{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FMJ35XIKSAM442T2Z3RNLHTKHE","short_pith_number":"pith:FMJ35XIK","canonical_record":{"source":{"id":"2411.09941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-15T04:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"438a1feb81dc7921433a6a989551cc30150269a17cb27f1e60449207c31b81e1","abstract_canon_sha256":"127eaf3e017db7f12716ea712ccf502c3aabd54fdc1bf76376537845bf34e434"},"schema_version":"1.0"},"canonical_sha256":"2b13bedd0a9019ce6a7acee2d59e6a392cdb6c4ab7a78bb88891758c3046864b","source":{"kind":"arxiv","id":"2411.09941","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09941","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09941v1","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09941","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_12","alias_value":"FMJ35XIKSAM4","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_16","alias_value":"FMJ35XIKSAM442T2","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_8","alias_value":"FMJ35XIK","created_at":"2026-07-05T09:35:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FMJ35XIKSAM442T2Z3RNLHTKHE","target":"record","payload":{"canonical_record":{"source":{"id":"2411.09941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-15T04:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"438a1feb81dc7921433a6a989551cc30150269a17cb27f1e60449207c31b81e1","abstract_canon_sha256":"127eaf3e017db7f12716ea712ccf502c3aabd54fdc1bf76376537845bf34e434"},"schema_version":"1.0"},"canonical_sha256":"2b13bedd0a9019ce6a7acee2d59e6a392cdb6c4ab7a78bb88891758c3046864b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:56.056134Z","signature_b64":"Jw5T0U7dHldnSU1MQvkRbPOXJkcfrHSCNwdCH+ArKJynyXdZ93CPWdiaUquO2hNs7siyF5eKHXZrGdnptKx6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b13bedd0a9019ce6a7acee2d59e6a392cdb6c4ab7a78bb88891758c3046864b","last_reissued_at":"2026-07-05T09:35:56.055626Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:56.055626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.09941","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":"2026-07-05T09:35:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zItYC+oGTCKOrPO9ucvGnChKzcTZ0E3Dx2oCiMTO5XgzUzyC54pOk+yKk5F8RetBIoXDDCQ1PMTyP7uaZsnGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:22:43.188034Z"},"content_sha256":"8ef2f2fde27c4e3ba812c8a05027c96d5544c18433298a08d5470f9dde1c1f57","schema_version":"1.0","event_id":"sha256:8ef2f2fde27c4e3ba812c8a05027c96d5544c18433298a08d5470f9dde1c1f57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FMJ35XIKSAM442T2Z3RNLHTKHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Qualitative properties of positive solutions of a mixed order nonlinear Schr\\\"{o}dinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Jiwen Zhang, Serena Dipierro, Xifeng SU","submitted_at":"2024-11-15T04:38:14Z","abstract_excerpt":"In this paper, we deal with the following mixed local/nonlocal Schr\\\"{o}dinger equation\n  \\begin{equation*}\n  \\left\\{\n  \\begin{array}{ll}\n  - \\Delta u + (-\\Delta)^s u+u = u^p \\quad \\hbox{in $\\mathbb{R}^n$,}\n  u>0 \\quad \\hbox{in $\\mathbb{R}^n$,}\n  \\lim\\limits_{|x|\\to+\\infty}u(x)=0,\n  \\end{array}\n  \\right.\n  \\end{equation*} where $n\\geqslant2$, $s\\in (0,1)$ and $p\\in\\left(1,\\frac{n+2}{n-2}\\right)$.\n  The existence of positive solutions for the above problem is proved, relying on some new regularity results. In addition, we study the power-type decay and the radial symmetry properties of such sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09941","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.09941/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:35:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1BuKCiMKTlS5VrF3ZFm2iqVO3WW2xPjf/cpnIX5Lb4WSvqksZJMkCRS1ip2xPnZEL6rCFeELzHxWJuGFq9nBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:22:43.188559Z"},"content_sha256":"ff7a5354626e9add97367c8278484736adeef21b0556eb511a89f2131c851180","schema_version":"1.0","event_id":"sha256:ff7a5354626e9add97367c8278484736adeef21b0556eb511a89f2131c851180"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMJ35XIKSAM442T2Z3RNLHTKHE/bundle.json","state_url":"https://pith.science/pith/FMJ35XIKSAM442T2Z3RNLHTKHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMJ35XIKSAM442T2Z3RNLHTKHE/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":"2026-08-13T11:22:43Z","links":{"resolver":"https://pith.science/pith/FMJ35XIKSAM442T2Z3RNLHTKHE","bundle":"https://pith.science/pith/FMJ35XIKSAM442T2Z3RNLHTKHE/bundle.json","state":"https://pith.science/pith/FMJ35XIKSAM442T2Z3RNLHTKHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMJ35XIKSAM442T2Z3RNLHTKHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FMJ35XIKSAM442T2Z3RNLHTKHE","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":"127eaf3e017db7f12716ea712ccf502c3aabd54fdc1bf76376537845bf34e434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-15T04:38:14Z","title_canon_sha256":"438a1feb81dc7921433a6a989551cc30150269a17cb27f1e60449207c31b81e1"},"schema_version":"1.0","source":{"id":"2411.09941","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09941","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09941v1","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09941","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_12","alias_value":"FMJ35XIKSAM4","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_16","alias_value":"FMJ35XIKSAM442T2","created_at":"2026-07-05T09:35:56Z"},{"alias_kind":"pith_short_8","alias_value":"FMJ35XIK","created_at":"2026-07-05T09:35:56Z"}],"graph_snapshots":[{"event_id":"sha256:ff7a5354626e9add97367c8278484736adeef21b0556eb511a89f2131c851180","target":"graph","created_at":"2026-07-05T09:35:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.09941/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we deal with the following mixed local/nonlocal Schr\\\"{o}dinger equation\n  \\begin{equation*}\n  \\left\\{\n  \\begin{array}{ll}\n  - \\Delta u + (-\\Delta)^s u+u = u^p \\quad \\hbox{in $\\mathbb{R}^n$,}\n  u>0 \\quad \\hbox{in $\\mathbb{R}^n$,}\n  \\lim\\limits_{|x|\\to+\\infty}u(x)=0,\n  \\end{array}\n  \\right.\n  \\end{equation*} where $n\\geqslant2$, $s\\in (0,1)$ and $p\\in\\left(1,\\frac{n+2}{n-2}\\right)$.\n  The existence of positive solutions for the above problem is proved, relying on some new regularity results. In addition, we study the power-type decay and the radial symmetry properties of such sol","authors_text":"Enrico Valdinoci, Jiwen Zhang, Serena Dipierro, Xifeng SU","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-15T04:38:14Z","title":"Qualitative properties of positive solutions of a mixed order nonlinear Schr\\\"{o}dinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09941","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":"sha256:8ef2f2fde27c4e3ba812c8a05027c96d5544c18433298a08d5470f9dde1c1f57","target":"record","created_at":"2026-07-05T09:35:56Z","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":"127eaf3e017db7f12716ea712ccf502c3aabd54fdc1bf76376537845bf34e434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-15T04:38:14Z","title_canon_sha256":"438a1feb81dc7921433a6a989551cc30150269a17cb27f1e60449207c31b81e1"},"schema_version":"1.0","source":{"id":"2411.09941","kind":"arxiv","version":1}},"canonical_sha256":"2b13bedd0a9019ce6a7acee2d59e6a392cdb6c4ab7a78bb88891758c3046864b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b13bedd0a9019ce6a7acee2d59e6a392cdb6c4ab7a78bb88891758c3046864b","first_computed_at":"2026-07-05T09:35:56.055626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:35:56.055626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jw5T0U7dHldnSU1MQvkRbPOXJkcfrHSCNwdCH+ArKJynyXdZ93CPWdiaUquO2hNs7siyF5eKHXZrGdnptKx6Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:35:56.056134Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.09941","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ef2f2fde27c4e3ba812c8a05027c96d5544c18433298a08d5470f9dde1c1f57","sha256:ff7a5354626e9add97367c8278484736adeef21b0556eb511a89f2131c851180"],"state_sha256":"c79f951be39679c340365fb2700d4faa45bb3b6586d7771d87e1c619630711d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ondbGXMzy8oIb/FHTNQyYdOnZdNyPE1R0lqRfOM6lgLfy0eSRCjK6zGUAok5vdZ7h6ZAaJbD4m5/S9spjpCwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T11:22:43.206600Z","bundle_sha256":"94b924da8987b361d0fa3e408e2633178179b0879b905ffd90b1d0703000ef03"}}