{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z3K7SXA5INZYNSMTXJMK2SRU2L","short_pith_number":"pith:Z3K7SXA5","canonical_record":{"source":{"id":"1404.1074","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T00:56:13Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"0e99cdc95f93a5abde4d98bea79d4494546f724d92e5228d37c61def76b4cba8","abstract_canon_sha256":"028ddb315b5b29827e7f1137fb495b39852cb416b42814da5dc033258953562f"},"schema_version":"1.0"},"canonical_sha256":"ced5f95c1d437386c993ba58ad4a34d2fe65d4a45d6e4b0746eb0369699e3491","source":{"kind":"arxiv","id":"1404.1074","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1074","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1074v3","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1074","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"Z3K7SXA5INZY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3K7SXA5INZYNSMT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3K7SXA5","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z3K7SXA5INZYNSMTXJMK2SRU2L","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1074","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T00:56:13Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"0e99cdc95f93a5abde4d98bea79d4494546f724d92e5228d37c61def76b4cba8","abstract_canon_sha256":"028ddb315b5b29827e7f1137fb495b39852cb416b42814da5dc033258953562f"},"schema_version":"1.0"},"canonical_sha256":"ced5f95c1d437386c993ba58ad4a34d2fe65d4a45d6e4b0746eb0369699e3491","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:00.410913Z","signature_b64":"iK9ZFbInEQv1JOO1R8h+ZeCX1bC7bdlFvZnZbW8ck3vNvhEsIZ70QJ57x++p27R1rxNDfIa32WYO7p5weKmCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ced5f95c1d437386c993ba58ad4a34d2fe65d4a45d6e4b0746eb0369699e3491","last_reissued_at":"2026-05-18T02:44:00.410339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:00.410339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1074","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8hyEHg0NiHqaHfHcIujXoB4VNf5EHtd2UnhcEm8c7oTu+SOztXsq6MR44Tw22DrXW6pa8+QwqajXa3/VIL7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:59:59.870121Z"},"content_sha256":"d1186475c56e88986a28ce987159a83d77ab1a5c096d5493bbe31761c591bcf7","schema_version":"1.0","event_id":"sha256:d1186475c56e88986a28ce987159a83d77ab1a5c096d5493bbe31761c591bcf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z3K7SXA5INZYNSMTXJMK2SRU2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Jost-Pais-type reduction of (modified) Fredholm determinants for semi-separable operators in infinite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Fritz Gesztesy, Roger Nichols","submitted_at":"2014-04-03T00:56:13Z","abstract_excerpt":"We study the analog of semi-separable integral kernels in $\\mathcal{H}$ of the type $$ K(x,x')=\\begin{cases} F_1(x)G_1(x'), & a<x'< x< b, \\\\ F_2(x)G_2(x'), & a<x<x'<b, \\end{cases} $$ where $-\\infty\\leq a<b\\leq \\infty$, and for a.e.\\ $x \\in (a,b)$, $F_j (x) \\in \\mathcal{B}_2(\\mathcal{H}_j,\\mathcal{H})$ and $G_j(x) \\in \\mathcal{B}_2(\\mathcal{H},\\mathcal{H}_j)$ such that $F_j(\\cdot)$ and $G_j(\\cdot)$ are uniformly measurable, and $$ \\|F_j(\\cdot)\\|_{\\mathcal{B}_2(\\mathcal{H}_j,\\mathcal{H})} \\in L^2((a,b)), \\; \\|G_j (\\cdot)\\|_{\\mathcal{B}_2(\\mathcal{H},\\mathcal{H}_j)} \\in L^2((a,b)), \\quad j=1,2, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1074","kind":"arxiv","version":3},"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":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dSoylDtDpSuSTK9bDwhEs3SJv7u2YUr4JISS/QAEHuJFaPAYOnk/luaEK8i8BxUS+0/U6sfjFFKXrgjFbcyrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:59:59.870492Z"},"content_sha256":"f3e87d8c9491203c339d4b4a597cc7fde0a03c3d32e75fa48b4571ac0f2ea8a4","schema_version":"1.0","event_id":"sha256:f3e87d8c9491203c339d4b4a597cc7fde0a03c3d32e75fa48b4571ac0f2ea8a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3K7SXA5INZYNSMTXJMK2SRU2L/bundle.json","state_url":"https://pith.science/pith/Z3K7SXA5INZYNSMTXJMK2SRU2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3K7SXA5INZYNSMTXJMK2SRU2L/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":"2026-06-03T02:59:59Z","links":{"resolver":"https://pith.science/pith/Z3K7SXA5INZYNSMTXJMK2SRU2L","bundle":"https://pith.science/pith/Z3K7SXA5INZYNSMTXJMK2SRU2L/bundle.json","state":"https://pith.science/pith/Z3K7SXA5INZYNSMTXJMK2SRU2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3K7SXA5INZYNSMTXJMK2SRU2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z3K7SXA5INZYNSMTXJMK2SRU2L","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":"028ddb315b5b29827e7f1137fb495b39852cb416b42814da5dc033258953562f","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T00:56:13Z","title_canon_sha256":"0e99cdc95f93a5abde4d98bea79d4494546f724d92e5228d37c61def76b4cba8"},"schema_version":"1.0","source":{"id":"1404.1074","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1074","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1074v3","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1074","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"Z3K7SXA5INZY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3K7SXA5INZYNSMT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3K7SXA5","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:f3e87d8c9491203c339d4b4a597cc7fde0a03c3d32e75fa48b4571ac0f2ea8a4","target":"graph","created_at":"2026-05-18T02:44:00Z","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":"We study the analog of semi-separable integral kernels in $\\mathcal{H}$ of the type $$ K(x,x')=\\begin{cases} F_1(x)G_1(x'), & a<x'< x< b, \\\\ F_2(x)G_2(x'), & a<x<x'<b, \\end{cases} $$ where $-\\infty\\leq a<b\\leq \\infty$, and for a.e.\\ $x \\in (a,b)$, $F_j (x) \\in \\mathcal{B}_2(\\mathcal{H}_j,\\mathcal{H})$ and $G_j(x) \\in \\mathcal{B}_2(\\mathcal{H},\\mathcal{H}_j)$ such that $F_j(\\cdot)$ and $G_j(\\cdot)$ are uniformly measurable, and $$ \\|F_j(\\cdot)\\|_{\\mathcal{B}_2(\\mathcal{H}_j,\\mathcal{H})} \\in L^2((a,b)), \\; \\|G_j (\\cdot)\\|_{\\mathcal{B}_2(\\mathcal{H},\\mathcal{H}_j)} \\in L^2((a,b)), \\quad j=1,2, $","authors_text":"Fritz Gesztesy, Roger Nichols","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T00:56:13Z","title":"A Jost-Pais-type reduction of (modified) Fredholm determinants for semi-separable operators in infinite dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1074","kind":"arxiv","version":3},"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:d1186475c56e88986a28ce987159a83d77ab1a5c096d5493bbe31761c591bcf7","target":"record","created_at":"2026-05-18T02:44:00Z","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":"028ddb315b5b29827e7f1137fb495b39852cb416b42814da5dc033258953562f","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T00:56:13Z","title_canon_sha256":"0e99cdc95f93a5abde4d98bea79d4494546f724d92e5228d37c61def76b4cba8"},"schema_version":"1.0","source":{"id":"1404.1074","kind":"arxiv","version":3}},"canonical_sha256":"ced5f95c1d437386c993ba58ad4a34d2fe65d4a45d6e4b0746eb0369699e3491","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ced5f95c1d437386c993ba58ad4a34d2fe65d4a45d6e4b0746eb0369699e3491","first_computed_at":"2026-05-18T02:44:00.410339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:00.410339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iK9ZFbInEQv1JOO1R8h+ZeCX1bC7bdlFvZnZbW8ck3vNvhEsIZ70QJ57x++p27R1rxNDfIa32WYO7p5weKmCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:00.410913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1074","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1186475c56e88986a28ce987159a83d77ab1a5c096d5493bbe31761c591bcf7","sha256:f3e87d8c9491203c339d4b4a597cc7fde0a03c3d32e75fa48b4571ac0f2ea8a4"],"state_sha256":"a14e74ac8f24cc5b7f9c94f4f8e304417a5a220d0b68eafa17c7ab3042df230d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/g+NEKEjY3zogdFrYF8SA1+e6dUB+12Hxp5D/pjENOR0DvK4Xw1JAx2KsArrnkYRiuie8L2z86xvXHcRQEJJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:59:59.872566Z","bundle_sha256":"7ef7766034879e8d424b72974f4d72047cd3bb020d3b5dae42a84e9808323e73"}}