{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OWI7K44Q64AIAQABVSYZJKDOKO","short_pith_number":"pith:OWI7K44Q","canonical_record":{"source":{"id":"1505.04422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-17T17:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"6271e584fe8b00f7865282c0c6680baabbaaf0aa0b32eca638e74a38fb864428","abstract_canon_sha256":"9dba3c3e0a92da0affc2815941747e24239db48222d9d53acf8fe1b631e42f26"},"schema_version":"1.0"},"canonical_sha256":"7591f57390f700804001acb194a86e5395bf206d8ad1bb5c304bf18e0643e65a","source":{"kind":"arxiv","id":"1505.04422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04422","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04422v1","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04422","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"OWI7K44Q64AI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OWI7K44Q64AIAQAB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OWI7K44Q","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OWI7K44Q64AIAQABVSYZJKDOKO","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-17T17:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"6271e584fe8b00f7865282c0c6680baabbaaf0aa0b32eca638e74a38fb864428","abstract_canon_sha256":"9dba3c3e0a92da0affc2815941747e24239db48222d9d53acf8fe1b631e42f26"},"schema_version":"1.0"},"canonical_sha256":"7591f57390f700804001acb194a86e5395bf206d8ad1bb5c304bf18e0643e65a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:25.464922Z","signature_b64":"lYu6hebubVLJ6KGhMbfvfX5sqTnkK4TLvDhmDzZXNy60KTGjhyh3jCcH42Uo/w7l3vclziaMQtL/ZsnW4sEMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7591f57390f700804001acb194a86e5395bf206d8ad1bb5c304bf18e0643e65a","last_reissued_at":"2026-05-18T02:07:25.464547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:25.464547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04422","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XpoKEwzjLSCJPdAIaeVsUB2po+/IKvYI+50bQILwffbsW3Klv7QhH5W8y1em0YcuXR+u9IE9vUX7m9LgXKFMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:50:24.837860Z"},"content_sha256":"83bf6510fa1fafccb66a5d61b6c346cb1ec7c3502628263a3d167843051a20d1","schema_version":"1.0","event_id":"sha256:83bf6510fa1fafccb66a5d61b6c346cb1ec7c3502628263a3d167843051a20d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OWI7K44Q64AIAQABVSYZJKDOKO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A twisted $\\bar{\\partial}_f$-Neumann problem and Toeplitz $n$-tuples from singularity theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hao Wen, Huijun Fan","submitted_at":"2015-05-17T17:33:46Z","abstract_excerpt":"A twisted $\\bar{\\partial}_f$-Neumann problem associated to a singularity $(\\mathscr{O}_n,f)$ is established. By constructing the connection to the Koszul complex for toeplitz $n$-tuples $(f_1,\\cdots,f_n)$ on Bergman spaces $B^0(D)$, we can solve this $\\bar{\\partial}_f$-Neumann problem. Moreover, we can compute the cohomology of the $L^2$ holomorphic Koszul complex $(B^*(D),\\partial f\\wedge)$ explicitly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04422","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":""},"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":"2026-05-18T02:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpcBp1FVkeHq5+5W0DoizNDmW4VVbHvYdYvXBbnVYftqjbPM4Sby6Vobi4sWyD1vYiJPOmq16olX0qnRh7XKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:50:24.838204Z"},"content_sha256":"93e6f6aa2d74c40a33fd391cc83a1f4835439a68d87fe2a7caedd03e8250e23d","schema_version":"1.0","event_id":"sha256:93e6f6aa2d74c40a33fd391cc83a1f4835439a68d87fe2a7caedd03e8250e23d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/bundle.json","state_url":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWI7K44Q64AIAQABVSYZJKDOKO/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":"2026-06-04T14:50:24Z","links":{"resolver":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO","bundle":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/bundle.json","state":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWI7K44Q64AIAQABVSYZJKDOKO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OWI7K44Q64AIAQABVSYZJKDOKO","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":"9dba3c3e0a92da0affc2815941747e24239db48222d9d53acf8fe1b631e42f26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-17T17:33:46Z","title_canon_sha256":"6271e584fe8b00f7865282c0c6680baabbaaf0aa0b32eca638e74a38fb864428"},"schema_version":"1.0","source":{"id":"1505.04422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04422","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04422v1","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04422","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"OWI7K44Q64AI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OWI7K44Q64AIAQAB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OWI7K44Q","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:93e6f6aa2d74c40a33fd391cc83a1f4835439a68d87fe2a7caedd03e8250e23d","target":"graph","created_at":"2026-05-18T02:07:25Z","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":"A twisted $\\bar{\\partial}_f$-Neumann problem associated to a singularity $(\\mathscr{O}_n,f)$ is established. By constructing the connection to the Koszul complex for toeplitz $n$-tuples $(f_1,\\cdots,f_n)$ on Bergman spaces $B^0(D)$, we can solve this $\\bar{\\partial}_f$-Neumann problem. Moreover, we can compute the cohomology of the $L^2$ holomorphic Koszul complex $(B^*(D),\\partial f\\wedge)$ explicitly","authors_text":"Hao Wen, Huijun Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-17T17:33:46Z","title":"A twisted $\\bar{\\partial}_f$-Neumann problem and Toeplitz $n$-tuples from singularity theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04422","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":"sha256:83bf6510fa1fafccb66a5d61b6c346cb1ec7c3502628263a3d167843051a20d1","target":"record","created_at":"2026-05-18T02:07:25Z","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":"9dba3c3e0a92da0affc2815941747e24239db48222d9d53acf8fe1b631e42f26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-17T17:33:46Z","title_canon_sha256":"6271e584fe8b00f7865282c0c6680baabbaaf0aa0b32eca638e74a38fb864428"},"schema_version":"1.0","source":{"id":"1505.04422","kind":"arxiv","version":1}},"canonical_sha256":"7591f57390f700804001acb194a86e5395bf206d8ad1bb5c304bf18e0643e65a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7591f57390f700804001acb194a86e5395bf206d8ad1bb5c304bf18e0643e65a","first_computed_at":"2026-05-18T02:07:25.464547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:25.464547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYu6hebubVLJ6KGhMbfvfX5sqTnkK4TLvDhmDzZXNy60KTGjhyh3jCcH42Uo/w7l3vclziaMQtL/ZsnW4sEMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:25.464922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83bf6510fa1fafccb66a5d61b6c346cb1ec7c3502628263a3d167843051a20d1","sha256:93e6f6aa2d74c40a33fd391cc83a1f4835439a68d87fe2a7caedd03e8250e23d"],"state_sha256":"e92ca6d12993740e7bcbfd0f219a9c69669e7a47a0b84f2a22449ae6c6d74e9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrj/9AcWWOTwGOtfAeNLegDYcH6wWEp6JOI2Wh67qv2xDeOsXdu4rwq71RAP6l6p+/qXYDzV7DNubq89I01cCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:50:24.840359Z","bundle_sha256":"e64e0d70c8395c4a90b5e54de6e4d1c032aa68f119bde4630450810feeeda4c5"}}