{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GI32SSAK7YS44626CQOMISMQIP","short_pith_number":"pith:GI32SSAK","canonical_record":{"source":{"id":"1701.07350","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T15:24:43Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"755b3cef4525372e190a324b0b795610fb8ae492917dc1f4d76b2d1fa5cddbc5","abstract_canon_sha256":"37cac0b165b29eea8fb65f1202535c57db6f5dd18da287b23cdbcadf8efab6ec"},"schema_version":"1.0"},"canonical_sha256":"3237a9480afe25ce7b5e141cc4499043d667497b856172d21aabf1d83c0a6d5c","source":{"kind":"arxiv","id":"1701.07350","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07350","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07350v2","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07350","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"GI32SSAK7YS4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GI32SSAK7YS44626","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GI32SSAK","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GI32SSAK7YS44626CQOMISMQIP","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07350","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T15:24:43Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"755b3cef4525372e190a324b0b795610fb8ae492917dc1f4d76b2d1fa5cddbc5","abstract_canon_sha256":"37cac0b165b29eea8fb65f1202535c57db6f5dd18da287b23cdbcadf8efab6ec"},"schema_version":"1.0"},"canonical_sha256":"3237a9480afe25ce7b5e141cc4499043d667497b856172d21aabf1d83c0a6d5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:31.547826Z","signature_b64":"p9rdjPm942e1QvM+6OJ34tsrKLU3z8OYeILQp3xHxjoJBVUKX/0oO2nt0wOL5ZeL8e4WPPl8CpWNYHzHkqJ7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3237a9480afe25ce7b5e141cc4499043d667497b856172d21aabf1d83c0a6d5c","last_reissued_at":"2026-05-18T00:24:31.547393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:31.547393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07350","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":"2026-05-18T00:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3EfA/fdYt/wRyUuOqwQ1EMIfk7pXsaCnIQSKDEJgznfE/rcXX5njjVSx5/VZztWGuL+qyLaJAxktcUM4UWlSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:14:06.388368Z"},"content_sha256":"2e8b8a0aac3bdbc6f3fc431afb2647bd63bc5e1a8caf949305398e80ef8f3fed","schema_version":"1.0","event_id":"sha256:2e8b8a0aac3bdbc6f3fc431afb2647bd63bc5e1a8caf949305398e80ef8f3fed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GI32SSAK7YS44626CQOMISMQIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global folds between Banach spaces as perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Andr\\'e Zaccur, Carlos Tomei, Marta Calanchi","submitted_at":"2017-01-25T15:24:43Z","abstract_excerpt":"Global folds between Banach spaces are obtained from a simple geometric construction: a Fredholm operator $T$ of index zero with one dimensional kernel is perturbed by a compatible nonlinear term $P$. The scheme encapsulates most of the known examples and suggests new ones. Concrete examples rely on the positivity of an eigenfunction. For the standard Nemitskii case $P(u) = f(u)$ (but $P$ might be nonlocal, non-variational), $T$ might be the Laplacian with different boundary conditions, as in the Ambrosetti-Prodi theorem, or the Schr\\\"{o}dinger operators associated with the quantum harmonic os"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07350","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":"2026-05-18T00:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40MJnh+zkv1SoyhlAXYBlBuR4ioWK740GTQVnUiBGlHL8Qt4c0H1L9Zhql+7cwfD7yO8lrOEQr4NRtiVP/CCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:14:06.389032Z"},"content_sha256":"71ca08a4888f37112bc3d0ee812f9576746dce8a3fa5ef60a522ddc6c306684e","schema_version":"1.0","event_id":"sha256:71ca08a4888f37112bc3d0ee812f9576746dce8a3fa5ef60a522ddc6c306684e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GI32SSAK7YS44626CQOMISMQIP/bundle.json","state_url":"https://pith.science/pith/GI32SSAK7YS44626CQOMISMQIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GI32SSAK7YS44626CQOMISMQIP/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":"2026-05-31T18:14:06Z","links":{"resolver":"https://pith.science/pith/GI32SSAK7YS44626CQOMISMQIP","bundle":"https://pith.science/pith/GI32SSAK7YS44626CQOMISMQIP/bundle.json","state":"https://pith.science/pith/GI32SSAK7YS44626CQOMISMQIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GI32SSAK7YS44626CQOMISMQIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GI32SSAK7YS44626CQOMISMQIP","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":"37cac0b165b29eea8fb65f1202535c57db6f5dd18da287b23cdbcadf8efab6ec","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T15:24:43Z","title_canon_sha256":"755b3cef4525372e190a324b0b795610fb8ae492917dc1f4d76b2d1fa5cddbc5"},"schema_version":"1.0","source":{"id":"1701.07350","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07350","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07350v2","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07350","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"GI32SSAK7YS4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GI32SSAK7YS44626","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GI32SSAK","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:71ca08a4888f37112bc3d0ee812f9576746dce8a3fa5ef60a522ddc6c306684e","target":"graph","created_at":"2026-05-18T00:24:31Z","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":"Global folds between Banach spaces are obtained from a simple geometric construction: a Fredholm operator $T$ of index zero with one dimensional kernel is perturbed by a compatible nonlinear term $P$. The scheme encapsulates most of the known examples and suggests new ones. Concrete examples rely on the positivity of an eigenfunction. For the standard Nemitskii case $P(u) = f(u)$ (but $P$ might be nonlocal, non-variational), $T$ might be the Laplacian with different boundary conditions, as in the Ambrosetti-Prodi theorem, or the Schr\\\"{o}dinger operators associated with the quantum harmonic os","authors_text":"Andr\\'e Zaccur, Carlos Tomei, Marta Calanchi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T15:24:43Z","title":"Global folds between Banach spaces as perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07350","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":"sha256:2e8b8a0aac3bdbc6f3fc431afb2647bd63bc5e1a8caf949305398e80ef8f3fed","target":"record","created_at":"2026-05-18T00:24:31Z","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":"37cac0b165b29eea8fb65f1202535c57db6f5dd18da287b23cdbcadf8efab6ec","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-25T15:24:43Z","title_canon_sha256":"755b3cef4525372e190a324b0b795610fb8ae492917dc1f4d76b2d1fa5cddbc5"},"schema_version":"1.0","source":{"id":"1701.07350","kind":"arxiv","version":2}},"canonical_sha256":"3237a9480afe25ce7b5e141cc4499043d667497b856172d21aabf1d83c0a6d5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3237a9480afe25ce7b5e141cc4499043d667497b856172d21aabf1d83c0a6d5c","first_computed_at":"2026-05-18T00:24:31.547393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:31.547393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p9rdjPm942e1QvM+6OJ34tsrKLU3z8OYeILQp3xHxjoJBVUKX/0oO2nt0wOL5ZeL8e4WPPl8CpWNYHzHkqJ7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:31.547826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07350","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e8b8a0aac3bdbc6f3fc431afb2647bd63bc5e1a8caf949305398e80ef8f3fed","sha256:71ca08a4888f37112bc3d0ee812f9576746dce8a3fa5ef60a522ddc6c306684e"],"state_sha256":"f79871cee588d67cc498439b7db83476983099b787ba1c10592be2985fa21878"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1HbJBpu+Scg/6SnxNDq2kSVyBkHFGsRwFyCVJqerX6wLteuNRTuCws0Dv/kQPjgiQhK9YHQ52t6ynYntK600BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:14:06.391447Z","bundle_sha256":"169e4d70167d2fcf0e57a79c2abb386b4eadf17c659eb618eadc18428782a36e"}}