{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DERHQPD7OJ6RBPO6BJL5UFFJHA","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":"124848cc47f78900c7275041a07144df70d7b91ca373fa7bedbca753df6611d5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T02:33:31Z","title_canon_sha256":"f6ffad3742aa7a61571216bc8825cd8a9dea18fe4f02da82d814b04aa8a79221"},"schema_version":"1.0","source":{"id":"2411.14686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14686","created_at":"2026-07-05T09:38:55Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14686v1","created_at":"2026-07-05T09:38:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14686","created_at":"2026-07-05T09:38:55Z"},{"alias_kind":"pith_short_12","alias_value":"DERHQPD7OJ6R","created_at":"2026-07-05T09:38:55Z"},{"alias_kind":"pith_short_16","alias_value":"DERHQPD7OJ6RBPO6","created_at":"2026-07-05T09:38:55Z"},{"alias_kind":"pith_short_8","alias_value":"DERHQPD7","created_at":"2026-07-05T09:38:55Z"}],"graph_snapshots":[{"event_id":"sha256:c5c299184541a929ea90072e42ccdf17199f70a612715ac3d14e75d0d1be6f44","target":"graph","created_at":"2026-07-05T09:38:55Z","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/2411.14686/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a complete classification of the existence/nonexistence of a solution with respect to the size of boundary data. Moreover, we give a result on the multiple existence of solutions via bifurcation theory. We also state results on Hardy-H\\'enon equations on infinite cones as a generalization.","authors_text":"Sho Katayama","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T02:33:31Z","title":"Supercritical Lane-Emden equation on a cone with an inhomogeneous Dirichlet boundary condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14686","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:a6da7c1fd2ee4b2f8098bac6cd135e2a6effbe8dd2f811fef54f6fba026226b4","target":"record","created_at":"2026-07-05T09:38:55Z","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":"124848cc47f78900c7275041a07144df70d7b91ca373fa7bedbca753df6611d5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T02:33:31Z","title_canon_sha256":"f6ffad3742aa7a61571216bc8825cd8a9dea18fe4f02da82d814b04aa8a79221"},"schema_version":"1.0","source":{"id":"2411.14686","kind":"arxiv","version":1}},"canonical_sha256":"1922783c7f727d10bdde0a57da14a938125447b036fe8831440e5577cf95ee68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1922783c7f727d10bdde0a57da14a938125447b036fe8831440e5577cf95ee68","first_computed_at":"2026-07-05T09:38:55.524517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:55.524517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCunoJLe+XIYCmIR2VOw7ortsaV9LBUrGMfQvDlFmukVx4+NVn3GPwM+cdVEzrm/1U1cuNUME/n/I7EgT6WFDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:55.524943Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6da7c1fd2ee4b2f8098bac6cd135e2a6effbe8dd2f811fef54f6fba026226b4","sha256:c5c299184541a929ea90072e42ccdf17199f70a612715ac3d14e75d0d1be6f44"],"state_sha256":"cfa35c4569e72f5e6718c0263a4d598240fcbad8774f81d7ada0f9e9acddd4f6"}