{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HMXXEMSF2DZLVDATK7ATZQ5OWI","short_pith_number":"pith:HMXXEMSF","canonical_record":{"source":{"id":"2505.12817","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-19T07:58:10Z","cross_cats_sorted":[],"title_canon_sha256":"9e59b8f352cdabbf420139f6af6f6b5e0dc61d8dda8d08131d0073da60287444","abstract_canon_sha256":"5e14835cbc57528655a90603ef2dc42b8593b797979834c01980e83209bbedbc"},"schema_version":"1.0"},"canonical_sha256":"3b2f723245d0f2ba8c1357c13cc3aeb20a99d8e35556f5b90b48f058cb168087","source":{"kind":"arxiv","id":"2505.12817","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12817","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12817v2","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12817","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"HMXXEMSF2DZL","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"pith_short_16","alias_value":"HMXXEMSF2DZLVDAT","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"pith_short_8","alias_value":"HMXXEMSF","created_at":"2026-07-05T11:46:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HMXXEMSF2DZLVDATK7ATZQ5OWI","target":"record","payload":{"canonical_record":{"source":{"id":"2505.12817","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-19T07:58:10Z","cross_cats_sorted":[],"title_canon_sha256":"9e59b8f352cdabbf420139f6af6f6b5e0dc61d8dda8d08131d0073da60287444","abstract_canon_sha256":"5e14835cbc57528655a90603ef2dc42b8593b797979834c01980e83209bbedbc"},"schema_version":"1.0"},"canonical_sha256":"3b2f723245d0f2ba8c1357c13cc3aeb20a99d8e35556f5b90b48f058cb168087","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:22.215966Z","signature_b64":"Qo5rcSTl1UD1KmCXDgKCqrNWmpykiLjc2Be94fu4b3I09+4uHM8Y8NFlfDiOfqX0iBYvJUXdIn3rEZXwJ4c3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b2f723245d0f2ba8c1357c13cc3aeb20a99d8e35556f5b90b48f058cb168087","last_reissued_at":"2026-07-05T11:46:22.215462Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:22.215462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.12817","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CjePFUeF+v6p2yVrCw979wlzYl5LB+ZA1Z2uUbijEuQruATIGCQrEoRCiCbFx9FpsZgW1mG9RSqjYHvECUApCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:34:10.119651Z"},"content_sha256":"2582e78e946a78f6a1c3a2c2ef1364d3b2687bcc2489aa91a618f9710e8a8728","schema_version":"1.0","event_id":"sha256:2582e78e946a78f6a1c3a2c2ef1364d3b2687bcc2489aa91a618f9710e8a8728"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HMXXEMSF2DZLVDATK7ATZQ5OWI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The log-concavity of eigenfunction to complex Monge-Amp\\`ere operator in $\\mathbb{C}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qi Zhou, Wei Zhang","submitted_at":"2025-05-19T07:58:10Z","abstract_excerpt":"Following the authors' recent work \\cite{Zhang-Zhou2025}, we further explore the convexity properties of solutions to the Dirichlet problem for the complex Monge-Amp\\`ere operator. In this paper, we establish the $\\log$-concavity of solutions to the Dirichlet eigenvalue problem for the complex Monge-Amp\\`ere operator on bounded, smooth, strictly convex domain in $\\mathbb{C}^2$. The key ingredients consist of the constant rank theorem and the deformation method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12817","kind":"arxiv","version":2},"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/2505.12817/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSBPHconYHnSR9zw3/Jec354EHq6nnNQqG0bfbmSLn6S/LtyZvVIst43fjzCblMf93D21gMYgvodnk13UT5xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:34:10.120171Z"},"content_sha256":"1762922a84d5d12798cac1bb937e160af3821e7dc63babce72ee36dafa570cd3","schema_version":"1.0","event_id":"sha256:1762922a84d5d12798cac1bb937e160af3821e7dc63babce72ee36dafa570cd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMXXEMSF2DZLVDATK7ATZQ5OWI/bundle.json","state_url":"https://pith.science/pith/HMXXEMSF2DZLVDATK7ATZQ5OWI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMXXEMSF2DZLVDATK7ATZQ5OWI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-20T23:34:10Z","links":{"resolver":"https://pith.science/pith/HMXXEMSF2DZLVDATK7ATZQ5OWI","bundle":"https://pith.science/pith/HMXXEMSF2DZLVDATK7ATZQ5OWI/bundle.json","state":"https://pith.science/pith/HMXXEMSF2DZLVDATK7ATZQ5OWI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMXXEMSF2DZLVDATK7ATZQ5OWI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HMXXEMSF2DZLVDATK7ATZQ5OWI","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":"5e14835cbc57528655a90603ef2dc42b8593b797979834c01980e83209bbedbc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-19T07:58:10Z","title_canon_sha256":"9e59b8f352cdabbf420139f6af6f6b5e0dc61d8dda8d08131d0073da60287444"},"schema_version":"1.0","source":{"id":"2505.12817","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12817","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12817v2","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12817","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"HMXXEMSF2DZL","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"pith_short_16","alias_value":"HMXXEMSF2DZLVDAT","created_at":"2026-07-05T11:46:22Z"},{"alias_kind":"pith_short_8","alias_value":"HMXXEMSF","created_at":"2026-07-05T11:46:22Z"}],"graph_snapshots":[{"event_id":"sha256:1762922a84d5d12798cac1bb937e160af3821e7dc63babce72ee36dafa570cd3","target":"graph","created_at":"2026-07-05T11:46:22Z","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/2505.12817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Following the authors' recent work \\cite{Zhang-Zhou2025}, we further explore the convexity properties of solutions to the Dirichlet problem for the complex Monge-Amp\\`ere operator. In this paper, we establish the $\\log$-concavity of solutions to the Dirichlet eigenvalue problem for the complex Monge-Amp\\`ere operator on bounded, smooth, strictly convex domain in $\\mathbb{C}^2$. The key ingredients consist of the constant rank theorem and the deformation method.","authors_text":"Qi Zhou, Wei Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-19T07:58:10Z","title":"The log-concavity of eigenfunction to complex Monge-Amp\\`ere operator in $\\mathbb{C}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12817","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":"sha256:2582e78e946a78f6a1c3a2c2ef1364d3b2687bcc2489aa91a618f9710e8a8728","target":"record","created_at":"2026-07-05T11:46:22Z","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":"5e14835cbc57528655a90603ef2dc42b8593b797979834c01980e83209bbedbc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-19T07:58:10Z","title_canon_sha256":"9e59b8f352cdabbf420139f6af6f6b5e0dc61d8dda8d08131d0073da60287444"},"schema_version":"1.0","source":{"id":"2505.12817","kind":"arxiv","version":2}},"canonical_sha256":"3b2f723245d0f2ba8c1357c13cc3aeb20a99d8e35556f5b90b48f058cb168087","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b2f723245d0f2ba8c1357c13cc3aeb20a99d8e35556f5b90b48f058cb168087","first_computed_at":"2026-07-05T11:46:22.215462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:22.215462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qo5rcSTl1UD1KmCXDgKCqrNWmpykiLjc2Be94fu4b3I09+4uHM8Y8NFlfDiOfqX0iBYvJUXdIn3rEZXwJ4c3Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:22.215966Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.12817","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2582e78e946a78f6a1c3a2c2ef1364d3b2687bcc2489aa91a618f9710e8a8728","sha256:1762922a84d5d12798cac1bb937e160af3821e7dc63babce72ee36dafa570cd3"],"state_sha256":"c4b30d7997a5b65cccf8c22bb914ca02d88272c32acfd8a50feaded73fbd3fae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8CthPyIPlKMo4SSn8cexBvfXvPHH39i4w4MymGUBW9f4waMY2XmU/c4QiJVyGDrG7Hvi0EhK3F7b2Snn6uGNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T23:34:10.125327Z","bundle_sha256":"cb47a1d93cebdc0c45bfa9941cad833801025af851e153a91432b843807f74c7"}}