{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:APKKPI53MSKQUHZVVHODPL2VOH","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":"08ce57c40640b75dc7745ea403e7cc144e62df9cad5c00acfeee06eed0f9c692","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-07-21T14:24:45Z","title_canon_sha256":"2e1bec1b8d4bcf2d19ed8e0e5de149427d77a03f620eff564d04cdeee8f544e3"},"schema_version":"1.0","source":{"id":"2607.19132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19132","created_at":"2026-07-22T01:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19132v1","created_at":"2026-07-22T01:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19132","created_at":"2026-07-22T01:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"APKKPI53MSKQ","created_at":"2026-07-22T01:24:10Z"},{"alias_kind":"pith_short_16","alias_value":"APKKPI53MSKQUHZV","created_at":"2026-07-22T01:24:10Z"},{"alias_kind":"pith_short_8","alias_value":"APKKPI53","created_at":"2026-07-22T01:24:10Z"}],"graph_snapshots":[{"event_id":"sha256:594e738a023794a21b5847a7347ba1a84897f9d179b80ec2ebbfdcc5079fe024","target":"graph","created_at":"2026-07-22T01:24:10Z","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/2607.19132/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that given a quasi-$m$-hyperconvex domain $\\Omega \\subset X$ in a compact K\\\"ahler manifold $(X, \\omega)$, and a function $\\varphi $ in the weighted energy class $\\mathcal{E}_\\chi^m(\\Omega, \\omega)$ with respect to a convex weight function $\\chi : \\mathbb{R} \\to \\mathbb{R}$, then there exists a maximal $\\omega$-$m$-subharmonic subextension $\\tilde{\\varphi}$ to $X$ that preserves the weighted energy and satisfies a good control properties for its Hessian measure $ \\mathbf{1}_\\Omega H_m(\\tilde{\\varphi}) \\leq \\mathbf{1}_\\Omega H_m(\\varphi) $. In the last part, we study the","authors_text":"Ayoub El-Gasmi, Hichame Amal, Sa\\\"id Asserda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-07-21T14:24:45Z","title":"Maximal subextension of $m$-subharmonic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19132","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":"sha256:7d1921b5f9e55881ac54cbb0b778481e006b3354529c1f98edd4117bc21ef20d","target":"record","created_at":"2026-07-22T01:24:10Z","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":"08ce57c40640b75dc7745ea403e7cc144e62df9cad5c00acfeee06eed0f9c692","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-07-21T14:24:45Z","title_canon_sha256":"2e1bec1b8d4bcf2d19ed8e0e5de149427d77a03f620eff564d04cdeee8f544e3"},"schema_version":"1.0","source":{"id":"2607.19132","kind":"arxiv","version":1}},"canonical_sha256":"03d4a7a3bb64950a1f35a9dc37af5571edda68c10d74fbcc245b8c9a91503c57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03d4a7a3bb64950a1f35a9dc37af5571edda68c10d74fbcc245b8c9a91503c57","first_computed_at":"2026-07-22T01:24:10.284852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:24:10.284852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCrEbfknu+Tpl6DUTOmN9WEgs4DmQcYOaaWZle8oYfTj7NpHXWgQ3bT7NjAZ7NOveH/CF/Z/uvM4JMs6v+MUCA==","signature_status":"signed_v1","signed_at":"2026-07-22T01:24:10.285699Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d1921b5f9e55881ac54cbb0b778481e006b3354529c1f98edd4117bc21ef20d","sha256:594e738a023794a21b5847a7347ba1a84897f9d179b80ec2ebbfdcc5079fe024"],"state_sha256":"ba2fedc0ea49ecbba233b508d517f294968db3fbbf693511ad8d11afbf469e63"}