{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5BT3RQQKUAYJ2JYQQB3NAPLJNN","short_pith_number":"pith:5BT3RQQK","schema_version":"1.0","canonical_sha256":"e867b8c20aa0309d27108076d03d696b734ce9840dd0f3834f6ce11fce7cc7df","source":{"kind":"arxiv","id":"1411.7907","version":2},"attestation_state":"computed","paper":{"title":"Majorization, 4G Theorem and Schr\\\"odinger perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Karol Szczypkowski, Krzysztof Bogdan, Yana Butko","submitted_at":"2014-11-28T15:34:20Z","abstract_excerpt":"Schr\\\"odinger perturbations of transition densities by singular potentials may fail to be comparable with the original transition density. For instance this is so for the transition density of a subordinator perturbed by any time-independent unbounded potential. In order to estimate such perturbations it is convenient to use an auxilary transition density as a majorant and the 4G inequality for the original transition density and the majorant. We prove the 4G inequality for the $1/2$-stable and inverse Gaussian subordinators, discuss the corresponding class of admissible potentials and indicat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.7907","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-28T15:34:20Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"1b9b1a635de3cd64305fdfeb639dc6efaacdf54ccf974dd39b71be58727201a2","abstract_canon_sha256":"1c09af5999f70cdb9899c06a05dd804732720080abe47611baa25feda7e77241"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:13.312105Z","signature_b64":"cMkZwmy0tSyS8Dg/vbWoiEGI+Po7Oi5zPK3KhZ6xUf5OzXWl9puUJGrfcmIxddy+vecohkgY8Tk9VmGPWF0SAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e867b8c20aa0309d27108076d03d696b734ce9840dd0f3834f6ce11fce7cc7df","last_reissued_at":"2026-05-18T00:41:13.311405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:13.311405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Majorization, 4G Theorem and Schr\\\"odinger perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Karol Szczypkowski, Krzysztof Bogdan, Yana Butko","submitted_at":"2014-11-28T15:34:20Z","abstract_excerpt":"Schr\\\"odinger perturbations of transition densities by singular potentials may fail to be comparable with the original transition density. For instance this is so for the transition density of a subordinator perturbed by any time-independent unbounded potential. In order to estimate such perturbations it is convenient to use an auxilary transition density as a majorant and the 4G inequality for the original transition density and the majorant. We prove the 4G inequality for the $1/2$-stable and inverse Gaussian subordinators, discuss the corresponding class of admissible potentials and indicat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7907","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.7907","created_at":"2026-05-18T00:41:13.311527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.7907v2","created_at":"2026-05-18T00:41:13.311527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7907","created_at":"2026-05-18T00:41:13.311527+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BT3RQQKUAYJ","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BT3RQQKUAYJ2JYQ","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BT3RQQK","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN","json":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN.json","graph_json":"https://pith.science/api/pith-number/5BT3RQQKUAYJ2JYQQB3NAPLJNN/graph.json","events_json":"https://pith.science/api/pith-number/5BT3RQQKUAYJ2JYQQB3NAPLJNN/events.json","paper":"https://pith.science/paper/5BT3RQQK"},"agent_actions":{"view_html":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN","download_json":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN.json","view_paper":"https://pith.science/paper/5BT3RQQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.7907&json=true","fetch_graph":"https://pith.science/api/pith-number/5BT3RQQKUAYJ2JYQQB3NAPLJNN/graph.json","fetch_events":"https://pith.science/api/pith-number/5BT3RQQKUAYJ2JYQQB3NAPLJNN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN/action/storage_attestation","attest_author":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN/action/author_attestation","sign_citation":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN/action/citation_signature","submit_replication":"https://pith.science/pith/5BT3RQQKUAYJ2JYQQB3NAPLJNN/action/replication_record"}},"created_at":"2026-05-18T00:41:13.311527+00:00","updated_at":"2026-05-18T00:41:13.311527+00:00"}