{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7DOZ57IY66VUVWEDV23CUC2X53","short_pith_number":"pith:7DOZ57IY","canonical_record":{"source":{"id":"1406.6830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T10:19:55Z","cross_cats_sorted":[],"title_canon_sha256":"dab16c57ad9d9014428b78fa657982af0147fdac93218a4a03f7813638a250a1","abstract_canon_sha256":"a4bdb2375391c54e95dbd17ed772dd13999a6cc8cb2fd99297cd945ed96f9d0c"},"schema_version":"1.0"},"canonical_sha256":"f8dd9efd18f7ab4ad883aeb62a0b57eee258bad9e30d05624d4a75f304e01c33","source":{"kind":"arxiv","id":"1406.6830","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6830","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6830v1","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6830","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"7DOZ57IY66VU","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7DOZ57IY66VUVWED","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7DOZ57IY","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7DOZ57IY66VUVWEDV23CUC2X53","target":"record","payload":{"canonical_record":{"source":{"id":"1406.6830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T10:19:55Z","cross_cats_sorted":[],"title_canon_sha256":"dab16c57ad9d9014428b78fa657982af0147fdac93218a4a03f7813638a250a1","abstract_canon_sha256":"a4bdb2375391c54e95dbd17ed772dd13999a6cc8cb2fd99297cd945ed96f9d0c"},"schema_version":"1.0"},"canonical_sha256":"f8dd9efd18f7ab4ad883aeb62a0b57eee258bad9e30d05624d4a75f304e01c33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:55.733865Z","signature_b64":"l8E0SydkgbnpWrkJ9tYODAS4Ovo7uTI0vnY5p2SAmxc5NzwCkHGKeSJJAxidDohd12Is834ON8Zb6Obxp18oDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8dd9efd18f7ab4ad883aeb62a0b57eee258bad9e30d05624d4a75f304e01c33","last_reissued_at":"2026-05-18T02:48:55.733369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:55.733369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.6830","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":"2026-05-18T02:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"voxHDvzkq4NRpMV8XcaOptzFoJ0OJlXflNZ2tHisYRC1E89iWaCuHjd1vixeCA28CD9bO+xueDck3SHSyRjQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:36:11.613530Z"},"content_sha256":"05fc6f7fcc9496045006559c2ef64a3794455b64cf5a3a3229934fc1a52c5866","schema_version":"1.0","event_id":"sha256:05fc6f7fcc9496045006559c2ef64a3794455b64cf5a3a3229934fc1a52c5866"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7DOZ57IY66VUVWEDV23CUC2X53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniel Alpay, Fabrizio Colombo, Irene Sabadini","submitted_at":"2014-06-26T10:19:55Z","abstract_excerpt":"In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [D. Alpay, F. Colombo, I. Sabadini, Krein-Langer factorization and related topics in the slice hyperholomorphic setting, J. Geom. Anal., 24 (2014), 843--872]. We treat both the case of functions with $\\kappa$ negative squares defined on subsets of the quaternionic unit ball or on subsets of the half space of quaternions with positive real part. A crucial tool in the proof of our results is the Schauder-Tychonoff theorem and an invariant s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6830","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":"2026-05-18T02:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EjmSVo8NlP+F58kJXPhRHDa/tzBWVmJ0Cvs8IHYdhOBOWle+cfVR0KDRRi1Wu4ad0/gGn+vkdhF8JFXWiSfcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:36:11.613889Z"},"content_sha256":"95e3c60e8180525357b872d57f99a61324e044d5c9819a681359ff67e5bc0d3c","schema_version":"1.0","event_id":"sha256:95e3c60e8180525357b872d57f99a61324e044d5c9819a681359ff67e5bc0d3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DOZ57IY66VUVWEDV23CUC2X53/bundle.json","state_url":"https://pith.science/pith/7DOZ57IY66VUVWEDV23CUC2X53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DOZ57IY66VUVWEDV23CUC2X53/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":"2026-06-01T21:36:11Z","links":{"resolver":"https://pith.science/pith/7DOZ57IY66VUVWEDV23CUC2X53","bundle":"https://pith.science/pith/7DOZ57IY66VUVWEDV23CUC2X53/bundle.json","state":"https://pith.science/pith/7DOZ57IY66VUVWEDV23CUC2X53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DOZ57IY66VUVWEDV23CUC2X53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7DOZ57IY66VUVWEDV23CUC2X53","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":"a4bdb2375391c54e95dbd17ed772dd13999a6cc8cb2fd99297cd945ed96f9d0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T10:19:55Z","title_canon_sha256":"dab16c57ad9d9014428b78fa657982af0147fdac93218a4a03f7813638a250a1"},"schema_version":"1.0","source":{"id":"1406.6830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6830","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6830v1","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6830","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"7DOZ57IY66VU","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7DOZ57IY66VUVWED","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7DOZ57IY","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:95e3c60e8180525357b872d57f99a61324e044d5c9819a681359ff67e5bc0d3c","target":"graph","created_at":"2026-05-18T02:48:55Z","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":"In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [D. Alpay, F. Colombo, I. Sabadini, Krein-Langer factorization and related topics in the slice hyperholomorphic setting, J. Geom. Anal., 24 (2014), 843--872]. We treat both the case of functions with $\\kappa$ negative squares defined on subsets of the quaternionic unit ball or on subsets of the half space of quaternions with positive real part. A crucial tool in the proof of our results is the Schauder-Tychonoff theorem and an invariant s","authors_text":"Daniel Alpay, Fabrizio Colombo, Irene Sabadini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T10:19:55Z","title":"Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6830","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":"sha256:05fc6f7fcc9496045006559c2ef64a3794455b64cf5a3a3229934fc1a52c5866","target":"record","created_at":"2026-05-18T02:48:55Z","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":"a4bdb2375391c54e95dbd17ed772dd13999a6cc8cb2fd99297cd945ed96f9d0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T10:19:55Z","title_canon_sha256":"dab16c57ad9d9014428b78fa657982af0147fdac93218a4a03f7813638a250a1"},"schema_version":"1.0","source":{"id":"1406.6830","kind":"arxiv","version":1}},"canonical_sha256":"f8dd9efd18f7ab4ad883aeb62a0b57eee258bad9e30d05624d4a75f304e01c33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8dd9efd18f7ab4ad883aeb62a0b57eee258bad9e30d05624d4a75f304e01c33","first_computed_at":"2026-05-18T02:48:55.733369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:55.733369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l8E0SydkgbnpWrkJ9tYODAS4Ovo7uTI0vnY5p2SAmxc5NzwCkHGKeSJJAxidDohd12Is834ON8Zb6Obxp18oDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:55.733865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05fc6f7fcc9496045006559c2ef64a3794455b64cf5a3a3229934fc1a52c5866","sha256:95e3c60e8180525357b872d57f99a61324e044d5c9819a681359ff67e5bc0d3c"],"state_sha256":"63ce37301c6e949322189ab54cfacfe3fecdca50ccd46a28336f82aa52d75cac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UN8RskFuhWQCkLF+lUclqX37TNzLWa1/tGAXSm6g75SpYUfC/1yV4l3+naP3ED1zLO4/w70ncq/vMc1ZTaYYBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:36:11.615803Z","bundle_sha256":"23107448a94885d3fac61fee3608b3c078ece0724c361eab2cec87965fbf0162"}}