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The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface.\n  We give explicite descriptions of the moduli spaces associated with the triple $(\\Hom(\\C^r,\\C^{r_0}), \\alpha_{\\rm can},U(r))$, where $\\alpha_{\\rm can}$ denotes the canonical action of $\\hat K=U(r)\\times"},"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":"math/0102119","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2001-02-15T17:38:22Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"000f87e300b55d9b007366a655e42f1ad938e1a41d18306f4629c9a357af9fc0","abstract_canon_sha256":"65ffc02cf0bb2cfb26e08291afa6a2b92dc7faf2bdd8fbfbb22b8668b491cb5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:28:15.338103Z","signature_b64":"C26AaiIhxJatkYO3CXom6Q4gV0E6dcBzow5BjjeNNPnERldz88Hom3+AFEP7iyB+iWWUO0FwQE6/L4X5urxxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56f67574631655768f19f1f398b0c5f6d01b211fa88dcfabd34682d3626669d3","last_reissued_at":"2026-07-04T16:28:15.337714Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:28:15.337714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gauge theoretical equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces","license":"","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.SG","authors_text":"A. 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