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The standard question (along the lines of Singularity Theory) is the finite-(\\Sigma,G)-determinacy of matrices.\n  In our previous work this determinacy question was reduced to the study of the tangent spaces to \\Sigma and to the orbit, T_{(\\Sigma,A)}, T_{(GA,A)}, and their quotient: the tangent module to the miniversal deformation. In particular, the order of determinacy is controlled by the annihilator of this tangent module.\n  Then"},"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":"1604.06247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-21T10:31:29Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"ef6e02aa2b9369032959a449d86ece803fc976637c31c6545268f9ac72e449c0","abstract_canon_sha256":"a52a1d551c0a0851cf9388999e419019f35398f50fd72174e3e1fc2e5a528b80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:32.215471Z","signature_b64":"Hwi82PNrVPdZpbCURiDzcDYQgKgkvQZ2jLeEghbkc3awO/NzzqEG+eHjBFoaaO/3wEBnjBTxEYwa5Ma7UkpBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae758cfe1d549cd83e6758e4abb6490f73ff75e8e4de5b27edb22a72867d8205","last_reissued_at":"2026-05-18T01:16:32.214778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:32.214778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite determinacy of matrices over local rings.II. 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