{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DZBHXFM5E662AKSZKNYWKGQD7S","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":"a7801fa4c7363923c11e93e5b19ae86d90d27f822ff1f993cf258a6714fea4b9","cross_cats_sorted":["math.CV","math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-11T13:57:11Z","title_canon_sha256":"bf4be0e538f3b663a051fb36989ee664a2ca703cf2b34d37bafa22e1f7ffa446"},"schema_version":"1.0","source":{"id":"2606.13373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13373","created_at":"2026-06-12T01:09:58Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13373v1","created_at":"2026-06-12T01:09:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13373","created_at":"2026-06-12T01:09:58Z"},{"alias_kind":"pith_short_12","alias_value":"DZBHXFM5E662","created_at":"2026-06-12T01:09:58Z"},{"alias_kind":"pith_short_16","alias_value":"DZBHXFM5E662AKSZ","created_at":"2026-06-12T01:09:58Z"},{"alias_kind":"pith_short_8","alias_value":"DZBHXFM5","created_at":"2026-06-12T01:09:58Z"}],"graph_snapshots":[{"event_id":"sha256:4d461f0d40929c8af2b232cf6620086536f93c58259a59f33629d28cb712eca7","target":"graph","created_at":"2026-06-12T01:09:58Z","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/2606.13373/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{W}=\\mathcal{W}_{n}\\boxtimes\\mathcal{W}_{d-n}$ be a $d$-web on $(\\mathbb{C}^2,0)$, where $\\mathcal{W}_n$ is an $n$-web with a totally invariant irreducible curve~$C$, and $\\mathcal{W}_{d-n}$ is a regular $(d-n)$-web transverse to $C$. We show that the curvature of $\\mathcal{W}$ is holomorphic along $C$ if and only if the curvature of $\\mathcal{W}_n$ is holomorphic along $C$. When $\\mathcal{W}_n$ is non-degenerate along $C$, we prove that $K(\\mathcal{W}_n)$, and hence $K(\\mathcal{W})$, is holomorphic along $C.$ We deduce that, if $\\mathcal{W}_n$ is irreducible and $\\mathrm{mult}\\le","authors_text":"Samir Bedrouni","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-11T13:57:11Z","title":"On the holomorphy of the curvature of planar webs along an invariant curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13373","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:f2fd158d9055b2f1ba2b981bacb2c1e2709891e789e3978015ebaf47fde98b17","target":"record","created_at":"2026-06-12T01:09:58Z","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":"a7801fa4c7363923c11e93e5b19ae86d90d27f822ff1f993cf258a6714fea4b9","cross_cats_sorted":["math.CV","math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-11T13:57:11Z","title_canon_sha256":"bf4be0e538f3b663a051fb36989ee664a2ca703cf2b34d37bafa22e1f7ffa446"},"schema_version":"1.0","source":{"id":"2606.13373","kind":"arxiv","version":1}},"canonical_sha256":"1e427b959d27bda02a595371651a03fcb714f7464373f744edff885fe4369f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e427b959d27bda02a595371651a03fcb714f7464373f744edff885fe4369f72","first_computed_at":"2026-06-12T01:09:58.278481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:58.278481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aZ11lLnCRw4o6tjiLmdw1ud9Flz2QstoAAOvvqyk1n/Aou4QxXmsD3lgISm5I7MMmxmjOpUCoweaINiparBHBg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:58.279312Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2fd158d9055b2f1ba2b981bacb2c1e2709891e789e3978015ebaf47fde98b17","sha256:4d461f0d40929c8af2b232cf6620086536f93c58259a59f33629d28cb712eca7"],"state_sha256":"83f197bee276836ffc711e87db330cac4d542577739987c520246c55e4e4b99d"}