{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:V3ZBT35PVIXLOB4LHRX6TO2YNY","short_pith_number":"pith:V3ZBT35P","canonical_record":{"source":{"id":"1410.7224","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T10:54:47Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"c19409af103dc32866aed01787ca2572a5cba022e0df0fbeb00294020b886faa","abstract_canon_sha256":"e70c623c9e6521802b0a6690d07bd0f83a8bf1626220ac3c56ae370e8aaf91f4"},"schema_version":"1.0"},"canonical_sha256":"aef219efafaa2eb7078b3c6fe9bb586e2ce533e5949fbaf4be54a177d96e254a","source":{"kind":"arxiv","id":"1410.7224","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7224","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7224v2","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7224","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"V3ZBT35PVIXL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V3ZBT35PVIXLOB4L","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V3ZBT35P","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:V3ZBT35PVIXLOB4LHRX6TO2YNY","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7224","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T10:54:47Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"c19409af103dc32866aed01787ca2572a5cba022e0df0fbeb00294020b886faa","abstract_canon_sha256":"e70c623c9e6521802b0a6690d07bd0f83a8bf1626220ac3c56ae370e8aaf91f4"},"schema_version":"1.0"},"canonical_sha256":"aef219efafaa2eb7078b3c6fe9bb586e2ce533e5949fbaf4be54a177d96e254a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:14.237396Z","signature_b64":"QYNl6J4jRYDnESySfEP+KGR4ojMseGp4KPEaE8F9QB5+AW74vU1ajJ/9GpH7Ulz1KzcpoyRPIjJDTK/jByjOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aef219efafaa2eb7078b3c6fe9bb586e2ce533e5949fbaf4be54a177d96e254a","last_reissued_at":"2026-05-18T01:19:14.236506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:14.236506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7224","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":"2026-05-18T01:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xwYqbl8UIjrsFVI5jxQyCiJpAkG4+Sn3bPwi0AUbBJX5NeYsLTwF1E67ntmWYm/8w/n6UjVWc8xcmBJu1f5ODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:51:46.285364Z"},"content_sha256":"9e8ff0959850462e5517763757e9f838888f7c04204abc93250717afdc45cae3","schema_version":"1.0","event_id":"sha256:9e8ff0959850462e5517763757e9f838888f7c04204abc93250717afdc45cae3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:V3ZBT35PVIXLOB4LHRX6TO2YNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Fredholm property of bisingular pseudodifferential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"J. Seiler, M. Borsero","submitted_at":"2014-10-24T10:54:47Z","abstract_excerpt":"For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \\times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \\times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7224","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":"2026-05-18T01:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPGujIs/FyI3faK5nYzi0tGkQhZerYa/48Sy6A9lanQks6Kx/6k6cX7EWED5NhZoYubDcorEhv22dNiFxd04AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:51:46.285730Z"},"content_sha256":"c73b8373258476cffb0459699aebb273278bf5d33f050dc4f934703de5195bce","schema_version":"1.0","event_id":"sha256:c73b8373258476cffb0459699aebb273278bf5d33f050dc4f934703de5195bce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3ZBT35PVIXLOB4LHRX6TO2YNY/bundle.json","state_url":"https://pith.science/pith/V3ZBT35PVIXLOB4LHRX6TO2YNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3ZBT35PVIXLOB4LHRX6TO2YNY/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":"2026-06-23T01:51:46Z","links":{"resolver":"https://pith.science/pith/V3ZBT35PVIXLOB4LHRX6TO2YNY","bundle":"https://pith.science/pith/V3ZBT35PVIXLOB4LHRX6TO2YNY/bundle.json","state":"https://pith.science/pith/V3ZBT35PVIXLOB4LHRX6TO2YNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3ZBT35PVIXLOB4LHRX6TO2YNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V3ZBT35PVIXLOB4LHRX6TO2YNY","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":"e70c623c9e6521802b0a6690d07bd0f83a8bf1626220ac3c56ae370e8aaf91f4","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T10:54:47Z","title_canon_sha256":"c19409af103dc32866aed01787ca2572a5cba022e0df0fbeb00294020b886faa"},"schema_version":"1.0","source":{"id":"1410.7224","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7224","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7224v2","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7224","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"V3ZBT35PVIXL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V3ZBT35PVIXLOB4L","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V3ZBT35P","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:c73b8373258476cffb0459699aebb273278bf5d33f050dc4f934703de5195bce","target":"graph","created_at":"2026-05-18T01:19:14Z","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 operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \\times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \\times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators.","authors_text":"J. Seiler, M. Borsero","cross_cats":["math.CA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T10:54:47Z","title":"On the Fredholm property of bisingular pseudodifferential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7224","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":"sha256:9e8ff0959850462e5517763757e9f838888f7c04204abc93250717afdc45cae3","target":"record","created_at":"2026-05-18T01:19:14Z","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":"e70c623c9e6521802b0a6690d07bd0f83a8bf1626220ac3c56ae370e8aaf91f4","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-24T10:54:47Z","title_canon_sha256":"c19409af103dc32866aed01787ca2572a5cba022e0df0fbeb00294020b886faa"},"schema_version":"1.0","source":{"id":"1410.7224","kind":"arxiv","version":2}},"canonical_sha256":"aef219efafaa2eb7078b3c6fe9bb586e2ce533e5949fbaf4be54a177d96e254a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aef219efafaa2eb7078b3c6fe9bb586e2ce533e5949fbaf4be54a177d96e254a","first_computed_at":"2026-05-18T01:19:14.236506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:14.236506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QYNl6J4jRYDnESySfEP+KGR4ojMseGp4KPEaE8F9QB5+AW74vU1ajJ/9GpH7Ulz1KzcpoyRPIjJDTK/jByjOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:14.237396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7224","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e8ff0959850462e5517763757e9f838888f7c04204abc93250717afdc45cae3","sha256:c73b8373258476cffb0459699aebb273278bf5d33f050dc4f934703de5195bce"],"state_sha256":"2985179a4c808be69be66493cb5a5ed120d253009056b361716f17ec2fa4e852"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sxgwY8SX3BAAHnJyxDy0AMcSVwCXF4lnIOjTmSsFGUNSrqd0r71ay6tDouE6m1f2EW05B8/jk1RpsFXucqBGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:51:46.287701Z","bundle_sha256":"f8f706c04a4a839f925cfe1d318283fd326eea842432a5a7dd009b35a96d8098"}}