{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QPBJVOESNQIJYFJELC6RJF5ARB","short_pith_number":"pith:QPBJVOES","canonical_record":{"source":{"id":"1802.03380","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-09T18:42:47Z","cross_cats_sorted":[],"title_canon_sha256":"7c65768d5e8ac8373fb3379cfb5e714da2ca037c2ea9a40741b423d7d5fac25e","abstract_canon_sha256":"b6f4d08f156988105805004c19bc93d8ebf56033209e980c9c278360d0faad83"},"schema_version":"1.0"},"canonical_sha256":"83c29ab8926c109c152458bd1497a08856f1da570f30ebe7526b3c495a098400","source":{"kind":"arxiv","id":"1802.03380","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03380","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03380v3","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03380","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"QPBJVOESNQIJ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPBJVOESNQIJYFJE","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPBJVOES","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QPBJVOESNQIJYFJELC6RJF5ARB","target":"record","payload":{"canonical_record":{"source":{"id":"1802.03380","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-09T18:42:47Z","cross_cats_sorted":[],"title_canon_sha256":"7c65768d5e8ac8373fb3379cfb5e714da2ca037c2ea9a40741b423d7d5fac25e","abstract_canon_sha256":"b6f4d08f156988105805004c19bc93d8ebf56033209e980c9c278360d0faad83"},"schema_version":"1.0"},"canonical_sha256":"83c29ab8926c109c152458bd1497a08856f1da570f30ebe7526b3c495a098400","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:24.541733Z","signature_b64":"PnIBCdVgTOHYRBqVeoCxeddXVTjVbrhc8EQbCYlW8ufuP1zC0Ovt4rDpRPa6F3YOPqZrGo1FbeflBMlFcrpvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83c29ab8926c109c152458bd1497a08856f1da570f30ebe7526b3c495a098400","last_reissued_at":"2026-05-18T00:12:24.541141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:24.541141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.03380","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":"2026-05-18T00:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3O9Xso1XwQsJOvfXSe/VA84O5EGev5ov3OIQ3U4tJfAVv2UHcSp/6U26AumQpxQJsi0Qn7bbif8iZQC5fxdGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:19:07.295933Z"},"content_sha256":"3ed030db5dba49679ab52ea3a929c09ce9a4b7d96b1661012dd14739c170d857","schema_version":"1.0","event_id":"sha256:3ed030db5dba49679ab52ea3a929c09ce9a4b7d96b1661012dd14739c170d857"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QPBJVOESNQIJYFJELC6RJF5ARB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Schr\\\"odinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Pietro d'Avenia","submitted_at":"2018-02-09T18:42:47Z","abstract_excerpt":"We study the following nonlinear Schr\\\"odinger-Bopp-Podolsky system \\[ \\begin{cases} -\\Delta u + \\omega u + q^{2}\\phi u = |u|^{p-2}u -\\Delta \\phi + a^2 \\Delta^2 \\phi = 4\\pi u^2 \\end{cases} \\hbox{ in }\\mathbb{R}^3 \\] with $a,\\omega>0$. We prove existence and nonexistence results depending on the parameters $q,p$. Moreover we also show that, in the radial case, the solutions we find tend to solutions of the classical Schr\\\"odinger-Poisson system as $a\\to0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03380","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":"2026-05-18T00:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2JFoPk2Xt6QvTKlH7VSB00bMBQzm2RGaFKtWgHHQQqYiX1wvHiDwgaXGAzDTGZoNb5J+iL5NkJWPhACoLgIMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:19:07.296311Z"},"content_sha256":"0bbe2eb067d0245429f85ea505a0662e42c4477d7b157ddfcadf6c58908b129e","schema_version":"1.0","event_id":"sha256:0bbe2eb067d0245429f85ea505a0662e42c4477d7b157ddfcadf6c58908b129e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPBJVOESNQIJYFJELC6RJF5ARB/bundle.json","state_url":"https://pith.science/pith/QPBJVOESNQIJYFJELC6RJF5ARB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPBJVOESNQIJYFJELC6RJF5ARB/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":"2026-06-04T23:19:07Z","links":{"resolver":"https://pith.science/pith/QPBJVOESNQIJYFJELC6RJF5ARB","bundle":"https://pith.science/pith/QPBJVOESNQIJYFJELC6RJF5ARB/bundle.json","state":"https://pith.science/pith/QPBJVOESNQIJYFJELC6RJF5ARB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPBJVOESNQIJYFJELC6RJF5ARB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QPBJVOESNQIJYFJELC6RJF5ARB","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":"b6f4d08f156988105805004c19bc93d8ebf56033209e980c9c278360d0faad83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-09T18:42:47Z","title_canon_sha256":"7c65768d5e8ac8373fb3379cfb5e714da2ca037c2ea9a40741b423d7d5fac25e"},"schema_version":"1.0","source":{"id":"1802.03380","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03380","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03380v3","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03380","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"QPBJVOESNQIJ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPBJVOESNQIJYFJE","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPBJVOES","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:0bbe2eb067d0245429f85ea505a0662e42c4477d7b157ddfcadf6c58908b129e","target":"graph","created_at":"2026-05-18T00:12:24Z","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 nonlinear Schr\\\"odinger-Bopp-Podolsky system \\[ \\begin{cases} -\\Delta u + \\omega u + q^{2}\\phi u = |u|^{p-2}u -\\Delta \\phi + a^2 \\Delta^2 \\phi = 4\\pi u^2 \\end{cases} \\hbox{ in }\\mathbb{R}^3 \\] with $a,\\omega>0$. We prove existence and nonexistence results depending on the parameters $q,p$. Moreover we also show that, in the radial case, the solutions we find tend to solutions of the classical Schr\\\"odinger-Poisson system as $a\\to0$.","authors_text":"Gaetano Siciliano, Pietro d'Avenia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-09T18:42:47Z","title":"Nonlinear Schr\\\"odinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03380","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":"sha256:3ed030db5dba49679ab52ea3a929c09ce9a4b7d96b1661012dd14739c170d857","target":"record","created_at":"2026-05-18T00:12:24Z","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":"b6f4d08f156988105805004c19bc93d8ebf56033209e980c9c278360d0faad83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-09T18:42:47Z","title_canon_sha256":"7c65768d5e8ac8373fb3379cfb5e714da2ca037c2ea9a40741b423d7d5fac25e"},"schema_version":"1.0","source":{"id":"1802.03380","kind":"arxiv","version":3}},"canonical_sha256":"83c29ab8926c109c152458bd1497a08856f1da570f30ebe7526b3c495a098400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83c29ab8926c109c152458bd1497a08856f1da570f30ebe7526b3c495a098400","first_computed_at":"2026-05-18T00:12:24.541141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:24.541141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PnIBCdVgTOHYRBqVeoCxeddXVTjVbrhc8EQbCYlW8ufuP1zC0Ovt4rDpRPa6F3YOPqZrGo1FbeflBMlFcrpvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:24.541733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03380","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ed030db5dba49679ab52ea3a929c09ce9a4b7d96b1661012dd14739c170d857","sha256:0bbe2eb067d0245429f85ea505a0662e42c4477d7b157ddfcadf6c58908b129e"],"state_sha256":"7ce2fdb8e26b6844afef82a4c0e8c05c0db26864f08e6bbe32766633277e6248"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsyVReuULCMeUmqCs4r65Umao+QuyjHboUoRkXqdDnHHuHdnJclrDr2tLql9xh6JedrCcHmySvSdd5pThMvdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:19:07.299283Z","bundle_sha256":"bf13b06fccda9f3c35d8712d8b14925c0a56123a022893049744362cf57e5b25"}}