{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CPQZD2PHI3B3E5R2ZGPFU6P7ZU","short_pith_number":"pith:CPQZD2PH","canonical_record":{"source":{"id":"1608.00790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-02T12:33:12Z","cross_cats_sorted":[],"title_canon_sha256":"007e421f9f05326d197a5fc45d491332a9a3afeeaa3a6dc6abd16a5a70ed7023","abstract_canon_sha256":"a6523fd3ff79ae7b9973cc199ac24e8d4a93a247569716c02b3a770dceb9f36f"},"schema_version":"1.0"},"canonical_sha256":"13e191e9e746c3b2763ac99e5a79ffcd258588284764dffe16b3fc92da7ace7e","source":{"kind":"arxiv","id":"1608.00790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00790","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00790v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00790","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"CPQZD2PHI3B3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CPQZD2PHI3B3E5R2","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CPQZD2PH","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CPQZD2PHI3B3E5R2ZGPFU6P7ZU","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-02T12:33:12Z","cross_cats_sorted":[],"title_canon_sha256":"007e421f9f05326d197a5fc45d491332a9a3afeeaa3a6dc6abd16a5a70ed7023","abstract_canon_sha256":"a6523fd3ff79ae7b9973cc199ac24e8d4a93a247569716c02b3a770dceb9f36f"},"schema_version":"1.0"},"canonical_sha256":"13e191e9e746c3b2763ac99e5a79ffcd258588284764dffe16b3fc92da7ace7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:00.982788Z","signature_b64":"TVXwz13zR25SY/Tj3T2udsIliuqvekdxHRxwRk3RteFxvEkLBey79K/NrOzkO4H0VVghqSRftGYcgs60krtMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13e191e9e746c3b2763ac99e5a79ffcd258588284764dffe16b3fc92da7ace7e","last_reissued_at":"2026-05-18T01:10:00.982225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:00.982225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00790","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZV7S04RHxXDCqhOfWJbKl2PwuYyoo1fD15C++C7bB279TuLoDpPUyuKb9P8iqIuncd8OqPcXENnvow8vuRRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:43:32.093685Z"},"content_sha256":"a43a72864778e682bf3be61611e435af4b9050e4331dda01f8fb3e2bda87cea8","schema_version":"1.0","event_id":"sha256:a43a72864778e682bf3be61611e435af4b9050e4331dda01f8fb3e2bda87cea8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CPQZD2PHI3B3E5R2ZGPFU6P7ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conformal invariants associated with quadratic differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric Schippers","submitted_at":"2016-08-02T12:33:12Z","abstract_excerpt":"Z. Nehari developed a general technique for obtaining inequalities for conformal maps and domain functions from contour integrals and the Dirichlet principle. Given a harmonic function with singularity on a domain $R$, it associates a monotonic functional of subdomains $D \\subseteq R$. In the case that $R$ is conformally equivalent to a disk, we extend Nehari's method by associating a functional to any quadratic differential on $R$ with specified singularities. Nehari's method corresponds to the special case that the quadratic differential is of the form $(\\partial q)^2$ for a singular harmoni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00790","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJbz12p6V4wWpOYcdvUpONITuUEaNLmTR/3cQZMbN/l0yUe3cYKX0KcbBWvfIqJMU409VWww+g2mgJQvfzGDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:43:32.094496Z"},"content_sha256":"e6660f1ab44840ac48898d4fe8ca40e8194a42b11379df32bde8797a08524a81","schema_version":"1.0","event_id":"sha256:e6660f1ab44840ac48898d4fe8ca40e8194a42b11379df32bde8797a08524a81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPQZD2PHI3B3E5R2ZGPFU6P7ZU/bundle.json","state_url":"https://pith.science/pith/CPQZD2PHI3B3E5R2ZGPFU6P7ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPQZD2PHI3B3E5R2ZGPFU6P7ZU/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":"2026-06-10T08:43:32Z","links":{"resolver":"https://pith.science/pith/CPQZD2PHI3B3E5R2ZGPFU6P7ZU","bundle":"https://pith.science/pith/CPQZD2PHI3B3E5R2ZGPFU6P7ZU/bundle.json","state":"https://pith.science/pith/CPQZD2PHI3B3E5R2ZGPFU6P7ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPQZD2PHI3B3E5R2ZGPFU6P7ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CPQZD2PHI3B3E5R2ZGPFU6P7ZU","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":"a6523fd3ff79ae7b9973cc199ac24e8d4a93a247569716c02b3a770dceb9f36f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-02T12:33:12Z","title_canon_sha256":"007e421f9f05326d197a5fc45d491332a9a3afeeaa3a6dc6abd16a5a70ed7023"},"schema_version":"1.0","source":{"id":"1608.00790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00790","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00790v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00790","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"CPQZD2PHI3B3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CPQZD2PHI3B3E5R2","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CPQZD2PH","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e6660f1ab44840ac48898d4fe8ca40e8194a42b11379df32bde8797a08524a81","target":"graph","created_at":"2026-05-18T01:10:00Z","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":"Z. Nehari developed a general technique for obtaining inequalities for conformal maps and domain functions from contour integrals and the Dirichlet principle. Given a harmonic function with singularity on a domain $R$, it associates a monotonic functional of subdomains $D \\subseteq R$. In the case that $R$ is conformally equivalent to a disk, we extend Nehari's method by associating a functional to any quadratic differential on $R$ with specified singularities. Nehari's method corresponds to the special case that the quadratic differential is of the form $(\\partial q)^2$ for a singular harmoni","authors_text":"Eric Schippers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-02T12:33:12Z","title":"Conformal invariants associated with quadratic differentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00790","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:a43a72864778e682bf3be61611e435af4b9050e4331dda01f8fb3e2bda87cea8","target":"record","created_at":"2026-05-18T01:10:00Z","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":"a6523fd3ff79ae7b9973cc199ac24e8d4a93a247569716c02b3a770dceb9f36f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-08-02T12:33:12Z","title_canon_sha256":"007e421f9f05326d197a5fc45d491332a9a3afeeaa3a6dc6abd16a5a70ed7023"},"schema_version":"1.0","source":{"id":"1608.00790","kind":"arxiv","version":1}},"canonical_sha256":"13e191e9e746c3b2763ac99e5a79ffcd258588284764dffe16b3fc92da7ace7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13e191e9e746c3b2763ac99e5a79ffcd258588284764dffe16b3fc92da7ace7e","first_computed_at":"2026-05-18T01:10:00.982225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:00.982225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TVXwz13zR25SY/Tj3T2udsIliuqvekdxHRxwRk3RteFxvEkLBey79K/NrOzkO4H0VVghqSRftGYcgs60krtMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:00.982788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a43a72864778e682bf3be61611e435af4b9050e4331dda01f8fb3e2bda87cea8","sha256:e6660f1ab44840ac48898d4fe8ca40e8194a42b11379df32bde8797a08524a81"],"state_sha256":"da8573721a9b757bb533752d23349506cb1857cb2700bf750d473cb18f182bbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xUxooPDxpbbz1nscjq11btF7/5ZUgA4REyEdiktSjt5t9eTwDDp4pnV87KtXtAQb9SWnlLh3Gl2BE9SwglfnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T08:43:32.098707Z","bundle_sha256":"6c731f3a6446ed9870aa6dc24235bf8443a2d1e9456341d5eca851e4dddcb478"}}