede05c2e65356254295"},"schema_version":"1.0","source":{"id":"2607.28376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28376","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28376v1","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28376","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"64GYK3QWELGV","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"pith_short_16","alias_value":"64GYK3QWELGVUAKH","created_at":"2026-07-31T01:37:28Z"},{"alias_kind":"pith_short_8","alias_value":"64GYK3QW","created_at":"2026-07-31T01:37:28Z"}],"graph_snapshots":[{"event_id":"sha256:6a53f7625971044d76fedbbd06b3bf2bd826afc97ed51bdb103a4d4afd309fc2","target":"graph","created_at":"2026-07-31T01:37:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.28376/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that, among all measurable sets $\\Omega \\subset \\mathbb{C}$ with finite area $s$, the disc of area $s$ maximizes the Ky Fan norm, which is defined as the sum of the first $N$ eigenvalues of the Toeplitz operator with symbol $\\mathbf{1}_{\\Omega }$ on the Fock space. For $N=1$ this reduces to Nicola-Tilli's celebrated Faber--Krahn inequality and for general $N$ the result was conjectured by Nicola, Riccardi and Tilli, who proved it for radial sets. The proof combines Ky Fan's maximum principle with methods from quantum information theory based on Fock rearrangements of density operators.","authors_text":"Lu\\'{\\i}s Daniel Abreu","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-30T15:36:05Z","title":"The isoperimetric inequality for the Ky Fan norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28376","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":"sha256:8b7ae02fc7066ef5b8cfb819b1cf0204220f761775d95e4385e60b65b9b330a3","target":"record","created_at":"2026-07-31T01:37:28Z","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":"6ff6154e4f69716eed996ebdd04d599a2928834c8119cd573d3a84a6cbc9847b","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-30T15:36:05Z","title_canon_sha256":"74fd4ee5f3971cf06c514123687bf6c54c409771e19fdede05c2e65356254295"},"schema_version":"1.0","source":{"id":"2607.28376","kind":"arxiv","version":1}},"canonical_sha256":"f70d856e1622cd5a014771f4bafe002ee5bc1b43487324e84fc2b970435b2b7d","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f70d856e1622cd5a014771f4bafe002ee5bc1b43487324e84fc2b970435b2b7d","first_computed_at":"2026-07-31T01:37:28.778905Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:37:28.778905Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.28376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b7ae02fc7066ef5b8cfb819b1cf0204220f761775d95e4385e60b65b9b330a3","sha256:6a53f7625971044d76fedbbd06b3bf2bd826afc97ed51bdb103a4d4afd309fc2"],"state_sha256":"68a047e6de47d0fb8f97beb8a876d6cc9b78ffc35b49518d72d404828257d1d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LKf/ceEUkhHNDR3ctndVxnX9mC9LFkelk+6cHXaE/XL7dqamhJoXyzEb4vPhybTSr/xtk1PkCtgH/NvxrYgLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:22:19.368410Z","bundle_sha256":"47118096dc4db27dcb026ef80896eedcad761d721f9f0bbf81143f647468a939"}}