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More precisely, if $\\pi_1$ and $\\pi_2$ are irreducible admissible generic representations of $\\mathrm{GL}_6(F)$ with the same central character, then \\[ \\gamma(s,\\pi_1\\otimes\\chi,\\wedge^3,\\psi)= \\gamma(s,\\pi_2\\otimes\\chi,\\wedge^3,\\psi) \\] for every sufficiently ramified character $\\chi$ of $F^\\times$, where $\\chi$ is regarded as a character of $\\mathrm{GL}_6(F)$ through the determinant. The proof uses the realization of the exterior cube representation by the maximal p"},"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":"2606.28091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-26T13:52:04Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"dc65bfcaebd2c88fd46c60136cd45451d3a4d51e4bff9b8889e0951c8d86b761","abstract_canon_sha256":"281e4bfd55cc6bafa604d6b2f581dc98f87de0924153a9c38d4876c852173c78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:14:57.683156Z","signature_b64":"emB8VP1/sS8WB33HRImYyL55TfNll5IeuJpW1UjKdEtG9JoW5TxpJSISlMQvnRdwBrMixghL7JFEwK9pfIkqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f03e27196624f00d128e5962e45386719f5645c300a299fcd8233a368bdef1a0","last_reissued_at":"2026-06-29T01:14:57.682772Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:14:57.682772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of the exterior cube $\\gamma$-factors for $\\mathrm{GL}(6)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dongming She, Taiwang Deng","submitted_at":"2026-06-26T13:52:04Z","abstract_excerpt":"We prove the stability of the Langlands-Shahidi local $\\gamma$-factor for the exterior cube representation of $\\mathrm{GL}_6$. More precisely, if $\\pi_1$ and $\\pi_2$ are irreducible admissible generic representations of $\\mathrm{GL}_6(F)$ with the same central character, then \\[ \\gamma(s,\\pi_1\\otimes\\chi,\\wedge^3,\\psi)= \\gamma(s,\\pi_2\\otimes\\chi,\\wedge^3,\\psi) \\] for every sufficiently ramified character $\\chi$ of $F^\\times$, where $\\chi$ is regarded as a character of $\\mathrm{GL}_6(F)$ through the determinant. 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