{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AWGN23WE72QK5GHIE4ZRY4RV5E","short_pith_number":"pith:AWGN23WE","canonical_record":{"source":{"id":"1208.2545","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-13T11:05:11Z","cross_cats_sorted":[],"title_canon_sha256":"13c275af97ed365cf79fa465372fa30fee502c1bc449c024c79978d2ece0737d","abstract_canon_sha256":"68c0af525188ad8776b1c38017b3db1b5cbcfbd02636ee793d2d37435afaf631"},"schema_version":"1.0"},"canonical_sha256":"058cdd6ec4fea0ae98e827331c7235e92367672ba86009a918d9abd84105a923","source":{"kind":"arxiv","id":"1208.2545","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2545","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2545v2","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2545","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"pith_short_12","alias_value":"AWGN23WE72QK","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AWGN23WE72QK5GHI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AWGN23WE","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AWGN23WE72QK5GHIE4ZRY4RV5E","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2545","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-13T11:05:11Z","cross_cats_sorted":[],"title_canon_sha256":"13c275af97ed365cf79fa465372fa30fee502c1bc449c024c79978d2ece0737d","abstract_canon_sha256":"68c0af525188ad8776b1c38017b3db1b5cbcfbd02636ee793d2d37435afaf631"},"schema_version":"1.0"},"canonical_sha256":"058cdd6ec4fea0ae98e827331c7235e92367672ba86009a918d9abd84105a923","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:16.459602Z","signature_b64":"b37zhvYLFf82FX5tvyrVRuhnLdiZ+CPL2rJy/8LK70wIEgOqDkzU5FZmzX93JJ+IrKW7FCa9oGIhQwRRHa2MAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"058cdd6ec4fea0ae98e827331c7235e92367672ba86009a918d9abd84105a923","last_reissued_at":"2026-05-18T01:55:16.459198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:16.459198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2545","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":"2026-05-18T01:55:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x/pb0HlbBQA88oPEj5Cqqi2Co2fjhNcIVLDtT54rDvweHN63qr0cDWiLXR74RPKjeG62dBOmjiYGvb6fyXPFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:59:27.914238Z"},"content_sha256":"bbd4d59c06c6be8a1c2d44a9d2ec5160d82bc0ffb766d5858ebd7a424d5ffcb2","schema_version":"1.0","event_id":"sha256:bbd4d59c06c6be8a1c2d44a9d2ec5160d82bc0ffb766d5858ebd7a424d5ffcb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AWGN23WE72QK5GHIE4ZRY4RV5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ground state solutions for nonlinear fractional Schr\\\"{o}dinger equations in $\\mathbb{R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Simone Secchi","submitted_at":"2012-08-13T11:05:11Z","abstract_excerpt":"We construct solutions to a class of Schr\\\"{o}dinger equations involving the fractional laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2545","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":"2026-05-18T01:55:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L73v9CqmpwV7qhMACtRUrUZZI8JyqPjtwmYGTabK8mXz8QW+Okt9MVpSStM+PsZTlFskUD/Up1asPXzCsWt9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:59:27.914595Z"},"content_sha256":"905bc6443546db89e2ed3ec41ff5924c7e40070def1047068d8a9665108918b3","schema_version":"1.0","event_id":"sha256:905bc6443546db89e2ed3ec41ff5924c7e40070def1047068d8a9665108918b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWGN23WE72QK5GHIE4ZRY4RV5E/bundle.json","state_url":"https://pith.science/pith/AWGN23WE72QK5GHIE4ZRY4RV5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWGN23WE72QK5GHIE4ZRY4RV5E/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":"2026-07-01T18:59:27Z","links":{"resolver":"https://pith.science/pith/AWGN23WE72QK5GHIE4ZRY4RV5E","bundle":"https://pith.science/pith/AWGN23WE72QK5GHIE4ZRY4RV5E/bundle.json","state":"https://pith.science/pith/AWGN23WE72QK5GHIE4ZRY4RV5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWGN23WE72QK5GHIE4ZRY4RV5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AWGN23WE72QK5GHIE4ZRY4RV5E","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":"68c0af525188ad8776b1c38017b3db1b5cbcfbd02636ee793d2d37435afaf631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-13T11:05:11Z","title_canon_sha256":"13c275af97ed365cf79fa465372fa30fee502c1bc449c024c79978d2ece0737d"},"schema_version":"1.0","source":{"id":"1208.2545","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2545","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2545v2","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2545","created_at":"2026-05-18T01:55:16Z"},{"alias_kind":"pith_short_12","alias_value":"AWGN23WE72QK","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AWGN23WE72QK5GHI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AWGN23WE","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:905bc6443546db89e2ed3ec41ff5924c7e40070def1047068d8a9665108918b3","target":"graph","created_at":"2026-05-18T01:55:16Z","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 construct solutions to a class of Schr\\\"{o}dinger equations involving the fractional laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.","authors_text":"Simone Secchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-13T11:05:11Z","title":"Ground state solutions for nonlinear fractional Schr\\\"{o}dinger equations in $\\mathbb{R}^N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2545","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:bbd4d59c06c6be8a1c2d44a9d2ec5160d82bc0ffb766d5858ebd7a424d5ffcb2","target":"record","created_at":"2026-05-18T01:55:16Z","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":"68c0af525188ad8776b1c38017b3db1b5cbcfbd02636ee793d2d37435afaf631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-13T11:05:11Z","title_canon_sha256":"13c275af97ed365cf79fa465372fa30fee502c1bc449c024c79978d2ece0737d"},"schema_version":"1.0","source":{"id":"1208.2545","kind":"arxiv","version":2}},"canonical_sha256":"058cdd6ec4fea0ae98e827331c7235e92367672ba86009a918d9abd84105a923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"058cdd6ec4fea0ae98e827331c7235e92367672ba86009a918d9abd84105a923","first_computed_at":"2026-05-18T01:55:16.459198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:16.459198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b37zhvYLFf82FX5tvyrVRuhnLdiZ+CPL2rJy/8LK70wIEgOqDkzU5FZmzX93JJ+IrKW7FCa9oGIhQwRRHa2MAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:16.459602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2545","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbd4d59c06c6be8a1c2d44a9d2ec5160d82bc0ffb766d5858ebd7a424d5ffcb2","sha256:905bc6443546db89e2ed3ec41ff5924c7e40070def1047068d8a9665108918b3"],"state_sha256":"629ad54402c5ef154c62f46ba726db5acc2941d1225f0c4dd41d90f6a9ef8526"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"horU/mIcnLJCPMAaqDR4+epWp23abbJOHKIv8rq+cvidtE7GK2aAFZZYNT+WNXrmfFBzIzFqiP45NEKF72hkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T18:59:27.916602Z","bundle_sha256":"eb56f388e4deda4ff517d226bbc196f28dce03aead12e7106a1c05ac2bbf89b9"}}