{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PGOYQPVEL7KBMNNF65NOTJ2FVB","short_pith_number":"pith:PGOYQPVE","canonical_record":{"source":{"id":"1502.04402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-16T01:34:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"384f804a5f0f9433e5ed2581ecfc654a5004974e35e9576d52d6be21d858cbe2","abstract_canon_sha256":"eb9337409e8f3211970e002524a15f8cff17986718703215216e1c036149b02c"},"schema_version":"1.0"},"canonical_sha256":"799d883ea45fd41635a5f75ae9a745a86d10dd2355400fd7c5b4dae546d61a26","source":{"kind":"arxiv","id":"1502.04402","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04402","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04402v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04402","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"PGOYQPVEL7KB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGOYQPVEL7KBMNNF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGOYQPVE","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PGOYQPVEL7KBMNNF65NOTJ2FVB","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-16T01:34:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"384f804a5f0f9433e5ed2581ecfc654a5004974e35e9576d52d6be21d858cbe2","abstract_canon_sha256":"eb9337409e8f3211970e002524a15f8cff17986718703215216e1c036149b02c"},"schema_version":"1.0"},"canonical_sha256":"799d883ea45fd41635a5f75ae9a745a86d10dd2355400fd7c5b4dae546d61a26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:59.840256Z","signature_b64":"Ab/vnBRefr2dElmjhfrUDNaylnHhUYGboLUnSPBjuwcYrR/utQKj4hSBTdAxmLSfF+5mdYRyh+pW76V+fYUhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"799d883ea45fd41635a5f75ae9a745a86d10dd2355400fd7c5b4dae546d61a26","last_reissued_at":"2026-05-18T02:26:59.839816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:59.839816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04402","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKhzSRHafwtjBqh4ENuU501Sl99rdFfQAxTjCazOGmvXEllkdO3O+CvTRlHUGPewLF9UJ9NZEDFCC0OUdvlxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:33:34.704832Z"},"content_sha256":"cfacfbe1edf9760f04c84f3a6d54a9af7e770dd91b64095983a2980df1ecc38b","schema_version":"1.0","event_id":"sha256:cfacfbe1edf9760f04c84f3a6d54a9af7e770dd91b64095983a2980df1ecc38b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PGOYQPVEL7KBMNNF65NOTJ2FVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order problem for canonical systems and a conjecture of Valent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Roman Romanov","submitted_at":"2015-02-16T01:34:47Z","abstract_excerpt":"We establish a sharp upper estimate for the order of a canonical system in terms of the Hamiltonian. This upper estimate becomes an equality in the case of Krein strings. As an application we prove a conjecture of Valent about the order of a certain class of Jacobi matrices with polynomial coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04402","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLdz2cWDIoTtVdmOYTm5suRnZHHrAGvyIlx8fRccc9QY48+N5ug2/23J86WSOQxYW1N4UBNVdw7wF9ZxEtnGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:33:34.705169Z"},"content_sha256":"930a52d1bb1390ffdbacd3adef026f2c62465673e77f769314f1aef5a62c92a0","schema_version":"1.0","event_id":"sha256:930a52d1bb1390ffdbacd3adef026f2c62465673e77f769314f1aef5a62c92a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGOYQPVEL7KBMNNF65NOTJ2FVB/bundle.json","state_url":"https://pith.science/pith/PGOYQPVEL7KBMNNF65NOTJ2FVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGOYQPVEL7KBMNNF65NOTJ2FVB/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":"2026-06-27T20:33:34Z","links":{"resolver":"https://pith.science/pith/PGOYQPVEL7KBMNNF65NOTJ2FVB","bundle":"https://pith.science/pith/PGOYQPVEL7KBMNNF65NOTJ2FVB/bundle.json","state":"https://pith.science/pith/PGOYQPVEL7KBMNNF65NOTJ2FVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGOYQPVEL7KBMNNF65NOTJ2FVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PGOYQPVEL7KBMNNF65NOTJ2FVB","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":"eb9337409e8f3211970e002524a15f8cff17986718703215216e1c036149b02c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-16T01:34:47Z","title_canon_sha256":"384f804a5f0f9433e5ed2581ecfc654a5004974e35e9576d52d6be21d858cbe2"},"schema_version":"1.0","source":{"id":"1502.04402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04402","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04402v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04402","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"PGOYQPVEL7KB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGOYQPVEL7KBMNNF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGOYQPVE","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:930a52d1bb1390ffdbacd3adef026f2c62465673e77f769314f1aef5a62c92a0","target":"graph","created_at":"2026-05-18T02:26:59Z","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 establish a sharp upper estimate for the order of a canonical system in terms of the Hamiltonian. This upper estimate becomes an equality in the case of Krein strings. As an application we prove a conjecture of Valent about the order of a certain class of Jacobi matrices with polynomial coefficients.","authors_text":"Roman Romanov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-16T01:34:47Z","title":"Order problem for canonical systems and a conjecture of Valent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04402","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:cfacfbe1edf9760f04c84f3a6d54a9af7e770dd91b64095983a2980df1ecc38b","target":"record","created_at":"2026-05-18T02:26:59Z","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":"eb9337409e8f3211970e002524a15f8cff17986718703215216e1c036149b02c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-16T01:34:47Z","title_canon_sha256":"384f804a5f0f9433e5ed2581ecfc654a5004974e35e9576d52d6be21d858cbe2"},"schema_version":"1.0","source":{"id":"1502.04402","kind":"arxiv","version":1}},"canonical_sha256":"799d883ea45fd41635a5f75ae9a745a86d10dd2355400fd7c5b4dae546d61a26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"799d883ea45fd41635a5f75ae9a745a86d10dd2355400fd7c5b4dae546d61a26","first_computed_at":"2026-05-18T02:26:59.839816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:59.839816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ab/vnBRefr2dElmjhfrUDNaylnHhUYGboLUnSPBjuwcYrR/utQKj4hSBTdAxmLSfF+5mdYRyh+pW76V+fYUhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:59.840256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfacfbe1edf9760f04c84f3a6d54a9af7e770dd91b64095983a2980df1ecc38b","sha256:930a52d1bb1390ffdbacd3adef026f2c62465673e77f769314f1aef5a62c92a0"],"state_sha256":"b5b286e6e3ff65643236a0972af34bffbf1931c06f37c8d958bec3e66f8b7e9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8IypATt13SBCbW+K6tMY0wfSNAedwfEW3E4NYWocj0nvzL9TrNdeQFLyIbEwsS3/HQmmN/0hGB+XqPoMMHCzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:33:34.707079Z","bundle_sha256":"6984cb10e1742e3da0fe3e381b0485d67081839ce03c5d44a49a90185830ad0b"}}