{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:KU5WCOGLZZF5BDEWZI4E3HBIGN","short_pith_number":"pith:KU5WCOGL","schema_version":"1.0","canonical_sha256":"553b6138cbce4bd08c96ca384d9c28337f9b39c1cda2fc076fb8f0437b277c61","source":{"kind":"arxiv","id":"2107.13192","version":1},"attestation_state":"computed","paper":{"title":"Hypercritical deformed Hermitian-Yang-Mills equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jianchun Chu, Man-Chun Lee","submitted_at":"2021-07-28T06:48:46Z","abstract_excerpt":"In this work, we study the deformed Hermitian-Yang-Mills equation on compact K\\\"ahler manifold. We introduce the notions of coerciveness and properness of the $\\mathcal{J}$-functional on the space of almost calibrated $(1,1)$-forms and show that they are both equivalent to the existence of solutions to the hypercritical deformed Hermitian-Yang-Mills equation."},"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":"2107.13192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-07-28T06:48:46Z","cross_cats_sorted":[],"title_canon_sha256":"f731440bc637b4398f758e7dfcef0ab961a78343bbc80681c07e2e463c88c5cd","abstract_canon_sha256":"c02b0efe53a8c2198e7ce78799947d4b3196519f6918170156c85b7c9a861592"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:01:27.628375Z","signature_b64":"pXJtedisZLxyiPOSp31RSSd46FR6Z1CGstPDl1UOB16rYMPI1eauaEmnXNDTjaqKgP4eauFyR/3PeaZFsrIxCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"553b6138cbce4bd08c96ca384d9c28337f9b39c1cda2fc076fb8f0437b277c61","last_reissued_at":"2026-07-05T03:01:27.627903Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:01:27.627903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypercritical deformed Hermitian-Yang-Mills equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jianchun Chu, Man-Chun Lee","submitted_at":"2021-07-28T06:48:46Z","abstract_excerpt":"In this work, we study the deformed Hermitian-Yang-Mills equation on compact K\\\"ahler manifold. We introduce the notions of coerciveness and properness of the $\\mathcal{J}$-functional on the space of almost calibrated $(1,1)$-forms and show that they are both equivalent to the existence of solutions to the hypercritical deformed Hermitian-Yang-Mills equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13192","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.13192/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2107.13192","created_at":"2026-07-05T03:01:27.627959+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.13192v1","created_at":"2026-07-05T03:01:27.627959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.13192","created_at":"2026-07-05T03:01:27.627959+00:00"},{"alias_kind":"pith_short_12","alias_value":"KU5WCOGLZZF5","created_at":"2026-07-05T03:01:27.627959+00:00"},{"alias_kind":"pith_short_16","alias_value":"KU5WCOGLZZF5BDEW","created_at":"2026-07-05T03:01:27.627959+00:00"},{"alias_kind":"pith_short_8","alias_value":"KU5WCOGL","created_at":"2026-07-05T03:01:27.627959+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.29258","citing_title":"Weak solutions of the generalized Monge-Amp\\`ere equation and the supercritical deformed Hermitian-Yang-Mills equation: boundary cases","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN","json":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN.json","graph_json":"https://pith.science/api/pith-number/KU5WCOGLZZF5BDEWZI4E3HBIGN/graph.json","events_json":"https://pith.science/api/pith-number/KU5WCOGLZZF5BDEWZI4E3HBIGN/events.json","paper":"https://pith.science/paper/KU5WCOGL"},"agent_actions":{"view_html":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN","download_json":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN.json","view_paper":"https://pith.science/paper/KU5WCOGL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.13192&json=true","fetch_graph":"https://pith.science/api/pith-number/KU5WCOGLZZF5BDEWZI4E3HBIGN/graph.json","fetch_events":"https://pith.science/api/pith-number/KU5WCOGLZZF5BDEWZI4E3HBIGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN/action/storage_attestation","attest_author":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN/action/author_attestation","sign_citation":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN/action/citation_signature","submit_replication":"https://pith.science/pith/KU5WCOGLZZF5BDEWZI4E3HBIGN/action/replication_record"}},"created_at":"2026-07-05T03:01:27.627959+00:00","updated_at":"2026-07-05T03:01:27.627959+00:00"}