{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UUGIZHWMFQSXQJLZ6NXSJP6QII","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8180bf7192d4954f7900f46417440e2f0b6a7834a1fd11050fe58af09e054672","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-22T16:49:07Z","title_canon_sha256":"dc646307dd339dce111eb8ab6405ea1f5a55e136d2bac20608ac6c0da9a5b962"},"schema_version":"1.0","source":{"id":"1206.5201","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5201","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5201v3","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5201","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"pith_short_12","alias_value":"UUGIZHWMFQSX","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UUGIZHWMFQSXQJLZ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UUGIZHWM","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:1769ccee1ac637eaf34e62016efa445bd6d04db4f3c5bf2713912830e5f06b2d","target":"graph","created_at":"2026-05-18T02:45:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study standing waves for a nonlinear Schr\\\"odinger equation on a star graph {$\\mathcal{G}$} i.e. $N$ half-lines joined at a vertex. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\\alpha\\leqslant 0$. The nonlinearity is of focusing power type. The dynamics is given by an equation of the form $ i \\frac{d}{dt}\\Psi_t = H \\Psi_t - | \\Psi_t |^{2\\mu} \\Psi_t $, where $H$ is the Hamiltonian operator which generates the linear Schr\\\"odinger dynamics. We show the existence of several families of standing waves for every sign of the coupling at the ve","authors_text":"C. Cacciapuoti, D. Finco, D. Noja, R. Adami","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-22T16:49:07Z","title":"Variational properties and orbital stability of standing waves for NLS equation on a star graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5201","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:973295a366b494d2c539187b10c7f41d8a9e06777f797eca6add4a344508042e","target":"record","created_at":"2026-05-18T02:45:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8180bf7192d4954f7900f46417440e2f0b6a7834a1fd11050fe58af09e054672","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-22T16:49:07Z","title_canon_sha256":"dc646307dd339dce111eb8ab6405ea1f5a55e136d2bac20608ac6c0da9a5b962"},"schema_version":"1.0","source":{"id":"1206.5201","kind":"arxiv","version":3}},"canonical_sha256":"a50c8c9ecc2c25782579f36f24bfd0421eac454a121be2d19b97953464ceb783","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a50c8c9ecc2c25782579f36f24bfd0421eac454a121be2d19b97953464ceb783","first_computed_at":"2026-05-18T02:45:39.681062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:39.681062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXC424IuZg7TstOxh82AZSd3+yO1qBl0J70N2p/oU4Wnj354LcGbAv6dlETbcllnlZgfsZBno36G6/FlLOvzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:39.681642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5201","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:973295a366b494d2c539187b10c7f41d8a9e06777f797eca6add4a344508042e","sha256:1769ccee1ac637eaf34e62016efa445bd6d04db4f3c5bf2713912830e5f06b2d"],"state_sha256":"088fde554d3a10b6cba3b89508e0d8b50e0001bb5bfd525e36ac4361a21e7358"}