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This obstruction detects infinite new families of knots that represent elements of order 4 in the algebraic concordance group that are not of order 4 in concordance."},"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":"0908.0005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-31T20:37:20Z","cross_cats_sorted":[],"title_canon_sha256":"e8b7ff9723b8572acd4b8528775e6009a95171bbdaedc1e9ab5d3cb2073e4905","abstract_canon_sha256":"d8f288c6ca1f8a561875945e480c5833949a0b996f0ae5162c9ba694d8ee918f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:09.346015Z","signature_b64":"LQ9QDMgyOt5PPPi1as5JF30E1SnIATJ3VfR6F2XMQHmwzW2GgWP8EIqZrXlpzgkSfBJSkXEXvR1WExJKCDpLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de9447e4d029c4243d4171e2dbaced1970d6005b0109a9f3585bfd349e7c1f41","last_reissued_at":"2026-05-18T03:12:09.345198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:09.345198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stabilizing Four-Torsion in Classical Knot Concordance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Charles Livingston, Swatee Naik","submitted_at":"2009-07-31T20:37:20Z","abstract_excerpt":"Let $M_K$ be the 2-fold branched cover of a knot $K in $S^3$. 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