{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FILQ7ELSQSU2ZIFX7HSEXI3BMC","short_pith_number":"pith:FILQ7ELS","canonical_record":{"source":{"id":"1508.04279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-08-18T11:28:41Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"23be2f4f25d4298a7976ad9b5d00a6c382feac23c53affb47b0d46e92268c56d","abstract_canon_sha256":"cfa7bc917e4ff96272b8c518a25a018e6049c897f74d2908a9308f52a721405b"},"schema_version":"1.0"},"canonical_sha256":"2a170f917284a9aca0b7f9e44ba36160a22ccefded6954bc3e23145e0f7e4696","source":{"kind":"arxiv","id":"1508.04279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04279","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04279v2","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04279","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"FILQ7ELSQSU2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FILQ7ELSQSU2ZIFX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FILQ7ELS","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FILQ7ELSQSU2ZIFX7HSEXI3BMC","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-08-18T11:28:41Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"23be2f4f25d4298a7976ad9b5d00a6c382feac23c53affb47b0d46e92268c56d","abstract_canon_sha256":"cfa7bc917e4ff96272b8c518a25a018e6049c897f74d2908a9308f52a721405b"},"schema_version":"1.0"},"canonical_sha256":"2a170f917284a9aca0b7f9e44ba36160a22ccefded6954bc3e23145e0f7e4696","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:45.027781Z","signature_b64":"ju4NbxkU5dGkkLJzNC54Hn+dgnY16YE+UdtMM8cw7FCF2vHO014FVZE/p9NiOhdIfLvx3sZtd+Q3au5u3LAVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a170f917284a9aca0b7f9e44ba36160a22ccefded6954bc3e23145e0f7e4696","last_reissued_at":"2026-05-18T01:29:45.027107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:45.027107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04279","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":"2026-05-18T01:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0HEFiZOujJJ1fIBX4bq5L/ahJQjjvDyI5oOlyZoi4yiR4GEAoOhPxpxOU9KnbmwDbYFupVaqX6hXoTjVVsA7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:53:37.292091Z"},"content_sha256":"4dd25daca7b876a99cc1ad413c529b5498aa68b87a8279bc6c80cafe2dd03887","schema_version":"1.0","event_id":"sha256:4dd25daca7b876a99cc1ad413c529b5498aa68b87a8279bc6c80cafe2dd03887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FILQ7ELSQSU2ZIFX7HSEXI3BMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization principle for compact Hankel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Dmitri Yafaev","submitted_at":"2015-08-18T11:28:41Z","abstract_excerpt":"In the power scale, the asymptotic behavior of the singular values of a compact Hankel operator is determined by the behavior of the symbol in a neighborhood of its singular support. In this paper, we discuss the localization principle which says that the contributions of disjoint parts of the singular support of the symbol to the asymptotic behavior of the singular values are independent of each other. We apply this principle to Hankel integral operators and to infinite Hankel matrices. In both cases, we describe a wide class of Hankel operators with power-like asymptotics of singular values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04279","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":"2026-05-18T01:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Em8YF+iB+QllIEY5bY+j+Z0L74CsnD1ekaO9Hd1S3Ga656vvgliiKAZpa7iBuXeEPvsGPbdHyZuN0B8WMlX6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:53:37.292446Z"},"content_sha256":"080acf1eb9de95d5065d3f048b4d2c661beca2274d0652938d89ffd3ff0c9108","schema_version":"1.0","event_id":"sha256:080acf1eb9de95d5065d3f048b4d2c661beca2274d0652938d89ffd3ff0c9108"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FILQ7ELSQSU2ZIFX7HSEXI3BMC/bundle.json","state_url":"https://pith.science/pith/FILQ7ELSQSU2ZIFX7HSEXI3BMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FILQ7ELSQSU2ZIFX7HSEXI3BMC/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":"2026-06-02T19:53:37Z","links":{"resolver":"https://pith.science/pith/FILQ7ELSQSU2ZIFX7HSEXI3BMC","bundle":"https://pith.science/pith/FILQ7ELSQSU2ZIFX7HSEXI3BMC/bundle.json","state":"https://pith.science/pith/FILQ7ELSQSU2ZIFX7HSEXI3BMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FILQ7ELSQSU2ZIFX7HSEXI3BMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FILQ7ELSQSU2ZIFX7HSEXI3BMC","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":"cfa7bc917e4ff96272b8c518a25a018e6049c897f74d2908a9308f52a721405b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-08-18T11:28:41Z","title_canon_sha256":"23be2f4f25d4298a7976ad9b5d00a6c382feac23c53affb47b0d46e92268c56d"},"schema_version":"1.0","source":{"id":"1508.04279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04279","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04279v2","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04279","created_at":"2026-05-18T01:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"FILQ7ELSQSU2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FILQ7ELSQSU2ZIFX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FILQ7ELS","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:080acf1eb9de95d5065d3f048b4d2c661beca2274d0652938d89ffd3ff0c9108","target":"graph","created_at":"2026-05-18T01:29:45Z","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 the power scale, the asymptotic behavior of the singular values of a compact Hankel operator is determined by the behavior of the symbol in a neighborhood of its singular support. In this paper, we discuss the localization principle which says that the contributions of disjoint parts of the singular support of the symbol to the asymptotic behavior of the singular values are independent of each other. We apply this principle to Hankel integral operators and to infinite Hankel matrices. In both cases, we describe a wide class of Hankel operators with power-like asymptotics of singular values.","authors_text":"Alexander Pushnitski, Dmitri Yafaev","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-08-18T11:28:41Z","title":"Localization principle for compact Hankel operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04279","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":"sha256:4dd25daca7b876a99cc1ad413c529b5498aa68b87a8279bc6c80cafe2dd03887","target":"record","created_at":"2026-05-18T01:29:45Z","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":"cfa7bc917e4ff96272b8c518a25a018e6049c897f74d2908a9308f52a721405b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-08-18T11:28:41Z","title_canon_sha256":"23be2f4f25d4298a7976ad9b5d00a6c382feac23c53affb47b0d46e92268c56d"},"schema_version":"1.0","source":{"id":"1508.04279","kind":"arxiv","version":2}},"canonical_sha256":"2a170f917284a9aca0b7f9e44ba36160a22ccefded6954bc3e23145e0f7e4696","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a170f917284a9aca0b7f9e44ba36160a22ccefded6954bc3e23145e0f7e4696","first_computed_at":"2026-05-18T01:29:45.027107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:45.027107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ju4NbxkU5dGkkLJzNC54Hn+dgnY16YE+UdtMM8cw7FCF2vHO014FVZE/p9NiOhdIfLvx3sZtd+Q3au5u3LAVCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:45.027781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dd25daca7b876a99cc1ad413c529b5498aa68b87a8279bc6c80cafe2dd03887","sha256:080acf1eb9de95d5065d3f048b4d2c661beca2274d0652938d89ffd3ff0c9108"],"state_sha256":"0e7b72d7e601e1e080d214e16d7c10c5c41675b05aa226e07c7b31ba315b3695"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mdVvkmZGNVYKzsPlBhQo4XgXS9E1CGT+7NYp5Fdck/YILCsuSdqtDm6b+O6xghUb5wgWzIzZ+m3gJsBM2Le1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:53:37.294290Z","bundle_sha256":"6304008e322b2ed8e855eef744be306448f48ac61a689cfbd08497db83f71197"}}