{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AVSZ7YH64GDNNIXNFDMYP66LWW","short_pith_number":"pith:AVSZ7YH6","canonical_record":{"source":{"id":"1611.00813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T21:10:12Z","cross_cats_sorted":[],"title_canon_sha256":"1d923fd869e505b78c17af1e057233a3620189217af6eb73473c388ec1fb9e6e","abstract_canon_sha256":"a73efa1109b68f71fdc5dfc1ac903537bc35651d7fe97db2c4ee8f6d9820959f"},"schema_version":"1.0"},"canonical_sha256":"05659fe0fee186d6a2ed28d987fbcbb594e9799caee463631729ec03d299b236","source":{"kind":"arxiv","id":"1611.00813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00813","created_at":"2026-05-18T00:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00813v1","created_at":"2026-05-18T00:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00813","created_at":"2026-05-18T00:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"AVSZ7YH64GDN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AVSZ7YH64GDNNIXN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AVSZ7YH6","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AVSZ7YH64GDNNIXNFDMYP66LWW","target":"record","payload":{"canonical_record":{"source":{"id":"1611.00813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T21:10:12Z","cross_cats_sorted":[],"title_canon_sha256":"1d923fd869e505b78c17af1e057233a3620189217af6eb73473c388ec1fb9e6e","abstract_canon_sha256":"a73efa1109b68f71fdc5dfc1ac903537bc35651d7fe97db2c4ee8f6d9820959f"},"schema_version":"1.0"},"canonical_sha256":"05659fe0fee186d6a2ed28d987fbcbb594e9799caee463631729ec03d299b236","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:23.966240Z","signature_b64":"jYMv4dt6rNLFux6a+xfo5qJPg2IVdJfLw0Mr3TOxQZkoU7kg6PD8/44ZYpmLuqKlZkwbs/bu8ePoVg6LsOfTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05659fe0fee186d6a2ed28d987fbcbb594e9799caee463631729ec03d299b236","last_reissued_at":"2026-05-18T00:11:23.965720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:23.965720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.00813","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":"2026-05-18T00:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPx+mlIc7Dy5jMhcwjW4K60g23+n/OsICz0Gi2Cp6QuhxM/mgXGkpI+jY1m8YuQ7/MOc9zUu+7IEMWZSLnDbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:25:52.516948Z"},"content_sha256":"01e7b437d8fd4c8051af05fc3cf766553d2722f4a23bc8acdfe56711e103cdb0","schema_version":"1.0","event_id":"sha256:01e7b437d8fd4c8051af05fc3cf766553d2722f4a23bc8acdfe56711e103cdb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AVSZ7YH64GDNNIXNFDMYP66LWW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymmetric truncated Toeplitz operators on finite-dimensional spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bartosz {\\L}anucha, Joanna Jurasik","submitted_at":"2016-11-02T21:10:12Z","abstract_excerpt":"In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. Our results are generalizations of the results known for truncated Toeplitz operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00813","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":"2026-05-18T00:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZAQve9JwxSwKUAkMiQCSr1KBN71Tqm8yRUNS28r5E/J9LNcGM5cxoGJ1iVjAB8xeY798vSfB85295xdz+L2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:25:52.517290Z"},"content_sha256":"c3316d1142a2e9895391890e7687909342672757f4ccb199196fd7b1d33822e0","schema_version":"1.0","event_id":"sha256:c3316d1142a2e9895391890e7687909342672757f4ccb199196fd7b1d33822e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVSZ7YH64GDNNIXNFDMYP66LWW/bundle.json","state_url":"https://pith.science/pith/AVSZ7YH64GDNNIXNFDMYP66LWW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVSZ7YH64GDNNIXNFDMYP66LWW/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":"2026-06-22T15:25:52Z","links":{"resolver":"https://pith.science/pith/AVSZ7YH64GDNNIXNFDMYP66LWW","bundle":"https://pith.science/pith/AVSZ7YH64GDNNIXNFDMYP66LWW/bundle.json","state":"https://pith.science/pith/AVSZ7YH64GDNNIXNFDMYP66LWW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVSZ7YH64GDNNIXNFDMYP66LWW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AVSZ7YH64GDNNIXNFDMYP66LWW","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":"a73efa1109b68f71fdc5dfc1ac903537bc35651d7fe97db2c4ee8f6d9820959f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T21:10:12Z","title_canon_sha256":"1d923fd869e505b78c17af1e057233a3620189217af6eb73473c388ec1fb9e6e"},"schema_version":"1.0","source":{"id":"1611.00813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00813","created_at":"2026-05-18T00:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00813v1","created_at":"2026-05-18T00:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00813","created_at":"2026-05-18T00:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"AVSZ7YH64GDN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AVSZ7YH64GDNNIXN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AVSZ7YH6","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:c3316d1142a2e9895391890e7687909342672757f4ccb199196fd7b1d33822e0","target":"graph","created_at":"2026-05-18T00:11:23Z","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 consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. Our results are generalizations of the results known for truncated Toeplitz operators.","authors_text":"Bartosz {\\L}anucha, Joanna Jurasik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T21:10:12Z","title":"Asymmetric truncated Toeplitz operators on finite-dimensional spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00813","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":"sha256:01e7b437d8fd4c8051af05fc3cf766553d2722f4a23bc8acdfe56711e103cdb0","target":"record","created_at":"2026-05-18T00:11:23Z","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":"a73efa1109b68f71fdc5dfc1ac903537bc35651d7fe97db2c4ee8f6d9820959f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T21:10:12Z","title_canon_sha256":"1d923fd869e505b78c17af1e057233a3620189217af6eb73473c388ec1fb9e6e"},"schema_version":"1.0","source":{"id":"1611.00813","kind":"arxiv","version":1}},"canonical_sha256":"05659fe0fee186d6a2ed28d987fbcbb594e9799caee463631729ec03d299b236","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05659fe0fee186d6a2ed28d987fbcbb594e9799caee463631729ec03d299b236","first_computed_at":"2026-05-18T00:11:23.965720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:23.965720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jYMv4dt6rNLFux6a+xfo5qJPg2IVdJfLw0Mr3TOxQZkoU7kg6PD8/44ZYpmLuqKlZkwbs/bu8ePoVg6LsOfTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:23.966240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01e7b437d8fd4c8051af05fc3cf766553d2722f4a23bc8acdfe56711e103cdb0","sha256:c3316d1142a2e9895391890e7687909342672757f4ccb199196fd7b1d33822e0"],"state_sha256":"9be4a856c41783f34370bb6e86cab2e1972c7fea0421c2b162e06ce5bb447bd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8lP2T7TavhoZf2lhaEXbT8co21yvLdOKn+tu7TpL4jOSk4uRbngaHe4/e1V8Zv7i83pFl2/ELYWJJJdwXO8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:25:52.519245Z","bundle_sha256":"b8c882c1b75768314fb67d134e7b80a76a20ed73945079b7e3e254d4c0b84a47"}}