{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7Y5HVESS7SPPZFLVYEC7QFLYDT","short_pith_number":"pith:7Y5HVESS","canonical_record":{"source":{"id":"1605.01875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-06T09:49:09Z","cross_cats_sorted":[],"title_canon_sha256":"28dd3f68a0199ce0b395096037672ed91ad8e25aae47ed7c2f0b561d8eec4370","abstract_canon_sha256":"364c389fe354284d114c8bc78417dc63860fd2c70c581029f135e13ae993cf05"},"schema_version":"1.0"},"canonical_sha256":"fe3a7a9252fc9efc9575c105f815781ce3dad7c13a7805bf954a0eed8988cb11","source":{"kind":"arxiv","id":"1605.01875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01875","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01875v1","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01875","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"7Y5HVESS7SPP","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7Y5HVESS7SPPZFLV","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7Y5HVESS","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7Y5HVESS7SPPZFLVYEC7QFLYDT","target":"record","payload":{"canonical_record":{"source":{"id":"1605.01875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-06T09:49:09Z","cross_cats_sorted":[],"title_canon_sha256":"28dd3f68a0199ce0b395096037672ed91ad8e25aae47ed7c2f0b561d8eec4370","abstract_canon_sha256":"364c389fe354284d114c8bc78417dc63860fd2c70c581029f135e13ae993cf05"},"schema_version":"1.0"},"canonical_sha256":"fe3a7a9252fc9efc9575c105f815781ce3dad7c13a7805bf954a0eed8988cb11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:01.252999Z","signature_b64":"fm7xCh+xFh7hI34YjRMDSq7UsEwC73/dLE6KxiCsDsIwHz0NvzqD0474/xwcmxo37LE9TP4KISA8997pMlRzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3a7a9252fc9efc9575c105f815781ce3dad7c13a7805bf954a0eed8988cb11","last_reissued_at":"2026-05-18T00:48:01.252474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:01.252474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.01875","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":"2026-05-18T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s61ZGrWKf6rAZT/MZOzl8/Ly+HtYUsSKYtgV4WUZsWsRm+0FLrv4pHSqQNkbuvG1ytNs/D9/upl0gC3EDXEbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:40:30.659770Z"},"content_sha256":"c480cc8964f601050835ad70ca3a5a357e1ef1528439fb77e8a9a26e1252f80e","schema_version":"1.0","event_id":"sha256:c480cc8964f601050835ad70ca3a5a357e1ef1528439fb77e8a9a26e1252f80e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7Y5HVESS7SPPZFLVYEC7QFLYDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic aspects of the Tzitz\\'eica equation: blow-up analysis and existence results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aleks Jevnikar, Wen Yang","submitted_at":"2016-05-06T09:49:09Z","abstract_excerpt":"We are concerned with the following class of equations with exponential nonlinearities: $$\n  \\Delta u+h_1e^u-h_2e^{-2u}=0 \\qquad \\mbox{in } B_1\\subset\\mathbb{R}^2, $$ which is related to the Tzitz\\'eica equation. Here $h_1, h_2$ are two smooth positive functions. The purpose of the paper is to initiate the analytical study of the above equation and to give a quite complete picture both for what concerns the blow-up phenomena and the existence issue.\n  In the first part of the paper we provide a quantization of local blow-up masses associated to a blowing-up sequence of solutions. Next we exclu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01875","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":"2026-05-18T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c46GaH03yDqH7SJModcWLQIWT+79TcDe/RYsmsvFvB1epIwAoIZggkZS4f3C7lEvhRdIRQCyzc/mg3q7LVJlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:40:30.660119Z"},"content_sha256":"b9c5ea5701d3d29a7427739f1617272154956f8dc9f123dc0685d8e66994b1f9","schema_version":"1.0","event_id":"sha256:b9c5ea5701d3d29a7427739f1617272154956f8dc9f123dc0685d8e66994b1f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Y5HVESS7SPPZFLVYEC7QFLYDT/bundle.json","state_url":"https://pith.science/pith/7Y5HVESS7SPPZFLVYEC7QFLYDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Y5HVESS7SPPZFLVYEC7QFLYDT/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":"2026-06-22T23:40:30Z","links":{"resolver":"https://pith.science/pith/7Y5HVESS7SPPZFLVYEC7QFLYDT","bundle":"https://pith.science/pith/7Y5HVESS7SPPZFLVYEC7QFLYDT/bundle.json","state":"https://pith.science/pith/7Y5HVESS7SPPZFLVYEC7QFLYDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Y5HVESS7SPPZFLVYEC7QFLYDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7Y5HVESS7SPPZFLVYEC7QFLYDT","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":"364c389fe354284d114c8bc78417dc63860fd2c70c581029f135e13ae993cf05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-06T09:49:09Z","title_canon_sha256":"28dd3f68a0199ce0b395096037672ed91ad8e25aae47ed7c2f0b561d8eec4370"},"schema_version":"1.0","source":{"id":"1605.01875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01875","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01875v1","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01875","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"7Y5HVESS7SPP","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7Y5HVESS7SPPZFLV","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7Y5HVESS","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:b9c5ea5701d3d29a7427739f1617272154956f8dc9f123dc0685d8e66994b1f9","target":"graph","created_at":"2026-05-18T00:48:01Z","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 are concerned with the following class of equations with exponential nonlinearities: $$\n  \\Delta u+h_1e^u-h_2e^{-2u}=0 \\qquad \\mbox{in } B_1\\subset\\mathbb{R}^2, $$ which is related to the Tzitz\\'eica equation. Here $h_1, h_2$ are two smooth positive functions. The purpose of the paper is to initiate the analytical study of the above equation and to give a quite complete picture both for what concerns the blow-up phenomena and the existence issue.\n  In the first part of the paper we provide a quantization of local blow-up masses associated to a blowing-up sequence of solutions. Next we exclu","authors_text":"Aleks Jevnikar, Wen Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-06T09:49:09Z","title":"Analytic aspects of the Tzitz\\'eica equation: blow-up analysis and existence results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01875","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:c480cc8964f601050835ad70ca3a5a357e1ef1528439fb77e8a9a26e1252f80e","target":"record","created_at":"2026-05-18T00:48:01Z","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":"364c389fe354284d114c8bc78417dc63860fd2c70c581029f135e13ae993cf05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-06T09:49:09Z","title_canon_sha256":"28dd3f68a0199ce0b395096037672ed91ad8e25aae47ed7c2f0b561d8eec4370"},"schema_version":"1.0","source":{"id":"1605.01875","kind":"arxiv","version":1}},"canonical_sha256":"fe3a7a9252fc9efc9575c105f815781ce3dad7c13a7805bf954a0eed8988cb11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe3a7a9252fc9efc9575c105f815781ce3dad7c13a7805bf954a0eed8988cb11","first_computed_at":"2026-05-18T00:48:01.252474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:01.252474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fm7xCh+xFh7hI34YjRMDSq7UsEwC73/dLE6KxiCsDsIwHz0NvzqD0474/xwcmxo37LE9TP4KISA8997pMlRzAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:01.252999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c480cc8964f601050835ad70ca3a5a357e1ef1528439fb77e8a9a26e1252f80e","sha256:b9c5ea5701d3d29a7427739f1617272154956f8dc9f123dc0685d8e66994b1f9"],"state_sha256":"21b0037db6059852d59fc038db3e7327b805d81c9ff2d52a86dd4189259934fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"scFJHstuQyC4r4G06f1l8AxPGlZ7O1tBozXTmN6ovFE16LtLEtpXUSaEAlJn0PmBo6Je2Cs3lN2ldC563/MyBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:40:30.662088Z","bundle_sha256":"51fb3fcf73996a91c03aa63c32ead0c9fd65e561577c06c584adf32d972db4d8"}}