{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SS2YEM7BDVHFVYJJQSX37BXTHT","short_pith_number":"pith:SS2YEM7B","schema_version":"1.0","canonical_sha256":"94b58233e11d4e5ae12984afbf86f33ccaeab3e6ca37f1610f73d56e227fbdf9","source":{"kind":"arxiv","id":"2606.04635","version":1},"attestation_state":"computed","paper":{"title":"Gaussian decay for the Harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Manish Chaurasia","submitted_at":"2026-06-03T09:07:12Z","abstract_excerpt":"We consider the Schr\\\"odinger equation associated with the harmonic oscillator and show that if the initial data and its Fourier transform are dominated by Gaussian functions of widths $a>0$ and $b>0$, respectively, satisfying $ab<1$, then the evolved solution and its Fourier transform are dominated by a Gaussian of width $\\frac{1}{2}\\left(\\frac{1}{a}+\\frac{1}{b}- \\sqrt{\\left(\\frac{1}{a}+\\frac{1}{b}\\right)^2-4}\\right),$ for all times except for a discrete set, and for all times in one dimension. In the one-dimensional case, we prove that these estimates are sharp. Moreover, for a more restrict"},"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":"2606.04635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-03T09:07:12Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c66502c1cb96d0ec1cbab647afce700bbfb4fe40d03a0ee5bf599246ec55f47f","abstract_canon_sha256":"a466fa78e7392bc253c5d5257df25e82313afd15f0b13abb07cb28c6e1503777"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:52.019516Z","signature_b64":"QKeD6iyVpFIuIiZ6+TSzLkz0lTIDfcEd7N5AlMj/pYIwpWi77NGRNHbSVgxWMN9zTi2mjySfvC1XSqgrBHIlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94b58233e11d4e5ae12984afbf86f33ccaeab3e6ca37f1610f73d56e227fbdf9","last_reissued_at":"2026-06-04T01:09:52.018589Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:52.018589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian decay for the Harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Manish Chaurasia","submitted_at":"2026-06-03T09:07:12Z","abstract_excerpt":"We consider the Schr\\\"odinger equation associated with the harmonic oscillator and show that if the initial data and its Fourier transform are dominated by Gaussian functions of widths $a>0$ and $b>0$, respectively, satisfying $ab<1$, then the evolved solution and its Fourier transform are dominated by a Gaussian of width $\\frac{1}{2}\\left(\\frac{1}{a}+\\frac{1}{b}- \\sqrt{\\left(\\frac{1}{a}+\\frac{1}{b}\\right)^2-4}\\right),$ for all times except for a discrete set, and for all times in one dimension. In the one-dimensional case, we prove that these estimates are sharp. Moreover, for a more restrict"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04635","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04635/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.04635","created_at":"2026-06-04T01:09:52.018793+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04635v1","created_at":"2026-06-04T01:09:52.018793+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04635","created_at":"2026-06-04T01:09:52.018793+00:00"},{"alias_kind":"pith_short_12","alias_value":"SS2YEM7BDVHF","created_at":"2026-06-04T01:09:52.018793+00:00"},{"alias_kind":"pith_short_16","alias_value":"SS2YEM7BDVHFVYJJ","created_at":"2026-06-04T01:09:52.018793+00:00"},{"alias_kind":"pith_short_8","alias_value":"SS2YEM7B","created_at":"2026-06-04T01:09:52.018793+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/SS2YEM7BDVHFVYJJQSX37BXTHT","json":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT.json","graph_json":"https://pith.science/api/pith-number/SS2YEM7BDVHFVYJJQSX37BXTHT/graph.json","events_json":"https://pith.science/api/pith-number/SS2YEM7BDVHFVYJJQSX37BXTHT/events.json","paper":"https://pith.science/paper/SS2YEM7B"},"agent_actions":{"view_html":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT","download_json":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT.json","view_paper":"https://pith.science/paper/SS2YEM7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04635&json=true","fetch_graph":"https://pith.science/api/pith-number/SS2YEM7BDVHFVYJJQSX37BXTHT/graph.json","fetch_events":"https://pith.science/api/pith-number/SS2YEM7BDVHFVYJJQSX37BXTHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT/action/storage_attestation","attest_author":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT/action/author_attestation","sign_citation":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT/action/citation_signature","submit_replication":"https://pith.science/pith/SS2YEM7BDVHFVYJJQSX37BXTHT/action/replication_record"}},"created_at":"2026-06-04T01:09:52.018793+00:00","updated_at":"2026-06-04T01:09:52.018793+00:00"}