{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3F3S3IMDXU4GZI33CZMDZBFIVI","short_pith_number":"pith:3F3S3IMD","schema_version":"1.0","canonical_sha256":"d9772da183bd386ca37b16583c84a8aa23d0c2aab34911d9d4e5d12f246dc5ab","source":{"kind":"arxiv","id":"2608.04540","version":1},"attestation_state":"computed","paper":{"title":"An Infinitesimal Circular Morera Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Ao Xiao, Qiteng Guo","submitted_at":"2026-08-05T07:16:34Z","abstract_excerpt":"We prove an infinitesimal circular version of Morera's theorem. Let $D\\subset\\mathbb{C}$ be a domain and let $f\\in C(D)$. If, at every $a\\in D$, $\\int_{\\vert{}\\zeta-a\\vert{}=r}f(\\zeta)\\,d\\zeta=o(r^2)$ as $r\\to0^+$, then $f$ is holomorphic in $D$. In particular, exact vanishing of all sufficiently small centered circular integrals implies holomorphicity. The proof uses a local distributional $\\partial$-primitive, a circular identity for weak $\\partial$-derivatives, and a pointwise asymptotic mean-value criterion for harmonicity."},"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":"2608.04540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-08-05T07:16:34Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3e1cf092bf91afb3c6ad0e2653671948a74981e53a767742e58e587a92f4e34a","abstract_canon_sha256":"904d2b89f7d788b55b4f6cad203e6c96cfb97bccf8656a9821adb77cb8d523b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:35:48.181569Z","signature_b64":"g37QDzuy6xcNqw1QFZTH0pkNt8Kwh2HSwu9egfrqT/CBkUtaxoZwEBy2g92b2ij76zM6mJvkcuPdlHIrYCZhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9772da183bd386ca37b16583c84a8aa23d0c2aab34911d9d4e5d12f246dc5ab","last_reissued_at":"2026-08-06T01:35:48.180144Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:35:48.180144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Infinitesimal Circular Morera Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Ao Xiao, Qiteng Guo","submitted_at":"2026-08-05T07:16:34Z","abstract_excerpt":"We prove an infinitesimal circular version of Morera's theorem. Let $D\\subset\\mathbb{C}$ be a domain and let $f\\in C(D)$. If, at every $a\\in D$, $\\int_{\\vert{}\\zeta-a\\vert{}=r}f(\\zeta)\\,d\\zeta=o(r^2)$ as $r\\to0^+$, then $f$ is holomorphic in $D$. In particular, exact vanishing of all sufficiently small centered circular integrals implies holomorphicity. The proof uses a local distributional $\\partial$-primitive, a circular identity for weak $\\partial$-derivatives, and a pointwise asymptotic mean-value criterion for harmonicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04540","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/2608.04540/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":"2608.04540","created_at":"2026-08-06T01:35:48.181942+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04540v1","created_at":"2026-08-06T01:35:48.181942+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04540","created_at":"2026-08-06T01:35:48.181942+00:00"},{"alias_kind":"pith_short_12","alias_value":"3F3S3IMDXU4G","created_at":"2026-08-06T01:35:48.181942+00:00"},{"alias_kind":"pith_short_16","alias_value":"3F3S3IMDXU4GZI33","created_at":"2026-08-06T01:35:48.181942+00:00"},{"alias_kind":"pith_short_8","alias_value":"3F3S3IMD","created_at":"2026-08-06T01:35:48.181942+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI","json":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI.json","graph_json":"https://pith.science/api/pith-number/3F3S3IMDXU4GZI33CZMDZBFIVI/graph.json","events_json":"https://pith.science/api/pith-number/3F3S3IMDXU4GZI33CZMDZBFIVI/events.json","paper":"https://pith.science/paper/3F3S3IMD"},"agent_actions":{"view_html":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI","download_json":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI.json","view_paper":"https://pith.science/paper/3F3S3IMD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04540&json=true","fetch_graph":"https://pith.science/api/pith-number/3F3S3IMDXU4GZI33CZMDZBFIVI/graph.json","fetch_events":"https://pith.science/api/pith-number/3F3S3IMDXU4GZI33CZMDZBFIVI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI/action/storage_attestation","attest_author":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI/action/author_attestation","sign_citation":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI/action/citation_signature","submit_replication":"https://pith.science/pith/3F3S3IMDXU4GZI33CZMDZBFIVI/action/replication_record"}},"created_at":"2026-08-06T01:35:48.181942+00:00","updated_at":"2026-08-06T01:35:48.181942+00:00"}