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Generalizing a result of Ng and Sabloff for the case q =2, we show the augmentation numbers, Aug_m(L,q), are determined by specializing the m-graded ruling polynomial, R^m_L(z), at z = q^{1/2}-q^{-1/2}. As a corollary, we deduce that the ruling polynomials are determined by the Legendrian contact homology DGA."},"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":"1308.4662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-21T19:08:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ad5a4d81e414b0b2ce6e5cad66f3e76e991593a9e66e581ca86df64223026a54","abstract_canon_sha256":"c9ae73f764661c4dab1f13287f5258bf9c04137e124cfe6de10ddb8317978c0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.568149Z","signature_b64":"M4liAuxdXpjL6NDXaU6XS4XvAO6UqTCk8hmCBN50NZBYzcKLYrlM7BiuKe7swRRZw7nP+BkNP9PEAsdm43T6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e466a62677783e5723e364edd15c72653da70d92606fee92fad9ec7864de9e2f","last_reissued_at":"2026-05-18T00:44:29.567610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.567610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ruling polynomials and augmentations over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Dan Rutherford, Michael B. 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