{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XS6FOFKBHWL7W3AGJPFRMX2F7F","short_pith_number":"pith:XS6FOFKB","schema_version":"1.0","canonical_sha256":"bcbc5715413d97fb6c064bcb165f45f9775cdcd162ef0f0262051a28fec48e2e","source":{"kind":"arxiv","id":"2501.01258","version":1},"attestation_state":"computed","paper":{"title":"Quantitative observability for the Schr\\\"{o}dinger equation with an anharmonic oscillator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Gengsheng Wang, Ming Wang, Shanlin Huang","submitted_at":"2025-01-02T13:53:35Z","abstract_excerpt":"This paper studies the observability inequalities for the Schr\\\"{o}dinger equation associated with an anharmonic oscillator $H=-\\frac{\\d^2}{\\d x^2}+|x|$. We build up the observability inequality over an arbitrarily short time interval $(0,T)$, with an explicit expression for the observation constant $C_{obs}$ in terms of $T$, for some observable set that has a different geometric structure compared to those discussed in \\cite{HWW}. We obtain the sufficient conditions and the necessary conditions for observable sets, respectively. We also present counterexamples to demonstrate that half-lines a"},"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":"2501.01258","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-01-02T13:53:35Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"83b39b785da8c33bbcf637b859ef15fd1e3e84c83bfb64776395dc2cc854b32d","abstract_canon_sha256":"ced531c2e8e603cbd315a91ca964bdce2b8ef1a9ba37037016005c333a04a787"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:16.941918Z","signature_b64":"eAcESXysbQzgLcG/J0Ym9wn2D1D34ZCV483tmm7tZqPdMEa/aeJIRgdCjSpUBwQiJG+w1+fbqW5kCTNM6itzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcbc5715413d97fb6c064bcb165f45f9775cdcd162ef0f0262051a28fec48e2e","last_reissued_at":"2026-07-05T09:56:16.941465Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:16.941465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative observability for the Schr\\\"{o}dinger equation with an anharmonic oscillator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Gengsheng Wang, Ming Wang, Shanlin Huang","submitted_at":"2025-01-02T13:53:35Z","abstract_excerpt":"This paper studies the observability inequalities for the Schr\\\"{o}dinger equation associated with an anharmonic oscillator $H=-\\frac{\\d^2}{\\d x^2}+|x|$. We build up the observability inequality over an arbitrarily short time interval $(0,T)$, with an explicit expression for the observation constant $C_{obs}$ in terms of $T$, for some observable set that has a different geometric structure compared to those discussed in \\cite{HWW}. We obtain the sufficient conditions and the necessary conditions for observable sets, respectively. We also present counterexamples to demonstrate that half-lines a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01258","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/2501.01258/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":"2501.01258","created_at":"2026-07-05T09:56:16.941522+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.01258v1","created_at":"2026-07-05T09:56:16.941522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01258","created_at":"2026-07-05T09:56:16.941522+00:00"},{"alias_kind":"pith_short_12","alias_value":"XS6FOFKBHWL7","created_at":"2026-07-05T09:56:16.941522+00:00"},{"alias_kind":"pith_short_16","alias_value":"XS6FOFKBHWL7W3AG","created_at":"2026-07-05T09:56:16.941522+00:00"},{"alias_kind":"pith_short_8","alias_value":"XS6FOFKB","created_at":"2026-07-05T09:56:16.941522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.13740","citing_title":"The periodic KdV with control on space-time measurable sets","ref_index":25,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F","json":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F.json","graph_json":"https://pith.science/api/pith-number/XS6FOFKBHWL7W3AGJPFRMX2F7F/graph.json","events_json":"https://pith.science/api/pith-number/XS6FOFKBHWL7W3AGJPFRMX2F7F/events.json","paper":"https://pith.science/paper/XS6FOFKB"},"agent_actions":{"view_html":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F","download_json":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F.json","view_paper":"https://pith.science/paper/XS6FOFKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.01258&json=true","fetch_graph":"https://pith.science/api/pith-number/XS6FOFKBHWL7W3AGJPFRMX2F7F/graph.json","fetch_events":"https://pith.science/api/pith-number/XS6FOFKBHWL7W3AGJPFRMX2F7F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F/action/storage_attestation","attest_author":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F/action/author_attestation","sign_citation":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F/action/citation_signature","submit_replication":"https://pith.science/pith/XS6FOFKBHWL7W3AGJPFRMX2F7F/action/replication_record"}},"created_at":"2026-07-05T09:56:16.941522+00:00","updated_at":"2026-07-05T09:56:16.941522+00:00"}