{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QUB5BG5QNX7IM7GBHCICWUU2RP","short_pith_number":"pith:QUB5BG5Q","canonical_record":{"source":{"id":"2601.17643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-25T01:31:29Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"411cb585ce50e666aa3f7eccbf993d4c260f120eabbb2152df3a8612ea86e67d","abstract_canon_sha256":"58210061d2c595873ba69ce6334be6d57d1ac0d8941df0a25e7e4f30901472d5"},"schema_version":"1.0"},"canonical_sha256":"8503d09bb06dfe867cc138902b529a8bf7a3619532051cc8be9c8928cd151639","source":{"kind":"arxiv","id":"2601.17643","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.17643","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"2601.17643v2","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.17643","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"QUB5BG5QNX7I","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_16","alias_value":"QUB5BG5QNX7IM7GB","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_8","alias_value":"QUB5BG5Q","created_at":"2026-06-29T00:14:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QUB5BG5QNX7IM7GBHCICWUU2RP","target":"record","payload":{"canonical_record":{"source":{"id":"2601.17643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-25T01:31:29Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"411cb585ce50e666aa3f7eccbf993d4c260f120eabbb2152df3a8612ea86e67d","abstract_canon_sha256":"58210061d2c595873ba69ce6334be6d57d1ac0d8941df0a25e7e4f30901472d5"},"schema_version":"1.0"},"canonical_sha256":"8503d09bb06dfe867cc138902b529a8bf7a3619532051cc8be9c8928cd151639","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T00:14:01.919125Z","signature_b64":"gbpThc/u/gwAc0zz4ccTCxkFQv0m/Dro+OEUG9TF5iKf6YWOCuNJicyfUUHS0sEtr8yaZRd/KY5TorLALzYJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8503d09bb06dfe867cc138902b529a8bf7a3619532051cc8be9c8928cd151639","last_reissued_at":"2026-06-29T00:14:01.918661Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T00:14:01.918661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.17643","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":"2026-06-29T00:14:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E8vwxeUR8tapiF4evVEBp9vj+P40u7DEdOjUANjLWQOoQ5LBvOL0sgrcOhVhdFKUqxugN/3e1QVeiP1X5jpkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T03:44:59.884178Z"},"content_sha256":"9d74f38783aaa79f40b9863bb16186286d2eab50df9f21619b7eb5ae262d94a3","schema_version":"1.0","event_id":"sha256:9d74f38783aaa79f40b9863bb16186286d2eab50df9f21619b7eb5ae262d94a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QUB5BG5QNX7IM7GBHCICWUU2RP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic Approximation and Resolvent Estimates for Semiclassical Non-Self-Adjoint Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.SP","authors_text":"Stepan Malkov","submitted_at":"2026-01-25T01:31:29Z","abstract_excerpt":"We study resolvent estimates and bounds on the low lying spectrum for a broad class of non-self-adjoint non-elliptic $h$-pseudodifferential operators with critical points. Imposing dynamical conditions on the average of the real part of the principal symbol along the Hamilton flow of the imaginary part, we establish precise semiclassical resolvent estimates in an $O(h)$-neighborhood of the boundary of the semiclassical pseudospectrum, away from the eigenvalues of quantizations of the quadratic approximations of the principal symbols of the operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.17643","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.17643/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-29T00:14:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzTLMPYayfDGxGiHmKBAXMbokEASe+TI1vKQHx17K18BBeTGUKNHfvx0QM12kqHHA4CCHRQF5RAYquLm/SZyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T03:44:59.884677Z"},"content_sha256":"87a9a994b75908fe6a5a8905cbf1fed7ac1bf10d3bcc836168e1b38762143443","schema_version":"1.0","event_id":"sha256:87a9a994b75908fe6a5a8905cbf1fed7ac1bf10d3bcc836168e1b38762143443"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QUB5BG5QNX7IM7GBHCICWUU2RP/bundle.json","state_url":"https://pith.science/pith/QUB5BG5QNX7IM7GBHCICWUU2RP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QUB5BG5QNX7IM7GBHCICWUU2RP/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":"2026-08-15T03:44:59Z","links":{"resolver":"https://pith.science/pith/QUB5BG5QNX7IM7GBHCICWUU2RP","bundle":"https://pith.science/pith/QUB5BG5QNX7IM7GBHCICWUU2RP/bundle.json","state":"https://pith.science/pith/QUB5BG5QNX7IM7GBHCICWUU2RP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QUB5BG5QNX7IM7GBHCICWUU2RP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QUB5BG5QNX7IM7GBHCICWUU2RP","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":"58210061d2c595873ba69ce6334be6d57d1ac0d8941df0a25e7e4f30901472d5","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-25T01:31:29Z","title_canon_sha256":"411cb585ce50e666aa3f7eccbf993d4c260f120eabbb2152df3a8612ea86e67d"},"schema_version":"1.0","source":{"id":"2601.17643","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.17643","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"2601.17643v2","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.17643","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"QUB5BG5QNX7I","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_16","alias_value":"QUB5BG5QNX7IM7GB","created_at":"2026-06-29T00:14:01Z"},{"alias_kind":"pith_short_8","alias_value":"QUB5BG5Q","created_at":"2026-06-29T00:14:01Z"}],"graph_snapshots":[{"event_id":"sha256:87a9a994b75908fe6a5a8905cbf1fed7ac1bf10d3bcc836168e1b38762143443","target":"graph","created_at":"2026-06-29T00:14:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.17643/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study resolvent estimates and bounds on the low lying spectrum for a broad class of non-self-adjoint non-elliptic $h$-pseudodifferential operators with critical points. Imposing dynamical conditions on the average of the real part of the principal symbol along the Hamilton flow of the imaginary part, we establish precise semiclassical resolvent estimates in an $O(h)$-neighborhood of the boundary of the semiclassical pseudospectrum, away from the eigenvalues of quantizations of the quadratic approximations of the principal symbols of the operators.","authors_text":"Stepan Malkov","cross_cats":["math.AP","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-25T01:31:29Z","title":"Harmonic Approximation and Resolvent Estimates for Semiclassical Non-Self-Adjoint Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.17643","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":"sha256:9d74f38783aaa79f40b9863bb16186286d2eab50df9f21619b7eb5ae262d94a3","target":"record","created_at":"2026-06-29T00:14:01Z","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":"58210061d2c595873ba69ce6334be6d57d1ac0d8941df0a25e7e4f30901472d5","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-01-25T01:31:29Z","title_canon_sha256":"411cb585ce50e666aa3f7eccbf993d4c260f120eabbb2152df3a8612ea86e67d"},"schema_version":"1.0","source":{"id":"2601.17643","kind":"arxiv","version":2}},"canonical_sha256":"8503d09bb06dfe867cc138902b529a8bf7a3619532051cc8be9c8928cd151639","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8503d09bb06dfe867cc138902b529a8bf7a3619532051cc8be9c8928cd151639","first_computed_at":"2026-06-29T00:14:01.918661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T00:14:01.918661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gbpThc/u/gwAc0zz4ccTCxkFQv0m/Dro+OEUG9TF5iKf6YWOCuNJicyfUUHS0sEtr8yaZRd/KY5TorLALzYJCA==","signature_status":"signed_v1","signed_at":"2026-06-29T00:14:01.919125Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.17643","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d74f38783aaa79f40b9863bb16186286d2eab50df9f21619b7eb5ae262d94a3","sha256:87a9a994b75908fe6a5a8905cbf1fed7ac1bf10d3bcc836168e1b38762143443"],"state_sha256":"1e6083910379edfa50af25f6204765f1b7944565d880c0317991eff91d031ebf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qdy3Hjka5y5rryAWwJ1MHyDIlInZg07EDP8iXxCfWsdpd4o2TO4WCnriQr16wULj0FPnzpY52pabncPIYgp6Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T03:44:59.888618Z","bundle_sha256":"44de4299765b65bf69e4ce2efb66e0084e91a767cd0682d984f201a9122d6312"}}