{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RKPPTZFV5HCI7EMI7KPQB4AQET","short_pith_number":"pith:RKPPTZFV","canonical_record":{"source":{"id":"1611.03319","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T14:44:38Z","cross_cats_sorted":[],"title_canon_sha256":"40c7d14f400ff82534e04033d14a8e5bca949ba415d2bc4a10557a076532cd30","abstract_canon_sha256":"0db4567e299e3dbb697c21f6e91b6f56fd025977aa9d2ea727c589c006ebb7c0"},"schema_version":"1.0"},"canonical_sha256":"8a9ef9e4b5e9c48f9188fa9f00f01024d4d35d42d21f40f12bd8b3ae921bef92","source":{"kind":"arxiv","id":"1611.03319","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03319","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03319v3","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03319","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"RKPPTZFV5HCI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RKPPTZFV5HCI7EMI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RKPPTZFV","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RKPPTZFV5HCI7EMI7KPQB4AQET","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03319","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T14:44:38Z","cross_cats_sorted":[],"title_canon_sha256":"40c7d14f400ff82534e04033d14a8e5bca949ba415d2bc4a10557a076532cd30","abstract_canon_sha256":"0db4567e299e3dbb697c21f6e91b6f56fd025977aa9d2ea727c589c006ebb7c0"},"schema_version":"1.0"},"canonical_sha256":"8a9ef9e4b5e9c48f9188fa9f00f01024d4d35d42d21f40f12bd8b3ae921bef92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:36.290787Z","signature_b64":"Oi+V3nvU3YNXiaI0KPJK0OL698CXbQaP4QKaAqNQo/3IfrUcgj2r2frhLUvDRrGQ5gdcKZZ2jFVcW9hlZ3ICBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a9ef9e4b5e9c48f9188fa9f00f01024d4d35d42d21f40f12bd8b3ae921bef92","last_reissued_at":"2026-05-18T00:31:36.290163Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:36.290163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03319","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZowmmtuPh0lDOO59NtuQOfENeul4+7o1eclaly4hLV0dd9pZCCNwwlR3m4AQDGA+rClWiBINRNK86uYpR1LzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:33:36.961392Z"},"content_sha256":"041fd91d3ddc047820e06e838653e96424fe61a3c48c0a8bb9a83b4a19bf5049","schema_version":"1.0","event_id":"sha256:041fd91d3ddc047820e06e838653e96424fe61a3c48c0a8bb9a83b4a19bf5049"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RKPPTZFV5HCI7EMI7KPQB4AQET","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic NLS equation on star graphs: existence and stability of standing waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alex H. Ardila","submitted_at":"2016-11-10T14:44:38Z","abstract_excerpt":"In this paper we consider the logarithmic Schr\\\"{o}dinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. Then we show the existence of several families of standing waves. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we show that the ground states are orbitally stable via a variational approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03319","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGvrpazvKy2TmNHaZnecySvEL5svaiEjTjJRuIP1RZJsr9pPaKC16GeSV8xCaUJvBryho90Btf78IzSp0+LECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:33:36.961742Z"},"content_sha256":"16122049e6b0bc1928fd8d9ba5792f281593930c3e627ddb945f44a0d741118f","schema_version":"1.0","event_id":"sha256:16122049e6b0bc1928fd8d9ba5792f281593930c3e627ddb945f44a0d741118f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKPPTZFV5HCI7EMI7KPQB4AQET/bundle.json","state_url":"https://pith.science/pith/RKPPTZFV5HCI7EMI7KPQB4AQET/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKPPTZFV5HCI7EMI7KPQB4AQET/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T09:33:36Z","links":{"resolver":"https://pith.science/pith/RKPPTZFV5HCI7EMI7KPQB4AQET","bundle":"https://pith.science/pith/RKPPTZFV5HCI7EMI7KPQB4AQET/bundle.json","state":"https://pith.science/pith/RKPPTZFV5HCI7EMI7KPQB4AQET/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKPPTZFV5HCI7EMI7KPQB4AQET/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RKPPTZFV5HCI7EMI7KPQB4AQET","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":"0db4567e299e3dbb697c21f6e91b6f56fd025977aa9d2ea727c589c006ebb7c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T14:44:38Z","title_canon_sha256":"40c7d14f400ff82534e04033d14a8e5bca949ba415d2bc4a10557a076532cd30"},"schema_version":"1.0","source":{"id":"1611.03319","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03319","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03319v3","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03319","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"RKPPTZFV5HCI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RKPPTZFV5HCI7EMI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RKPPTZFV","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:16122049e6b0bc1928fd8d9ba5792f281593930c3e627ddb945f44a0d741118f","target":"graph","created_at":"2026-05-18T00:31:36Z","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":"In this paper we consider the logarithmic Schr\\\"{o}dinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. Then we show the existence of several families of standing waves. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we show that the ground states are orbitally stable via a variational approach.","authors_text":"Alex H. Ardila","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T14:44:38Z","title":"Logarithmic NLS equation on star graphs: existence and stability of standing waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03319","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":"sha256:041fd91d3ddc047820e06e838653e96424fe61a3c48c0a8bb9a83b4a19bf5049","target":"record","created_at":"2026-05-18T00:31:36Z","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":"0db4567e299e3dbb697c21f6e91b6f56fd025977aa9d2ea727c589c006ebb7c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-10T14:44:38Z","title_canon_sha256":"40c7d14f400ff82534e04033d14a8e5bca949ba415d2bc4a10557a076532cd30"},"schema_version":"1.0","source":{"id":"1611.03319","kind":"arxiv","version":3}},"canonical_sha256":"8a9ef9e4b5e9c48f9188fa9f00f01024d4d35d42d21f40f12bd8b3ae921bef92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a9ef9e4b5e9c48f9188fa9f00f01024d4d35d42d21f40f12bd8b3ae921bef92","first_computed_at":"2026-05-18T00:31:36.290163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:36.290163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oi+V3nvU3YNXiaI0KPJK0OL698CXbQaP4QKaAqNQo/3IfrUcgj2r2frhLUvDRrGQ5gdcKZZ2jFVcW9hlZ3ICBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:36.290787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03319","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:041fd91d3ddc047820e06e838653e96424fe61a3c48c0a8bb9a83b4a19bf5049","sha256:16122049e6b0bc1928fd8d9ba5792f281593930c3e627ddb945f44a0d741118f"],"state_sha256":"d443a15a1df134867b01994930eee1f4ec63157b4a8c4768c548afdd34db2864"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dUVEIB6z7ib0GkUCVVs67eraSrOFhfsFhS3sgvgVjdWfjkUYHoMgdloN4dSCsCQMgInX3A2NnLdOQSZ/9kIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:33:36.963636Z","bundle_sha256":"de109f769d1c5cc3bc363f9c5c673fdee263deefc23b8f508cce98d851db3944"}}