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We consider the natural action of $SL_2$ on $Rat^{tm}_2$ induced from the action of $SL_2$ on $(\\mathbb{P}^1)^5$ and prove that the quotient space $Rat^{tm}_2/SL_2$ exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over $\\mathbb{Z}[1/2]$."},"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":"1408.3846","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-17T17:44:21Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"383cbcc995949b61a80fe274f58eaf8be8f6a571148794e1dcbc5f6145ca67b3","abstract_canon_sha256":"302b44db13e791724d1d2a812a30e1057a6742ec9892b45408f505b8e19f19c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:03.166281Z","signature_b64":"yL5OFmoR1Vj8wbWYlsJ2r1rAx3OZlpBEt2/RhYHNLul64Kiaix6UbyvfBm+jpulW4skSD600TyUdfDgGafcrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a00d2c0826fb3689c3b58c751eb75ce9d71bf8f0aa4f6244138f82d8b900f831","last_reissued_at":"2026-05-18T02:45:03.165796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:03.165796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Moduli Space of Totally Marked Degree Two Rational Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Anupam Bhatnagar","submitted_at":"2014-08-17T17:44:21Z","abstract_excerpt":"A rational map $\\phi: \\mathbb{P}^1 \\to \\mathbb{P}^1$ along with an ordered list of fixed and critical points is called a totally marked rational map. 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