{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:XOI36GKWLAPFJATI5RNJZMELIG","short_pith_number":"pith:XOI36GKW","canonical_record":{"source":{"id":"0911.4438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-23T16:22:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c7f4efda2e22a4a0671d04789eeed5028d03baf0b3d0a92a965976084f5ee404","abstract_canon_sha256":"4d21a9d4429c1e3c61bdd0ccefa4f46e7f0e540b6d12de7389e0cde2ad24f8b0"},"schema_version":"1.0"},"canonical_sha256":"bb91bf1956581e548268ec5a9cb08b41978618cb4bef4c17fab4383fda66dedc","source":{"kind":"arxiv","id":"0911.4438","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4438","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4438v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4438","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"XOI36GKWLAPF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XOI36GKWLAPFJATI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XOI36GKW","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:XOI36GKWLAPFJATI5RNJZMELIG","target":"record","payload":{"canonical_record":{"source":{"id":"0911.4438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-23T16:22:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c7f4efda2e22a4a0671d04789eeed5028d03baf0b3d0a92a965976084f5ee404","abstract_canon_sha256":"4d21a9d4429c1e3c61bdd0ccefa4f46e7f0e540b6d12de7389e0cde2ad24f8b0"},"schema_version":"1.0"},"canonical_sha256":"bb91bf1956581e548268ec5a9cb08b41978618cb4bef4c17fab4383fda66dedc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:07.190708Z","signature_b64":"EFncwzjPJtOycYszl0GM+WHWezMgXgbFpiX/gXzriinqMfo2QrpG/Foh6PhmuDj4ItwdMva9gOdpGZTSV+OBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb91bf1956581e548268ec5a9cb08b41978618cb4bef4c17fab4383fda66dedc","last_reissued_at":"2026-05-18T03:14:07.190221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:07.190221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.4438","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":"2026-05-18T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mis/X3JClPmOIa+Y1gjd0cJ938cOuIsNdTL2iB/rUYnYRz9qu5INTEauPWuqx4Rl9DspkP1TlEuqwudgLTdICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:38:46.962840Z"},"content_sha256":"5a1a053f68aeceeb14a093faf8b000952869b939a99e68e9214c58da9a43a696","schema_version":"1.0","event_id":"sha256:5a1a053f68aeceeb14a093faf8b000952869b939a99e68e9214c58da9a43a696"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:XOI36GKWLAPFJATI5RNJZMELIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundedness properties of fermionic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Peter Otte","submitted_at":"2009-11-23T16:22:33Z","abstract_excerpt":"The fermionic second quantization operator $d\\Gamma(B)$ is shown to be bounded by a power $N^{s/2}$ of the number operator $N$ given that the operator $B$ belongs to the $r$-th von Neumann-Schatten class, $s=2(r-1)/r$. Conversely, number operator estimates for $d\\Gamma(B)$ imply von Neumann-Schatten conditions on $B$. Quadratic creation and annihilation operators are treated as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4438","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":"2026-05-18T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHx3MaRyn/b7w6BOyetbNyzHuVo6/hn7ai6vVF8rE/ZNAW+ChGGzWIShi5iwiuNbujdaI+dBPlvKhnEAFe0wAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:38:46.963173Z"},"content_sha256":"08273d1d2d6a9c98991c7a8ffb63073e86bdf87c39d821c5267bc07f574cbfa1","schema_version":"1.0","event_id":"sha256:08273d1d2d6a9c98991c7a8ffb63073e86bdf87c39d821c5267bc07f574cbfa1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XOI36GKWLAPFJATI5RNJZMELIG/bundle.json","state_url":"https://pith.science/pith/XOI36GKWLAPFJATI5RNJZMELIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XOI36GKWLAPFJATI5RNJZMELIG/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":"2026-06-10T20:38:46Z","links":{"resolver":"https://pith.science/pith/XOI36GKWLAPFJATI5RNJZMELIG","bundle":"https://pith.science/pith/XOI36GKWLAPFJATI5RNJZMELIG/bundle.json","state":"https://pith.science/pith/XOI36GKWLAPFJATI5RNJZMELIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XOI36GKWLAPFJATI5RNJZMELIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XOI36GKWLAPFJATI5RNJZMELIG","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":"4d21a9d4429c1e3c61bdd0ccefa4f46e7f0e540b6d12de7389e0cde2ad24f8b0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-23T16:22:33Z","title_canon_sha256":"c7f4efda2e22a4a0671d04789eeed5028d03baf0b3d0a92a965976084f5ee404"},"schema_version":"1.0","source":{"id":"0911.4438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4438","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4438v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4438","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"XOI36GKWLAPF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XOI36GKWLAPFJATI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XOI36GKW","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:08273d1d2d6a9c98991c7a8ffb63073e86bdf87c39d821c5267bc07f574cbfa1","target":"graph","created_at":"2026-05-18T03:14:07Z","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":"The fermionic second quantization operator $d\\Gamma(B)$ is shown to be bounded by a power $N^{s/2}$ of the number operator $N$ given that the operator $B$ belongs to the $r$-th von Neumann-Schatten class, $s=2(r-1)/r$. Conversely, number operator estimates for $d\\Gamma(B)$ imply von Neumann-Schatten conditions on $B$. Quadratic creation and annihilation operators are treated as well.","authors_text":"Peter Otte","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-23T16:22:33Z","title":"Boundedness properties of fermionic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4438","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":"sha256:5a1a053f68aeceeb14a093faf8b000952869b939a99e68e9214c58da9a43a696","target":"record","created_at":"2026-05-18T03:14:07Z","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":"4d21a9d4429c1e3c61bdd0ccefa4f46e7f0e540b6d12de7389e0cde2ad24f8b0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-23T16:22:33Z","title_canon_sha256":"c7f4efda2e22a4a0671d04789eeed5028d03baf0b3d0a92a965976084f5ee404"},"schema_version":"1.0","source":{"id":"0911.4438","kind":"arxiv","version":1}},"canonical_sha256":"bb91bf1956581e548268ec5a9cb08b41978618cb4bef4c17fab4383fda66dedc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb91bf1956581e548268ec5a9cb08b41978618cb4bef4c17fab4383fda66dedc","first_computed_at":"2026-05-18T03:14:07.190221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:07.190221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EFncwzjPJtOycYszl0GM+WHWezMgXgbFpiX/gXzriinqMfo2QrpG/Foh6PhmuDj4ItwdMva9gOdpGZTSV+OBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:07.190708Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a1a053f68aeceeb14a093faf8b000952869b939a99e68e9214c58da9a43a696","sha256:08273d1d2d6a9c98991c7a8ffb63073e86bdf87c39d821c5267bc07f574cbfa1"],"state_sha256":"a0ebc6ca0d54fd2a720f97b8d3bc3a2949e8bf51fd982dff778203fb6b3388a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGFOA/CJyWFCaHXIZJiMhaaeLg4nYENl7584sm4Ag1EmoYz6TbjfiOff7i3gltgShmU3GwLpq+W8zB6DgJ1IAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T20:38:46.965040Z","bundle_sha256":"95d168034a5d3ebc1095789da58b3dc9f239ef563e9c58dff0342d9de2315f8f"}}