{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BMZWWK67IEAT3HNHCYHFO4HS5I","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":"0331c41cd84ef01175e2a1cd9cbb29f243854c3afc1a031c8e2b4077e28a9ca3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T12:24:43Z","title_canon_sha256":"6a3de1bea898b04d38657460101592752c7738ac4bb8fa7a07574a7617cb509a"},"schema_version":"1.0","source":{"id":"0904.4497","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4497","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4497v2","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4497","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"BMZWWK67IEAT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BMZWWK67IEAT3HNH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BMZWWK67","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a919447fbd03f131116e41f23db330623b569c2b6f896ac3ade4e43953f42f3b","target":"graph","created_at":"2026-05-18T04:20:38Z","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 that, in general, given a $p$-harmonic map $F:M\\to N$ and a convex function $H:N\\to\\mathbb{R}$, the composition $H\\circ F$ is not $p$-subharmonic. By assuming some rotational symmetry on manifolds and functions, we reduce the problem to an ordinary differential inequality. The key of the proof is an asymptotic estimate for the $p$-harmonic map under suitable assumptions on the manifolds.","authors_text":"Giona Veronelli","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T12:24:43Z","title":"On p-harmonic maps and convex functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4497","kind":"arxiv","version":2},"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":"sha256:2d0f2f84bfcab9549e699c10a3a5b46834a0ae92e9d329f753f0447429ca74a7","target":"record","created_at":"2026-05-18T04:20:38Z","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":"0331c41cd84ef01175e2a1cd9cbb29f243854c3afc1a031c8e2b4077e28a9ca3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T12:24:43Z","title_canon_sha256":"6a3de1bea898b04d38657460101592752c7738ac4bb8fa7a07574a7617cb509a"},"schema_version":"1.0","source":{"id":"0904.4497","kind":"arxiv","version":2}},"canonical_sha256":"0b336b2bdf41013d9da7160e5770f2ea228222ce99d397edf8be732cb61c86f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b336b2bdf41013d9da7160e5770f2ea228222ce99d397edf8be732cb61c86f0","first_computed_at":"2026-05-18T04:20:38.918257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:38.918257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iBeZPvsXSR1FY6bTQkSccjftXlIGmiVAW6GDAKzdlIj0w8OmaKJom7F09rZIOKJZyHLVaUbAgjMEN482RWqdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:38.919062Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4497","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d0f2f84bfcab9549e699c10a3a5b46834a0ae92e9d329f753f0447429ca74a7","sha256:a919447fbd03f131116e41f23db330623b569c2b6f896ac3ade4e43953f42f3b"],"state_sha256":"fb72976a19b84d06315601650ade47216f368633edd3fb350b9db7c9c851b954"}