{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NZGFXBPFYAAB772OFGAZUDZKZN","short_pith_number":"pith:NZGFXBPF","canonical_record":{"source":{"id":"1401.0271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T10:46:00Z","cross_cats_sorted":[],"title_canon_sha256":"22fc33352ec827685ed9b6338af7a95db1a5eb183dc7cdf4ee94c1aff5db1004","abstract_canon_sha256":"b023634a5a3708baa0d3459afde4c7d8475632d1d7006ff9f8394deaad36ecf2"},"schema_version":"1.0"},"canonical_sha256":"6e4c5b85e5c0001fff4e29819a0f2acb69e959081e974eabd0aa3e6b4a2425cf","source":{"kind":"arxiv","id":"1401.0271","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0271","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0271v1","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0271","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"pith_short_12","alias_value":"NZGFXBPFYAAB","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NZGFXBPFYAAB772O","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NZGFXBPF","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NZGFXBPFYAAB772OFGAZUDZKZN","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T10:46:00Z","cross_cats_sorted":[],"title_canon_sha256":"22fc33352ec827685ed9b6338af7a95db1a5eb183dc7cdf4ee94c1aff5db1004","abstract_canon_sha256":"b023634a5a3708baa0d3459afde4c7d8475632d1d7006ff9f8394deaad36ecf2"},"schema_version":"1.0"},"canonical_sha256":"6e4c5b85e5c0001fff4e29819a0f2acb69e959081e974eabd0aa3e6b4a2425cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:23.607975Z","signature_b64":"3GZhhb/z6qiWWH5+QWc9laN7qAqlXsDiUZ1Yi5+aIAGPk0nIGavDddkAGE0+5oIWL1jk1zbcdC9IYyKpbBzpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e4c5b85e5c0001fff4e29819a0f2acb69e959081e974eabd0aa3e6b4a2425cf","last_reissued_at":"2026-05-18T03:03:23.607072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:23.607072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0271","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4AmRfmu+Prf8weKaNT9Y49DKFV97hezjQ0m8qS+2YYShJo48T5z8FXfgrWu29f9J2149attYsdjp52k2qfKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:44:58.093998Z"},"content_sha256":"bdb32f34f6c6feba7d4fde90a739fd4aa7849c58599e781f2c415eb46e09c331","schema_version":"1.0","event_id":"sha256:bdb32f34f6c6feba7d4fde90a739fd4aa7849c58599e781f2c415eb46e09c331"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NZGFXBPFYAAB772OFGAZUDZKZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solutions without any symmetry for semilinear elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frank Pacard, Juncheng Wei, Monica Musso, Weiwei Ao","submitted_at":"2014-01-01T10:46:00Z","abstract_excerpt":"We prove the existence of infinitely many solitary waves for the nonlinear Klein-Gordon or Schr\\\"odinger equation $$ \\Delta u-u+ u^3 =0 , $$ in ${\\bf R}^2$, which have finite energy and whose maximal group of symmetry reduces to the identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0271","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tLK11suitObm+ZVhSRVCGUATre1fiQe36rtChRgT8X6cd1SRHT6tT6IVOOaSbLKphJt2IqlDs/VsYNIjgmByDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:44:58.094365Z"},"content_sha256":"e1ab82ef1f26c4a8edbad074daf00f6dfd3a520be8e06facdba8cf4045abc78c","schema_version":"1.0","event_id":"sha256:e1ab82ef1f26c4a8edbad074daf00f6dfd3a520be8e06facdba8cf4045abc78c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/bundle.json","state_url":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZGFXBPFYAAB772OFGAZUDZKZN/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":"2026-06-01T05:44:58Z","links":{"resolver":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN","bundle":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/bundle.json","state":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZGFXBPFYAAB772OFGAZUDZKZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NZGFXBPFYAAB772OFGAZUDZKZN","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":"b023634a5a3708baa0d3459afde4c7d8475632d1d7006ff9f8394deaad36ecf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T10:46:00Z","title_canon_sha256":"22fc33352ec827685ed9b6338af7a95db1a5eb183dc7cdf4ee94c1aff5db1004"},"schema_version":"1.0","source":{"id":"1401.0271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0271","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0271v1","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0271","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"pith_short_12","alias_value":"NZGFXBPFYAAB","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NZGFXBPFYAAB772O","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NZGFXBPF","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:e1ab82ef1f26c4a8edbad074daf00f6dfd3a520be8e06facdba8cf4045abc78c","target":"graph","created_at":"2026-05-18T03:03:23Z","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 prove the existence of infinitely many solitary waves for the nonlinear Klein-Gordon or Schr\\\"odinger equation $$ \\Delta u-u+ u^3 =0 , $$ in ${\\bf R}^2$, which have finite energy and whose maximal group of symmetry reduces to the identity.","authors_text":"Frank Pacard, Juncheng Wei, Monica Musso, Weiwei Ao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T10:46:00Z","title":"Solutions without any symmetry for semilinear elliptic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0271","kind":"arxiv","version":1},"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:bdb32f34f6c6feba7d4fde90a739fd4aa7849c58599e781f2c415eb46e09c331","target":"record","created_at":"2026-05-18T03:03:23Z","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":"b023634a5a3708baa0d3459afde4c7d8475632d1d7006ff9f8394deaad36ecf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T10:46:00Z","title_canon_sha256":"22fc33352ec827685ed9b6338af7a95db1a5eb183dc7cdf4ee94c1aff5db1004"},"schema_version":"1.0","source":{"id":"1401.0271","kind":"arxiv","version":1}},"canonical_sha256":"6e4c5b85e5c0001fff4e29819a0f2acb69e959081e974eabd0aa3e6b4a2425cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e4c5b85e5c0001fff4e29819a0f2acb69e959081e974eabd0aa3e6b4a2425cf","first_computed_at":"2026-05-18T03:03:23.607072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:23.607072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3GZhhb/z6qiWWH5+QWc9laN7qAqlXsDiUZ1Yi5+aIAGPk0nIGavDddkAGE0+5oIWL1jk1zbcdC9IYyKpbBzpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:23.607975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb32f34f6c6feba7d4fde90a739fd4aa7849c58599e781f2c415eb46e09c331","sha256:e1ab82ef1f26c4a8edbad074daf00f6dfd3a520be8e06facdba8cf4045abc78c"],"state_sha256":"c33d0943876ecaa1cd4f5b0371fdf1d93cef4dcc53afda96ff1838def1182226"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBxEYZc987hqy9w3cJXYSFVviwbtZ2HomrwZHhQrpy9IcqUfo0fndd6UreQ/2BYzntu6GKGXS6GcdIq7FCSmDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:44:58.096515Z","bundle_sha256":"7c2a3869c0ba4135104af26b43c59db4785b3021b30a52ada2121b02c5d0a615"}}