{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JAOPHNN63QOVUOZASO2NSH75L2","short_pith_number":"pith:JAOPHNN6","canonical_record":{"source":{"id":"1701.02885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T08:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"cd28c3f1c5976fd967ff80698ca92e838536f5b90aae306386e68e610e233af8","abstract_canon_sha256":"88f64402dc0daf7cc279c9d768ba6c0d3c6781d4c04d9da3c2497ba94952fa19"},"schema_version":"1.0"},"canonical_sha256":"481cf3b5bedc1d5a3b2093b4d91ffd5e966edd12c7f1a0b095c389165afa41cc","source":{"kind":"arxiv","id":"1701.02885","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02885","created_at":"2026-05-18T00:52:59Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02885v1","created_at":"2026-05-18T00:52:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02885","created_at":"2026-05-18T00:52:59Z"},{"alias_kind":"pith_short_12","alias_value":"JAOPHNN63QOV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JAOPHNN63QOVUOZA","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JAOPHNN6","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JAOPHNN63QOVUOZASO2NSH75L2","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T08:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"cd28c3f1c5976fd967ff80698ca92e838536f5b90aae306386e68e610e233af8","abstract_canon_sha256":"88f64402dc0daf7cc279c9d768ba6c0d3c6781d4c04d9da3c2497ba94952fa19"},"schema_version":"1.0"},"canonical_sha256":"481cf3b5bedc1d5a3b2093b4d91ffd5e966edd12c7f1a0b095c389165afa41cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:59.913863Z","signature_b64":"atFI48YbE8vnv55YRELTph7N5rkHoRrjlH++kEPdZ/Z+q4+5iQVpF5WyhcKfyvjwq3dMa8CyX98l3T5EiTskBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"481cf3b5bedc1d5a3b2093b4d91ffd5e966edd12c7f1a0b095c389165afa41cc","last_reissued_at":"2026-05-18T00:52:59.913361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:59.913361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02885","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":"2026-05-18T00:52:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p7YHyVj+g4Ooi+WCV26HcJMl1+Ir5DBt/xRrQjGGdno1zRQLj2tfaCX0elxCouab/e5OyTvYBemhVUx+e3tCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:17:29.082500Z"},"content_sha256":"1db2d7789b86729558ba1a034e4de4a07eb4cb6dab3e3cc6b8e43e19e55862be","schema_version":"1.0","event_id":"sha256:1db2d7789b86729558ba1a034e4de4a07eb4cb6dab3e3cc6b8e43e19e55862be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JAOPHNN63QOVUOZASO2NSH75L2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of solutions for a semirelativistic Hartree equation with unbounded potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Simone Secchi","submitted_at":"2017-01-11T08:31:53Z","abstract_excerpt":"We prove the existence of a solution to the semirelativistic Hartree equation $$\\sqrt{-\\Delta+m^2}u+ V(x) u = A(x)\\left( W * |u|^p \\right) |u|^{p-2}u $$ under suitable growth assumption on the potential functions $V$ and $A$. In particular, both can be unbounded from above."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02885","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":"2026-05-18T00:52:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Cn05nDF2kRlrbm66QzAmP7262Gsz7lKrthfXCRY7rD/GKW16BVDspIdZnXwaWA7GLsqltk5SaNg2l1JdwUTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:17:29.082966Z"},"content_sha256":"79f50dcb342f13aedd8fb0893df015caa7d7c579afc5b418cd79f6f89b590cad","schema_version":"1.0","event_id":"sha256:79f50dcb342f13aedd8fb0893df015caa7d7c579afc5b418cd79f6f89b590cad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAOPHNN63QOVUOZASO2NSH75L2/bundle.json","state_url":"https://pith.science/pith/JAOPHNN63QOVUOZASO2NSH75L2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAOPHNN63QOVUOZASO2NSH75L2/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":"2026-07-03T00:17:29Z","links":{"resolver":"https://pith.science/pith/JAOPHNN63QOVUOZASO2NSH75L2","bundle":"https://pith.science/pith/JAOPHNN63QOVUOZASO2NSH75L2/bundle.json","state":"https://pith.science/pith/JAOPHNN63QOVUOZASO2NSH75L2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAOPHNN63QOVUOZASO2NSH75L2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JAOPHNN63QOVUOZASO2NSH75L2","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":"88f64402dc0daf7cc279c9d768ba6c0d3c6781d4c04d9da3c2497ba94952fa19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T08:31:53Z","title_canon_sha256":"cd28c3f1c5976fd967ff80698ca92e838536f5b90aae306386e68e610e233af8"},"schema_version":"1.0","source":{"id":"1701.02885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02885","created_at":"2026-05-18T00:52:59Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02885v1","created_at":"2026-05-18T00:52:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02885","created_at":"2026-05-18T00:52:59Z"},{"alias_kind":"pith_short_12","alias_value":"JAOPHNN63QOV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JAOPHNN63QOVUOZA","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JAOPHNN6","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:79f50dcb342f13aedd8fb0893df015caa7d7c579afc5b418cd79f6f89b590cad","target":"graph","created_at":"2026-05-18T00:52:59Z","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 a solution to the semirelativistic Hartree equation $$\\sqrt{-\\Delta+m^2}u+ V(x) u = A(x)\\left( W * |u|^p \\right) |u|^{p-2}u $$ under suitable growth assumption on the potential functions $V$ and $A$. In particular, both can be unbounded from above.","authors_text":"Simone Secchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T08:31:53Z","title":"Existence of solutions for a semirelativistic Hartree equation with unbounded potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02885","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":"sha256:1db2d7789b86729558ba1a034e4de4a07eb4cb6dab3e3cc6b8e43e19e55862be","target":"record","created_at":"2026-05-18T00:52:59Z","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":"88f64402dc0daf7cc279c9d768ba6c0d3c6781d4c04d9da3c2497ba94952fa19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T08:31:53Z","title_canon_sha256":"cd28c3f1c5976fd967ff80698ca92e838536f5b90aae306386e68e610e233af8"},"schema_version":"1.0","source":{"id":"1701.02885","kind":"arxiv","version":1}},"canonical_sha256":"481cf3b5bedc1d5a3b2093b4d91ffd5e966edd12c7f1a0b095c389165afa41cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"481cf3b5bedc1d5a3b2093b4d91ffd5e966edd12c7f1a0b095c389165afa41cc","first_computed_at":"2026-05-18T00:52:59.913361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:59.913361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"atFI48YbE8vnv55YRELTph7N5rkHoRrjlH++kEPdZ/Z+q4+5iQVpF5WyhcKfyvjwq3dMa8CyX98l3T5EiTskBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:59.913863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1db2d7789b86729558ba1a034e4de4a07eb4cb6dab3e3cc6b8e43e19e55862be","sha256:79f50dcb342f13aedd8fb0893df015caa7d7c579afc5b418cd79f6f89b590cad"],"state_sha256":"96e283e93addd4bd08015f844e92c82cc22e5ae4bd67c3423894359910da31ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"87mVQZDvDge8rI3DbSstSUl7soQEo+qrCFnZLql5j7RxNb3fJG6QwWawRpgzqCgSf9ljdv14yTM+5PWC473HDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T00:17:29.085078Z","bundle_sha256":"41c170f78e9098f9fa6ab1734d901c289e219edb311c5515f6ff0fd33a286d77"}}