{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V4LH2AX42ORKQZHULEQ6ZFTMMW","short_pith_number":"pith:V4LH2AX4","canonical_record":{"source":{"id":"1606.00121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-01T05:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"5b13986492c92e39bbc6befd09a08b797917cd2b964be59d7f73d48f54fc301e","abstract_canon_sha256":"6ad7cc467a4ed25ca2b992ef300d8cf2bd12b3cb6fa518e1aeb048d67754ab93"},"schema_version":"1.0"},"canonical_sha256":"af167d02fcd3a2a864f45921ec966c65bdfdecf4d508ee2a0d7e512af9205475","source":{"kind":"arxiv","id":"1606.00121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00121","created_at":"2026-05-18T01:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00121v1","created_at":"2026-05-18T01:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00121","created_at":"2026-05-18T01:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"V4LH2AX42ORK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V4LH2AX42ORKQZHU","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V4LH2AX4","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V4LH2AX42ORKQZHULEQ6ZFTMMW","target":"record","payload":{"canonical_record":{"source":{"id":"1606.00121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-01T05:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"5b13986492c92e39bbc6befd09a08b797917cd2b964be59d7f73d48f54fc301e","abstract_canon_sha256":"6ad7cc467a4ed25ca2b992ef300d8cf2bd12b3cb6fa518e1aeb048d67754ab93"},"schema_version":"1.0"},"canonical_sha256":"af167d02fcd3a2a864f45921ec966c65bdfdecf4d508ee2a0d7e512af9205475","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:05.868391Z","signature_b64":"49IbiTYkGbElXL80QvGZrFVRg4XHTDaBdOQnBlmignLfZ1ApPVUuPWt72dIFVsEio5/s3hOrqHVaWoj7AI8iCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af167d02fcd3a2a864f45921ec966c65bdfdecf4d508ee2a0d7e512af9205475","last_reissued_at":"2026-05-18T01:13:05.868039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:05.868039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.00121","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":"2026-05-18T01:13:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OB4yfm+nB1viX3sfQCVlAH1v3Tuo6doosQFYf1r9rIJqfERyzjjqFtMVRsHRaCZ5e6eIE0FwOj6IwXnqXzdGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:46:09.869221Z"},"content_sha256":"2da3d2ba7b8be1db8e19c1b9a831cd6982fee762b0c8765a9cc5572011159412","schema_version":"1.0","event_id":"sha256:2da3d2ba7b8be1db8e19c1b9a831cd6982fee762b0c8765a9cc5572011159412"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V4LH2AX42ORKQZHULEQ6ZFTMMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling limits of discrete holomorphic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Zeping Zhu","submitted_at":"2016-06-01T05:38:02Z","abstract_excerpt":"One of the most natural and challenging issues in discrete complex analysis is to prove the convergence of discrete holomorphic functions to their continuous counterparts.\n  This article is to solve the open problem in the general setting. To this end we introduce new concepts of discrete surface measure and discrete outer normal vector and establish the discrete Cauchy-Pompeiu integral formula,\n  \\begin{eqnarray*} f(\\zeta)=\\displaystyle{\\int_{\\partial B^h}} \\mathcal{K}^h(z,\\zeta) f(z)dS^h(z)+\\displaystyle{\\int_{B^h}} E^h(\\zeta-z) \\partial_{\\bar z}^h f (z)dV^h(z),\\end{eqnarray*} which results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00121","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":"2026-05-18T01:13:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/TTlb7gj6LmXtXcqNldGSdcDJFBlvOSKVR3Ns31oQnJSsPg42i0G0m0nWtymmdV2+Z1h30z/yDsHWDlKf9GBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:46:09.869613Z"},"content_sha256":"4707df3edc2349bcd8beb56b001ce4b4800e1d48178c60c74d0f31cd14a19625","schema_version":"1.0","event_id":"sha256:4707df3edc2349bcd8beb56b001ce4b4800e1d48178c60c74d0f31cd14a19625"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4LH2AX42ORKQZHULEQ6ZFTMMW/bundle.json","state_url":"https://pith.science/pith/V4LH2AX42ORKQZHULEQ6ZFTMMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4LH2AX42ORKQZHULEQ6ZFTMMW/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":"2026-06-01T02:46:09Z","links":{"resolver":"https://pith.science/pith/V4LH2AX42ORKQZHULEQ6ZFTMMW","bundle":"https://pith.science/pith/V4LH2AX42ORKQZHULEQ6ZFTMMW/bundle.json","state":"https://pith.science/pith/V4LH2AX42ORKQZHULEQ6ZFTMMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4LH2AX42ORKQZHULEQ6ZFTMMW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V4LH2AX42ORKQZHULEQ6ZFTMMW","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":"6ad7cc467a4ed25ca2b992ef300d8cf2bd12b3cb6fa518e1aeb048d67754ab93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-01T05:38:02Z","title_canon_sha256":"5b13986492c92e39bbc6befd09a08b797917cd2b964be59d7f73d48f54fc301e"},"schema_version":"1.0","source":{"id":"1606.00121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00121","created_at":"2026-05-18T01:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00121v1","created_at":"2026-05-18T01:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00121","created_at":"2026-05-18T01:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"V4LH2AX42ORK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V4LH2AX42ORKQZHU","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V4LH2AX4","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:4707df3edc2349bcd8beb56b001ce4b4800e1d48178c60c74d0f31cd14a19625","target":"graph","created_at":"2026-05-18T01:13:05Z","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":"One of the most natural and challenging issues in discrete complex analysis is to prove the convergence of discrete holomorphic functions to their continuous counterparts.\n  This article is to solve the open problem in the general setting. To this end we introduce new concepts of discrete surface measure and discrete outer normal vector and establish the discrete Cauchy-Pompeiu integral formula,\n  \\begin{eqnarray*} f(\\zeta)=\\displaystyle{\\int_{\\partial B^h}} \\mathcal{K}^h(z,\\zeta) f(z)dS^h(z)+\\displaystyle{\\int_{B^h}} E^h(\\zeta-z) \\partial_{\\bar z}^h f (z)dV^h(z),\\end{eqnarray*} which results ","authors_text":"Guangbin Ren, Zeping Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-01T05:38:02Z","title":"Scaling limits of discrete holomorphic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00121","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":"sha256:2da3d2ba7b8be1db8e19c1b9a831cd6982fee762b0c8765a9cc5572011159412","target":"record","created_at":"2026-05-18T01:13:05Z","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":"6ad7cc467a4ed25ca2b992ef300d8cf2bd12b3cb6fa518e1aeb048d67754ab93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-01T05:38:02Z","title_canon_sha256":"5b13986492c92e39bbc6befd09a08b797917cd2b964be59d7f73d48f54fc301e"},"schema_version":"1.0","source":{"id":"1606.00121","kind":"arxiv","version":1}},"canonical_sha256":"af167d02fcd3a2a864f45921ec966c65bdfdecf4d508ee2a0d7e512af9205475","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af167d02fcd3a2a864f45921ec966c65bdfdecf4d508ee2a0d7e512af9205475","first_computed_at":"2026-05-18T01:13:05.868039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:05.868039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49IbiTYkGbElXL80QvGZrFVRg4XHTDaBdOQnBlmignLfZ1ApPVUuPWt72dIFVsEio5/s3hOrqHVaWoj7AI8iCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:05.868391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2da3d2ba7b8be1db8e19c1b9a831cd6982fee762b0c8765a9cc5572011159412","sha256:4707df3edc2349bcd8beb56b001ce4b4800e1d48178c60c74d0f31cd14a19625"],"state_sha256":"9c4f3a5a2b03b249a97d2f29dc3e9396774da37ec2d4158f2f824de2263f4a07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOKLW+L+4ed5s47jfm5ZugS17OgPG5EOj0RQ2o+yE7YULtwGeWBnmJAKNc1y5QgGZYWiRRTo+aY+POMMvpdaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:46:09.872015Z","bundle_sha256":"21dbcfeea8b2922b8aeb11ec5b5af3173a1aba93a06648a68a8d7df53d241fa7"}}