{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SMBUD4I5TWZA3QYZTMGO6OVEUV","short_pith_number":"pith:SMBUD4I5","schema_version":"1.0","canonical_sha256":"930341f11d9db20dc3199b0cef3aa4a541dbfbe42407d67105a2857fad20eead","source":{"kind":"arxiv","id":"1509.01810","version":1},"attestation_state":"computed","paper":{"title":"Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudio Cacciapuoti, Diego Noja, Domenico Finco, Riccardo Adami","submitted_at":"2015-09-06T13:18:08Z","abstract_excerpt":"On a star graph made of $N \\geq 3$ halflines (edges) we consider a Schr\\\"odinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. From previous works it is known that there exists a family of standing waves, symmetric with respect to the exchange of edges, that can be parametrized by the mass (or $L^2$-norm) of its elements. Furthermore, if the mass is small enough, then the corresponding symmetric standing wave is a ground state and, consequently, it is orbitally stable. On the other hand, if the mass is above a threshold value, th"},"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":"1509.01810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-06T13:18:08Z","cross_cats_sorted":[],"title_canon_sha256":"1f7882d54f6cea556bf910522142923d3b3f822f64408fe9f5df4fe12acd8339","abstract_canon_sha256":"b6ab52f78feb2d23c40bfb4ba0758a640a4a248670333a75a9b6c109a0533378"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:50.488832Z","signature_b64":"HlOK78fJjI7nD18HOj9qzj3z5zmhIFVPLYY8tYwZAjhFRzejmarmD2EMWKXbx8EpCS3OKPpgs5G28lhX6igVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"930341f11d9db20dc3199b0cef3aa4a541dbfbe42407d67105a2857fad20eead","last_reissued_at":"2026-05-18T01:33:50.488219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:50.488219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudio Cacciapuoti, Diego Noja, Domenico Finco, Riccardo Adami","submitted_at":"2015-09-06T13:18:08Z","abstract_excerpt":"On a star graph made of $N \\geq 3$ halflines (edges) we consider a Schr\\\"odinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. From previous works it is known that there exists a family of standing waves, symmetric with respect to the exchange of edges, that can be parametrized by the mass (or $L^2$-norm) of its elements. Furthermore, if the mass is small enough, then the corresponding symmetric standing wave is a ground state and, consequently, it is orbitally stable. On the other hand, if the mass is above a threshold value, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01810","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":""},"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":"1509.01810","created_at":"2026-05-18T01:33:50.488309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01810v1","created_at":"2026-05-18T01:33:50.488309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01810","created_at":"2026-05-18T01:33:50.488309+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMBUD4I5TWZA","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMBUD4I5TWZA3QYZ","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMBUD4I5","created_at":"2026-05-18T12:29:42.218222+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/SMBUD4I5TWZA3QYZTMGO6OVEUV","json":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV.json","graph_json":"https://pith.science/api/pith-number/SMBUD4I5TWZA3QYZTMGO6OVEUV/graph.json","events_json":"https://pith.science/api/pith-number/SMBUD4I5TWZA3QYZTMGO6OVEUV/events.json","paper":"https://pith.science/paper/SMBUD4I5"},"agent_actions":{"view_html":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV","download_json":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV.json","view_paper":"https://pith.science/paper/SMBUD4I5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01810&json=true","fetch_graph":"https://pith.science/api/pith-number/SMBUD4I5TWZA3QYZTMGO6OVEUV/graph.json","fetch_events":"https://pith.science/api/pith-number/SMBUD4I5TWZA3QYZTMGO6OVEUV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV/action/storage_attestation","attest_author":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV/action/author_attestation","sign_citation":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV/action/citation_signature","submit_replication":"https://pith.science/pith/SMBUD4I5TWZA3QYZTMGO6OVEUV/action/replication_record"}},"created_at":"2026-05-18T01:33:50.488309+00:00","updated_at":"2026-05-18T01:33:50.488309+00:00"}