{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:25O74OUWX4246UUBL6L6OBZLPV","short_pith_number":"pith:25O74OUW","canonical_record":{"source":{"id":"1907.05629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-12T08:53:04Z","cross_cats_sorted":["math.CV","math.SP"],"title_canon_sha256":"6e59438fe650a9d362df355a4a88a3a6df19cc8adf642f483f4541f2946f8087","abstract_canon_sha256":"12d5f64d386f930fc2bd5676c6965f8b5d086b1c4621f716aabd1723a30d6df1"},"schema_version":"1.0"},"canonical_sha256":"d75dfe3a96bf35cf52815f97e7072b7d600301383dc71e67118d3d12fa2a71e6","source":{"kind":"arxiv","id":"1907.05629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05629","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05629v1","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05629","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"25O74OUWX424","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"25O74OUWX4246UUB","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"25O74OUW","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:25O74OUWX4246UUBL6L6OBZLPV","target":"record","payload":{"canonical_record":{"source":{"id":"1907.05629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-12T08:53:04Z","cross_cats_sorted":["math.CV","math.SP"],"title_canon_sha256":"6e59438fe650a9d362df355a4a88a3a6df19cc8adf642f483f4541f2946f8087","abstract_canon_sha256":"12d5f64d386f930fc2bd5676c6965f8b5d086b1c4621f716aabd1723a30d6df1"},"schema_version":"1.0"},"canonical_sha256":"d75dfe3a96bf35cf52815f97e7072b7d600301383dc71e67118d3d12fa2a71e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:47.539841Z","signature_b64":"OmvxZUwLopk6TqennDHVUVCe9G7gkfavjqPtG5hL4hz4lWEkYNtHuZgyNpzK2v4anIwjZQqzJPYPQr7y1J5ODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d75dfe3a96bf35cf52815f97e7072b7d600301383dc71e67118d3d12fa2a71e6","last_reissued_at":"2026-05-17T23:40:47.539086Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:47.539086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.05629","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":"2026-05-17T23:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FO7FvOi46FGI07vGI7bZ0bP+2a/1swAwCF9UkWV4DDFLR84GilRdOyfy5ApX7uafc5Y/fl4sIcDMNEqUVEkyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:13.138604Z"},"content_sha256":"a030a78ba68d0f46c9c8a2bc2855b772e1416b0f5526842c86f6c5632aef9f9c","schema_version":"1.0","event_id":"sha256:a030a78ba68d0f46c9c8a2bc2855b772e1416b0f5526842c86f6c5632aef9f9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:25O74OUWX4246UUBL6L6OBZLPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The structure of Schmidt subspaces of Hankel operators: a short proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Alexander Pushnitski, Patrick Gerard","submitted_at":"2019-07-12T08:53:04Z","abstract_excerpt":"We give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant subspaces, and our proof uses Hitt's theorem on the structure of such subspaces. We also give a formula for the action of a Hankel operator on its Schmidt subspace."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05629","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":"2026-05-17T23:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0MUIBw6E1jKjdECGxXm9kaws3GBfEmWA7gfQDXNqp+ibpinlgSyudYB92N22CgZvUoEdsokgcJrJ1qLP5crDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:13.138957Z"},"content_sha256":"4d8fc595fb3c1aced7b4780fa54bda536f469ad26799984446903503bcfd1e31","schema_version":"1.0","event_id":"sha256:4d8fc595fb3c1aced7b4780fa54bda536f469ad26799984446903503bcfd1e31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25O74OUWX4246UUBL6L6OBZLPV/bundle.json","state_url":"https://pith.science/pith/25O74OUWX4246UUBL6L6OBZLPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25O74OUWX4246UUBL6L6OBZLPV/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":"2026-06-01T19:00:13Z","links":{"resolver":"https://pith.science/pith/25O74OUWX4246UUBL6L6OBZLPV","bundle":"https://pith.science/pith/25O74OUWX4246UUBL6L6OBZLPV/bundle.json","state":"https://pith.science/pith/25O74OUWX4246UUBL6L6OBZLPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25O74OUWX4246UUBL6L6OBZLPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:25O74OUWX4246UUBL6L6OBZLPV","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":"12d5f64d386f930fc2bd5676c6965f8b5d086b1c4621f716aabd1723a30d6df1","cross_cats_sorted":["math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-12T08:53:04Z","title_canon_sha256":"6e59438fe650a9d362df355a4a88a3a6df19cc8adf642f483f4541f2946f8087"},"schema_version":"1.0","source":{"id":"1907.05629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05629","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05629v1","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05629","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"25O74OUWX424","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"25O74OUWX4246UUB","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"25O74OUW","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:4d8fc595fb3c1aced7b4780fa54bda536f469ad26799984446903503bcfd1e31","target":"graph","created_at":"2026-05-17T23:40:47Z","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 give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant subspaces, and our proof uses Hitt's theorem on the structure of such subspaces. We also give a formula for the action of a Hankel operator on its Schmidt subspace.","authors_text":"Alexander Pushnitski, Patrick Gerard","cross_cats":["math.CV","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-12T08:53:04Z","title":"The structure of Schmidt subspaces of Hankel operators: a short proof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05629","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:a030a78ba68d0f46c9c8a2bc2855b772e1416b0f5526842c86f6c5632aef9f9c","target":"record","created_at":"2026-05-17T23:40:47Z","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":"12d5f64d386f930fc2bd5676c6965f8b5d086b1c4621f716aabd1723a30d6df1","cross_cats_sorted":["math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-12T08:53:04Z","title_canon_sha256":"6e59438fe650a9d362df355a4a88a3a6df19cc8adf642f483f4541f2946f8087"},"schema_version":"1.0","source":{"id":"1907.05629","kind":"arxiv","version":1}},"canonical_sha256":"d75dfe3a96bf35cf52815f97e7072b7d600301383dc71e67118d3d12fa2a71e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d75dfe3a96bf35cf52815f97e7072b7d600301383dc71e67118d3d12fa2a71e6","first_computed_at":"2026-05-17T23:40:47.539086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:47.539086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OmvxZUwLopk6TqennDHVUVCe9G7gkfavjqPtG5hL4hz4lWEkYNtHuZgyNpzK2v4anIwjZQqzJPYPQr7y1J5ODA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:47.539841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.05629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a030a78ba68d0f46c9c8a2bc2855b772e1416b0f5526842c86f6c5632aef9f9c","sha256:4d8fc595fb3c1aced7b4780fa54bda536f469ad26799984446903503bcfd1e31"],"state_sha256":"82dd398eae67a11dae80b71e66ba9df4015d67f06d31626ebcf0cc3cc219ef08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wWu8jZgeDZgu2igx8B/fhdQDl8utOY82zL+m7DmSxNcA3pIeumILbwBk6xfQA9lxDj0PZUSu9US0IgwoxmE0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:00:13.140904Z","bundle_sha256":"fc072853bdbdd481d8a3d29a43a0b37ba9353db6ca8bc8d07eaf683d33d2a838"}}