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This paper extracts the integer carried by the same field. When the zero set of $N$ is compactly contained in a bounded simply connected domain, the winding number of $N$ along any enclosing curve -- the pseudo-analytic charge $n \\in \\mathbb{Z}$ --"},"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":"2607.07910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-07-08T20:49:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"3f705c76f2e0371bef67a71241da40ab9d54d046c0a42450cb45f78909f54c59","abstract_canon_sha256":"fcb4cdc9906fd635da4af3cff169ccdf8c1e6d638bfd786477700dc986b43678"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T00:19:04.633178Z","signature_b64":"yD7Fe2CdYYiC8bqzjkaFcwtz4RIjbD93kqBxzvLBM61RMqL2KxMaZd23XvG8Gsrp68ox8XI4RKrlz0bKeljlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15498d32cf064d954bfceb57f3bd741d20815bcca335359ec33cad107b91ebb2","last_reissued_at":"2026-07-10T00:19:04.632746Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T00:19:04.632746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Pseudo-Analytic Charge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Daniel Alay\\'on-Solarz","submitted_at":"2026-07-08T20:49:15Z","abstract_excerpt":"The framed Beltrami--Vekua equation $\\Phi(w_{\\bar z} - \\mu w_z) + \\Psi(\\overline{w_z} - \\mu\\overline{w_{\\bar z}}) + \\mathfrak{a}w + \\mathfrak{b}\\bar w = \\mathfrak{f}$, with $|\\mu|<1$ and $|\\Phi|>|\\Psi|$, carries a numerator field $N = \\Phi\\mathfrak{b} - \\Psi\\mathfrak{a} - W_L(\\Phi,\\Psi)$ whose weighted modulus integrates to the pseudo-analytic mass. This paper extracts the integer carried by the same field. When the zero set of $N$ is compactly contained in a bounded simply connected domain, the winding number of $N$ along any enclosing curve -- the pseudo-analytic charge $n \\in \\mathbb{Z}$ --"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07910","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/2607.07910/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":"2607.07910","created_at":"2026-07-10T00:19:04.632810+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.07910v1","created_at":"2026-07-10T00:19:04.632810+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07910","created_at":"2026-07-10T00:19:04.632810+00:00"},{"alias_kind":"pith_short_12","alias_value":"CVEY2MWPAZGZ","created_at":"2026-07-10T00:19:04.632810+00:00"},{"alias_kind":"pith_short_16","alias_value":"CVEY2MWPAZGZKS74","created_at":"2026-07-10T00:19:04.632810+00:00"},{"alias_kind":"pith_short_8","alias_value":"CVEY2MWP","created_at":"2026-07-10T00:19:04.632810+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/CVEY2MWPAZGZKS745NL7HPLUDU","json":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU.json","graph_json":"https://pith.science/api/pith-number/CVEY2MWPAZGZKS745NL7HPLUDU/graph.json","events_json":"https://pith.science/api/pith-number/CVEY2MWPAZGZKS745NL7HPLUDU/events.json","paper":"https://pith.science/paper/CVEY2MWP"},"agent_actions":{"view_html":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU","download_json":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU.json","view_paper":"https://pith.science/paper/CVEY2MWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.07910&json=true","fetch_graph":"https://pith.science/api/pith-number/CVEY2MWPAZGZKS745NL7HPLUDU/graph.json","fetch_events":"https://pith.science/api/pith-number/CVEY2MWPAZGZKS745NL7HPLUDU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU/action/storage_attestation","attest_author":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU/action/author_attestation","sign_citation":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU/action/citation_signature","submit_replication":"https://pith.science/pith/CVEY2MWPAZGZKS745NL7HPLUDU/action/replication_record"}},"created_at":"2026-07-10T00:19:04.632810+00:00","updated_at":"2026-07-10T00:19:04.632810+00:00"}