{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TJ4PZABWS75J5HHAW324X6YEAD","short_pith_number":"pith:TJ4PZABW","schema_version":"1.0","canonical_sha256":"9a78fc803697fa9e9ce0b6f5cbfb0400fd613c18cb4e51052948a436423d09c0","source":{"kind":"arxiv","id":"2607.07115","version":1},"attestation_state":"computed","paper":{"title":"On the Gross-Pitaevskii model with a moving impurity: Cauchy problem and superfluidity criterion","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Martino Caliaro, Paolo Antonelli","submitted_at":"2026-07-08T07:56:46Z","abstract_excerpt":"We study the one-dimensional Gross-Pitaevskii equation with a traveling delta potential and non-zero conditions at infinity. This model describes the effect of a moving impurity in a quantum fluid. Firstly, we show that the associated Cauchy problem is globally well-posed in the energy space. This requires the definition of a conserved energy, which involves the notion of renormalized momentum. Secondly, we study the existence and stability of stationary states in a co-moving reference frame. It is known that there exists an impurity-dependent critical velocity above which no stationary state "},"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":"2607.07115","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T07:56:46Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8d40bc633a438e0db8fa1ee61ea34c5b9a2b8cdebf504122cb540f55c04c5b63","abstract_canon_sha256":"8651bab0ad1efd3caba852f700e65194b66c823243759c8a6f9eed790d610fbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:14.852864Z","signature_b64":"u5sYq05lPHZBFLFaXSzy6+cEfB4d5KftXGJ/IelqUMMMpjH3aHfx9aV7vCCoRhvA1w/jWObpuYA7GoIXvK01DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a78fc803697fa9e9ce0b6f5cbfb0400fd613c18cb4e51052948a436423d09c0","last_reissued_at":"2026-07-09T01:20:14.852364Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:14.852364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Gross-Pitaevskii model with a moving impurity: Cauchy problem and superfluidity criterion","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Martino Caliaro, Paolo Antonelli","submitted_at":"2026-07-08T07:56:46Z","abstract_excerpt":"We study the one-dimensional Gross-Pitaevskii equation with a traveling delta potential and non-zero conditions at infinity. This model describes the effect of a moving impurity in a quantum fluid. Firstly, we show that the associated Cauchy problem is globally well-posed in the energy space. This requires the definition of a conserved energy, which involves the notion of renormalized momentum. Secondly, we study the existence and stability of stationary states in a co-moving reference frame. It is known that there exists an impurity-dependent critical velocity above which no stationary state "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07115","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/2607.07115/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":"2607.07115","created_at":"2026-07-09T01:20:14.852427+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.07115v1","created_at":"2026-07-09T01:20:14.852427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07115","created_at":"2026-07-09T01:20:14.852427+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJ4PZABWS75J","created_at":"2026-07-09T01:20:14.852427+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJ4PZABWS75J5HHA","created_at":"2026-07-09T01:20:14.852427+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJ4PZABW","created_at":"2026-07-09T01:20:14.852427+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/TJ4PZABWS75J5HHAW324X6YEAD","json":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD.json","graph_json":"https://pith.science/api/pith-number/TJ4PZABWS75J5HHAW324X6YEAD/graph.json","events_json":"https://pith.science/api/pith-number/TJ4PZABWS75J5HHAW324X6YEAD/events.json","paper":"https://pith.science/paper/TJ4PZABW"},"agent_actions":{"view_html":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD","download_json":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD.json","view_paper":"https://pith.science/paper/TJ4PZABW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.07115&json=true","fetch_graph":"https://pith.science/api/pith-number/TJ4PZABWS75J5HHAW324X6YEAD/graph.json","fetch_events":"https://pith.science/api/pith-number/TJ4PZABWS75J5HHAW324X6YEAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD/action/storage_attestation","attest_author":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD/action/author_attestation","sign_citation":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD/action/citation_signature","submit_replication":"https://pith.science/pith/TJ4PZABWS75J5HHAW324X6YEAD/action/replication_record"}},"created_at":"2026-07-09T01:20:14.852427+00:00","updated_at":"2026-07-09T01:20:14.852427+00:00"}