{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7WS6DFFEU3QRCCKXGXGDHM4YTM","short_pith_number":"pith:7WS6DFFE","canonical_record":{"source":{"id":"1212.3773","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-16T10:44:45Z","cross_cats_sorted":[],"title_canon_sha256":"35264144da404aba99df2ad01bea6795abf60603b86656dcbeb61b1fc6da857d","abstract_canon_sha256":"cf5ec9a3d4a89021ca413663deee27e93fb4b8167e8b28134672e9cbaaf617c6"},"schema_version":"1.0"},"canonical_sha256":"fda5e194a4a6e111095735cc33b3989b13a68fc7ec74f797ea51e916f1ff5f20","source":{"kind":"arxiv","id":"1212.3773","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3773","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3773v2","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3773","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"pith_short_12","alias_value":"7WS6DFFEU3QR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7WS6DFFEU3QRCCKX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7WS6DFFE","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7WS6DFFEU3QRCCKXGXGDHM4YTM","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3773","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-16T10:44:45Z","cross_cats_sorted":[],"title_canon_sha256":"35264144da404aba99df2ad01bea6795abf60603b86656dcbeb61b1fc6da857d","abstract_canon_sha256":"cf5ec9a3d4a89021ca413663deee27e93fb4b8167e8b28134672e9cbaaf617c6"},"schema_version":"1.0"},"canonical_sha256":"fda5e194a4a6e111095735cc33b3989b13a68fc7ec74f797ea51e916f1ff5f20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:06.268384Z","signature_b64":"/1wtSuTSRLuaOVSbA1Jg9TdJ0gHy0lC9v/6UX3eZrbOxKGSKmLZFKZYGV0yDgqvSfaWVcuTPdtnCqGiq3W0IAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fda5e194a4a6e111095735cc33b3989b13a68fc7ec74f797ea51e916f1ff5f20","last_reissued_at":"2026-05-18T02:42:06.267901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:06.267901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3773","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fjUl3xJPPKUxx0XfLCJ9Hhajy/cTrtwdQkDYL3lN9KSZeMB4IQPF+Kc482ichLutHsjRbRBuZGKu82WHInh4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:14:14.094726Z"},"content_sha256":"778805e418ea57fc923ffa819015380dffff1ae8e76b026be2cb19569edc490f","schema_version":"1.0","event_id":"sha256:778805e418ea57fc923ffa819015380dffff1ae8e76b026be2cb19569edc490f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7WS6DFFEU3QRCCKXGXGDHM4YTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Wenming Zou, Zhijie Chen","submitted_at":"2012-12-16T10:44:45Z","abstract_excerpt":"We study the following coupled Schr\\\"{o}dinger equations which have appeared as several models from mathematical physics: {displaymath} {cases}-\\Delta u_1 +\\la_1 u_1 = \\mu_1 u_1^3+\\beta u_1 u_2^2, \\quad x\\in \\Omega, -\\Delta u_2 +\\la_2 u_2 =\\mu_2 u_2^3+\\beta u_1^2 u_2, \\quad x\\in \\Om, u_1=u_2=0 \\,\\,\\,\\hbox{on \\,$\\partial\\Om$}.{cases}{displaymath} Here $\\Om$ is a smooth bounded domain in $\\R^N (N=2, 3)$ or $\\Om=\\RN$, $\\la_1,\\, \\la_2$, $\\mu_1,\\,\\mu_2$ are all positive constants and the coupling constant $\\bb<0$. We show that this system has infinitely many sign-changing solutions. We also obtain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3773","kind":"arxiv","version":2},"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":"2026-05-18T02:42:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sETEVW3gNeN7Si1YdulZ+7LJmG7TjXwmaqTpjtlAbuXtUfflDE13FLnZtyZczOstrjNEsmaE20BOcKZ65Z33Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:14:14.095180Z"},"content_sha256":"4fb6924afaafefa7c681e65e41e94dfedeb9ff79e7ab76b51d6ea76b5f5ec933","schema_version":"1.0","event_id":"sha256:4fb6924afaafefa7c681e65e41e94dfedeb9ff79e7ab76b51d6ea76b5f5ec933"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7WS6DFFEU3QRCCKXGXGDHM4YTM/bundle.json","state_url":"https://pith.science/pith/7WS6DFFEU3QRCCKXGXGDHM4YTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7WS6DFFEU3QRCCKXGXGDHM4YTM/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":"2026-05-27T11:14:14Z","links":{"resolver":"https://pith.science/pith/7WS6DFFEU3QRCCKXGXGDHM4YTM","bundle":"https://pith.science/pith/7WS6DFFEU3QRCCKXGXGDHM4YTM/bundle.json","state":"https://pith.science/pith/7WS6DFFEU3QRCCKXGXGDHM4YTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7WS6DFFEU3QRCCKXGXGDHM4YTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7WS6DFFEU3QRCCKXGXGDHM4YTM","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":"cf5ec9a3d4a89021ca413663deee27e93fb4b8167e8b28134672e9cbaaf617c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-16T10:44:45Z","title_canon_sha256":"35264144da404aba99df2ad01bea6795abf60603b86656dcbeb61b1fc6da857d"},"schema_version":"1.0","source":{"id":"1212.3773","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3773","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3773v2","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3773","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"pith_short_12","alias_value":"7WS6DFFEU3QR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7WS6DFFEU3QRCCKX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7WS6DFFE","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:4fb6924afaafefa7c681e65e41e94dfedeb9ff79e7ab76b51d6ea76b5f5ec933","target":"graph","created_at":"2026-05-18T02:42:06Z","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 the following coupled Schr\\\"{o}dinger equations which have appeared as several models from mathematical physics: {displaymath} {cases}-\\Delta u_1 +\\la_1 u_1 = \\mu_1 u_1^3+\\beta u_1 u_2^2, \\quad x\\in \\Omega, -\\Delta u_2 +\\la_2 u_2 =\\mu_2 u_2^3+\\beta u_1^2 u_2, \\quad x\\in \\Om, u_1=u_2=0 \\,\\,\\,\\hbox{on \\,$\\partial\\Om$}.{cases}{displaymath} Here $\\Om$ is a smooth bounded domain in $\\R^N (N=2, 3)$ or $\\Om=\\RN$, $\\la_1,\\, \\la_2$, $\\mu_1,\\,\\mu_2$ are all positive constants and the coupling constant $\\bb<0$. We show that this system has infinitely many sign-changing solutions. We also obtain ","authors_text":"Chang-shou Lin, Wenming Zou, Zhijie Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-16T10:44:45Z","title":"Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3773","kind":"arxiv","version":2},"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":"sha256:778805e418ea57fc923ffa819015380dffff1ae8e76b026be2cb19569edc490f","target":"record","created_at":"2026-05-18T02:42:06Z","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":"cf5ec9a3d4a89021ca413663deee27e93fb4b8167e8b28134672e9cbaaf617c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-16T10:44:45Z","title_canon_sha256":"35264144da404aba99df2ad01bea6795abf60603b86656dcbeb61b1fc6da857d"},"schema_version":"1.0","source":{"id":"1212.3773","kind":"arxiv","version":2}},"canonical_sha256":"fda5e194a4a6e111095735cc33b3989b13a68fc7ec74f797ea51e916f1ff5f20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fda5e194a4a6e111095735cc33b3989b13a68fc7ec74f797ea51e916f1ff5f20","first_computed_at":"2026-05-18T02:42:06.267901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:06.267901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/1wtSuTSRLuaOVSbA1Jg9TdJ0gHy0lC9v/6UX3eZrbOxKGSKmLZFKZYGV0yDgqvSfaWVcuTPdtnCqGiq3W0IAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:06.268384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3773","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:778805e418ea57fc923ffa819015380dffff1ae8e76b026be2cb19569edc490f","sha256:4fb6924afaafefa7c681e65e41e94dfedeb9ff79e7ab76b51d6ea76b5f5ec933"],"state_sha256":"2c92c14b5b033a39db337ac1d7a2056407c201029f99a7ea2adc515675ca655d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7Qq7R7eSiSxjC9mo+2vzNEzd8o2WU55a548lb8HJJc2kkoABcAeU0on40XzPG0y52Ik5Or6GyqdsMCdJfoEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:14:14.097675Z","bundle_sha256":"2db6c57a1577b1873d1d3e20af87974d16e2bbb4cd8f9901b63e320cebb20803"}}