{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6YLIDFPQ6P53WPYCXS5QL2HJ47","short_pith_number":"pith:6YLIDFPQ","canonical_record":{"source":{"id":"1202.5204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-02-23T15:11:01Z","cross_cats_sorted":[],"title_canon_sha256":"05cd2f3c476c34cef3e504a1c8de4ab0c5454aec0b0caf6c4250afb3d10eac46","abstract_canon_sha256":"7cb327a8a2e8b0ee27dd09a46c9e52103ce75ec59372daa5361c5f574d02d184"},"schema_version":"1.0"},"canonical_sha256":"f6168195f0f3fbbb3f02bcbb05e8e9e7dbc065f9c68612aeafc3550ebde4541a","source":{"kind":"arxiv","id":"1202.5204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5204","created_at":"2026-05-18T04:01:38Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5204v1","created_at":"2026-05-18T04:01:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5204","created_at":"2026-05-18T04:01:38Z"},{"alias_kind":"pith_short_12","alias_value":"6YLIDFPQ6P53","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6YLIDFPQ6P53WPYC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6YLIDFPQ","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6YLIDFPQ6P53WPYCXS5QL2HJ47","target":"record","payload":{"canonical_record":{"source":{"id":"1202.5204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-02-23T15:11:01Z","cross_cats_sorted":[],"title_canon_sha256":"05cd2f3c476c34cef3e504a1c8de4ab0c5454aec0b0caf6c4250afb3d10eac46","abstract_canon_sha256":"7cb327a8a2e8b0ee27dd09a46c9e52103ce75ec59372daa5361c5f574d02d184"},"schema_version":"1.0"},"canonical_sha256":"f6168195f0f3fbbb3f02bcbb05e8e9e7dbc065f9c68612aeafc3550ebde4541a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:38.736726Z","signature_b64":"pr2iOtiDABodIvl2oqIDimvZoFlx0bI7fAIHP0GBLxQ+8S5i7ffYg7fS8xsggdzOoTyFCVkwGFMce13PFM1fBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6168195f0f3fbbb3f02bcbb05e8e9e7dbc065f9c68612aeafc3550ebde4541a","last_reissued_at":"2026-05-18T04:01:38.736149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:38.736149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.5204","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":"2026-05-18T04:01:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hynpN9rsWrKq2YK5d2zTbvoytCsXZjRMFoJ17TJEtMrlsoCC03sRXKJapH4H0mC96AWaFg8+pRL0bWYoLToKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:10:38.984180Z"},"content_sha256":"fbe0e788f96693c6d54b59c0ea32af8b7569548f7c87c066a50b815a950cdeb4","schema_version":"1.0","event_id":"sha256:fbe0e788f96693c6d54b59c0ea32af8b7569548f7c87c066a50b815a950cdeb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6YLIDFPQ6P53WPYCXS5QL2HJ47","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue Asymptotics of Perturbed Self-adjoint Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A. A. Shkalikov","submitted_at":"2012-02-23T15:11:01Z","abstract_excerpt":"We study perturbations of a self-adjoint positive operator $T$, provided that a perturbation operator $B$ satisfies \"local\" subordinate condition $\\|B\\varphi_k\\|\\leqslant b\\mu_k^{\\beta}$ with some $\\beta <1$ and $b>0$. Here $\\{\\varphi_k\\}_{k=1}^\\infty$ is an orthonormal system of the eigenvectors of the operator $T$ corresponding to the eigenvalues $\\{\\mu_k\\}_{k=1}^\\infty$. We introduce the concept of $\\alpha$-non-condensing sequence and prove the theorem on the comparison of the eigenvalue-counting functions of the operators $T$ and $T+B$. Namely, it is shown that if $\\{\\mu_k\\}$ is $\\alpha-$n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5204","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":"2026-05-18T04:01:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zDrtPXIx1TJ9vVKzLO37bcQtYat/wZHMG3brc9lVsdAbHNpl+Eo+jusNgtO8WgOK565aAC0bal4kZAoQqX61AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:10:38.984829Z"},"content_sha256":"966f4d185b779c6c5cdccd6c3dc8ec46d4e4cce913a75aa7ea445b4664091e3a","schema_version":"1.0","event_id":"sha256:966f4d185b779c6c5cdccd6c3dc8ec46d4e4cce913a75aa7ea445b4664091e3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YLIDFPQ6P53WPYCXS5QL2HJ47/bundle.json","state_url":"https://pith.science/pith/6YLIDFPQ6P53WPYCXS5QL2HJ47/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YLIDFPQ6P53WPYCXS5QL2HJ47/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":"2026-06-07T06:10:38Z","links":{"resolver":"https://pith.science/pith/6YLIDFPQ6P53WPYCXS5QL2HJ47","bundle":"https://pith.science/pith/6YLIDFPQ6P53WPYCXS5QL2HJ47/bundle.json","state":"https://pith.science/pith/6YLIDFPQ6P53WPYCXS5QL2HJ47/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YLIDFPQ6P53WPYCXS5QL2HJ47/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6YLIDFPQ6P53WPYCXS5QL2HJ47","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":"7cb327a8a2e8b0ee27dd09a46c9e52103ce75ec59372daa5361c5f574d02d184","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-02-23T15:11:01Z","title_canon_sha256":"05cd2f3c476c34cef3e504a1c8de4ab0c5454aec0b0caf6c4250afb3d10eac46"},"schema_version":"1.0","source":{"id":"1202.5204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5204","created_at":"2026-05-18T04:01:38Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5204v1","created_at":"2026-05-18T04:01:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5204","created_at":"2026-05-18T04:01:38Z"},{"alias_kind":"pith_short_12","alias_value":"6YLIDFPQ6P53","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6YLIDFPQ6P53WPYC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6YLIDFPQ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:966f4d185b779c6c5cdccd6c3dc8ec46d4e4cce913a75aa7ea445b4664091e3a","target":"graph","created_at":"2026-05-18T04:01:38Z","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 study perturbations of a self-adjoint positive operator $T$, provided that a perturbation operator $B$ satisfies \"local\" subordinate condition $\\|B\\varphi_k\\|\\leqslant b\\mu_k^{\\beta}$ with some $\\beta <1$ and $b>0$. Here $\\{\\varphi_k\\}_{k=1}^\\infty$ is an orthonormal system of the eigenvectors of the operator $T$ corresponding to the eigenvalues $\\{\\mu_k\\}_{k=1}^\\infty$. We introduce the concept of $\\alpha$-non-condensing sequence and prove the theorem on the comparison of the eigenvalue-counting functions of the operators $T$ and $T+B$. Namely, it is shown that if $\\{\\mu_k\\}$ is $\\alpha-$n","authors_text":"A. A. Shkalikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-02-23T15:11:01Z","title":"Eigenvalue Asymptotics of Perturbed Self-adjoint Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5204","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:fbe0e788f96693c6d54b59c0ea32af8b7569548f7c87c066a50b815a950cdeb4","target":"record","created_at":"2026-05-18T04:01:38Z","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":"7cb327a8a2e8b0ee27dd09a46c9e52103ce75ec59372daa5361c5f574d02d184","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-02-23T15:11:01Z","title_canon_sha256":"05cd2f3c476c34cef3e504a1c8de4ab0c5454aec0b0caf6c4250afb3d10eac46"},"schema_version":"1.0","source":{"id":"1202.5204","kind":"arxiv","version":1}},"canonical_sha256":"f6168195f0f3fbbb3f02bcbb05e8e9e7dbc065f9c68612aeafc3550ebde4541a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6168195f0f3fbbb3f02bcbb05e8e9e7dbc065f9c68612aeafc3550ebde4541a","first_computed_at":"2026-05-18T04:01:38.736149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:38.736149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pr2iOtiDABodIvl2oqIDimvZoFlx0bI7fAIHP0GBLxQ+8S5i7ffYg7fS8xsggdzOoTyFCVkwGFMce13PFM1fBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:38.736726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbe0e788f96693c6d54b59c0ea32af8b7569548f7c87c066a50b815a950cdeb4","sha256:966f4d185b779c6c5cdccd6c3dc8ec46d4e4cce913a75aa7ea445b4664091e3a"],"state_sha256":"96c901ad901f22e2347c0c374105913c75b3b8fd29cf95b49f322e1164c8ed0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"moL6crueAmgyxf1DriePFz77v+tKry7iIY3FAbpF3m4K+lBuVvKimrkto9UNVzupXiQUp1eb5XCLLy52szWrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:10:38.988264Z","bundle_sha256":"986f44d19415c75d5b1c2f8c7f6721f6f5ba3ba8603e9d1d86ab0f79bb20ef49"}}