{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HSUGCQOJWF5U66Y4CI5SWGZPCF","short_pith_number":"pith:HSUGCQOJ","schema_version":"1.0","canonical_sha256":"3ca86141c9b17b4f7b1c123b2b1b2f117b2853bb34ff7c51de2d3555526da3c1","source":{"kind":"arxiv","id":"1709.01106","version":1},"attestation_state":"computed","paper":{"title":"Bubbling solutions for Moser-Trudinger type equations on compact Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Monica Musso, Pablo Figueroa","submitted_at":"2017-09-04T18:20:28Z","abstract_excerpt":"We study an elliptic equation related to the Moser-Trudinger inequality on a compact Riemann surface $(S,g)$, $$ \\Delta_g u+\\lambda \\Biggl(ue^{u^2}-{1\\over |S|} \\int_S ue^{u^2} dv_g\\Biggl)=0,\\quad\\text{in $S$},\\qquad \\int_S u\\,dv_g=0, $$ where $\\lambda>0$ is a small parameter, $|S|$ is the area of $S$, $\\Delta_g$ is the Laplace-Beltrami operator and $dv_g$ is the area element. Given any integer $k\\geq 1$, under general conditions on $S$ we find a bubbling solution $u_\\lambda$ which blows up at exactly $k$ points in $S$, as $\\lambda \\to0$. When $S$ is a flat two-torus in rectangular form, we fi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.01106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-04T18:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"ff99e25815ee427073e9c5b293e87e4eaab30ebae63e4b96acd228f211f95e66","abstract_canon_sha256":"f4d87ed0d3ad23c97f23bbbbed4b0e986abdb5ea09c8dcb79b9c8cce64cf88d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:00.916129Z","signature_b64":"eZB0qWSqL+fuJKOOoG3GA84srg0mjPsJUpe6lvUInD2IsEZlWQkqoH9nfFBawZ/OypQksKepy/N/velrnif+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ca86141c9b17b4f7b1c123b2b1b2f117b2853bb34ff7c51de2d3555526da3c1","last_reissued_at":"2026-05-18T00:36:00.915704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:00.915704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bubbling solutions for Moser-Trudinger type equations on compact Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Monica Musso, Pablo Figueroa","submitted_at":"2017-09-04T18:20:28Z","abstract_excerpt":"We study an elliptic equation related to the Moser-Trudinger inequality on a compact Riemann surface $(S,g)$, $$ \\Delta_g u+\\lambda \\Biggl(ue^{u^2}-{1\\over |S|} \\int_S ue^{u^2} dv_g\\Biggl)=0,\\quad\\text{in $S$},\\qquad \\int_S u\\,dv_g=0, $$ where $\\lambda>0$ is a small parameter, $|S|$ is the area of $S$, $\\Delta_g$ is the Laplace-Beltrami operator and $dv_g$ is the area element. Given any integer $k\\geq 1$, under general conditions on $S$ we find a bubbling solution $u_\\lambda$ which blows up at exactly $k$ points in $S$, as $\\lambda \\to0$. When $S$ is a flat two-torus in rectangular form, we fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01106","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.01106","created_at":"2026-05-18T00:36:00.915778+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.01106v1","created_at":"2026-05-18T00:36:00.915778+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01106","created_at":"2026-05-18T00:36:00.915778+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSUGCQOJWF5U","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSUGCQOJWF5U66Y4","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSUGCQOJ","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF","json":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF.json","graph_json":"https://pith.science/api/pith-number/HSUGCQOJWF5U66Y4CI5SWGZPCF/graph.json","events_json":"https://pith.science/api/pith-number/HSUGCQOJWF5U66Y4CI5SWGZPCF/events.json","paper":"https://pith.science/paper/HSUGCQOJ"},"agent_actions":{"view_html":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF","download_json":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF.json","view_paper":"https://pith.science/paper/HSUGCQOJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.01106&json=true","fetch_graph":"https://pith.science/api/pith-number/HSUGCQOJWF5U66Y4CI5SWGZPCF/graph.json","fetch_events":"https://pith.science/api/pith-number/HSUGCQOJWF5U66Y4CI5SWGZPCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF/action/storage_attestation","attest_author":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF/action/author_attestation","sign_citation":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF/action/citation_signature","submit_replication":"https://pith.science/pith/HSUGCQOJWF5U66Y4CI5SWGZPCF/action/replication_record"}},"created_at":"2026-05-18T00:36:00.915778+00:00","updated_at":"2026-05-18T00:36:00.915778+00:00"}