{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YT6LKM72OB63CFWTYKNZ7UK2D4","short_pith_number":"pith:YT6LKM72","canonical_record":{"source":{"id":"2605.16658","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-15T21:54:13Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"556076b848477cd5735e14086083fd85e15446db6a1d14a5fc06a47a418a6059","abstract_canon_sha256":"45c53f09fcd6fc1303888c4b34b48f6d728fdb632e4fb5c799f2270f4838f68e"},"schema_version":"1.0"},"canonical_sha256":"c4fcb533fa707db116d3c29b9fd15a1f3e25dcf8e590d53f8de09681559e5138","source":{"kind":"arxiv","id":"2605.16658","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16658","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16658v1","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16658","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"YT6LKM72OB63","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"YT6LKM72OB63CFWT","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"YT6LKM72","created_at":"2026-05-20T00:02:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YT6LKM72OB63CFWTYKNZ7UK2D4","target":"record","payload":{"canonical_record":{"source":{"id":"2605.16658","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-15T21:54:13Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"556076b848477cd5735e14086083fd85e15446db6a1d14a5fc06a47a418a6059","abstract_canon_sha256":"45c53f09fcd6fc1303888c4b34b48f6d728fdb632e4fb5c799f2270f4838f68e"},"schema_version":"1.0"},"canonical_sha256":"c4fcb533fa707db116d3c29b9fd15a1f3e25dcf8e590d53f8de09681559e5138","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:34.839164Z","signature_b64":"SLqCAoxisbUW2dH8EYgxSLUqVFs212dDUBROtN8kkR56XtJrltBoUqEG5MD7ZRxSIrKA3AerJkPxYVsBnbwVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4fcb533fa707db116d3c29b9fd15a1f3e25dcf8e590d53f8de09681559e5138","last_reissued_at":"2026-05-20T00:02:34.838309Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:34.838309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.16658","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rt2PpK10R6BMxBvj3/aCsWqWSuxtJAzFXKL2W3EHzfSl3mLBszyGynrmfgPkICW2mBYYlpQL/MtIUZ7hJxwSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:47:41.070261Z"},"content_sha256":"302ef832b05eda206720e57f88d0861437cdd83808861dfa7e6a277a98f1b923","schema_version":"1.0","event_id":"sha256:302ef832b05eda206720e57f88d0861437cdd83808861dfa7e6a277a98f1b923"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YT6LKM72OB63CFWTYKNZ7UK2D4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic.","cross_cats":["math.GR","math.GT"],"primary_cat":"math.AG","authors_text":"Ariyan Javanpeykar, Benson Farb, Gregorio Baldi, Matthew Stover","submitted_at":"2026-05-15T21:54:13Z","abstract_excerpt":"Let $\\mathcal{C}$ be the moduli space of smooth complex cubic surfaces and let $\\pi_1(\\mathcal{C})$ be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $\\pi_1(\\mathcal{C})$ is characteristic. This can be interpreted as saying that the group theory of $\\pi_1(\\mathcal{C})$ ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that $\\mathcal{C}$ has no nontrivial biholomorphic automorphisms as complex analytic orbifold."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the ``divisor subgroup'' of π₁(C) is characteristic. This can be interpreted as saying that the group theory of π₁(C) ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that C has no nontrivial biholomorphic automorphisms as complex analytic orbifold.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The deduction that the characteristic property of the divisor subgroup, together with basic complex analysis, suffices to rule out all nontrivial biholomorphic automorphisms of C as an orbifold; this relies on an unstated but load-bearing identification of what constitutes a biholomorphic automorphism in the orbifold category and on the precise definition of the divisor subgroup being invariant under the relevant group actions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"76c457db597cbc5dcfa6fe4abc0107d3b566cf9287ba7655b2db69284c5a53d1"},"source":{"id":"2605.16658","kind":"arxiv","version":1},"verdict":{"id":"7984d9d6-9ef4-435e-94ae-c7dc688ad142","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:40:52.839112Z","strongest_claim":"We prove that the ``divisor subgroup'' of π₁(C) is characteristic. This can be interpreted as saying that the group theory of π₁(C) ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that C has no nontrivial biholomorphic automorphisms as complex analytic orbifold.","one_line_summary":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The deduction that the characteristic property of the divisor subgroup, together with basic complex analysis, suffices to rule out all nontrivial biholomorphic automorphisms of C as an orbifold; this relies on an unstated but load-bearing identification of what constitutes a biholomorphic automorphism in the orbifold category and on the precise definition of the divisor subgroup being invariant under the relevant group actions.","pith_extraction_headline":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16658/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:01:19.303010Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:51:13.496580Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.399967Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.519602Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ad24176442b57fa83908058f84137615c0ea34f3da23e137ee38e96f5fff8ba2"},"references":{"count":15,"sample":[{"doi":"","year":2002,"title":"D. Allcock, J. A. Carlson, and D. Toledo. The complex hyperbolic geometry of the moduli space of cubic surfaces. J. Algebr. Geom., 11(4):659–724, 2002","work_id":"87ea9e12-dd7c-4a94-8033-ed273a8761a9","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"D. Allcock, J. A. Carlson, and D. Toledo. Orthogonal complex hyperbolic arrangements. In Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000) , volume 312 of Contemp. Math. , pages 1–8. Amer","work_id":"a1f4ed53-0023-4d8d-a9b7-bc43927f9467","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1964,"title":"W. L. Baily, Jr. and A. Borel. On the compactification of arithmetically defined quotients of bounded symmetric domains. Bull. Amer. Math. Soc. , 70:588–593, 1964","work_id":"b1c33ebc-fe3d-4440-a1d9-0d829b062477","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"W. Bosma, J. Cannon, and C. Playoust. The Magma algebra system. I. The user language. J. Symbolic Comput., 24(3-4):235–265, 1997. Computational algebra and number theory (London, 1993)","work_id":"02d7e853-bfbd-441a-b7bb-7cc80b92a035","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"M. R. Bridson and A. Haefliger. Metric spaces of non-positive curvature, volume 319 of Grundlehren Math. Wiss. Berlin: Springer, 1999","work_id":"392c47f9-e253-4727-a9be-ace2c78a2eb4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":15,"snapshot_sha256":"f9639b6b71acee0754b86fd0970b00cc455647dcd0f46b20922b692d5d39434c","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"ea64dc2f5611a18303a17153cac9d1d526e345fdb291b12108602d2b96ede072"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"7984d9d6-9ef4-435e-94ae-c7dc688ad142"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"50nrZe/uSFcuwNKKa+jqCNA0sIDf3Kiu8oKi5pDGSPR02YhHAVJAsozlkKWK4hvI9nb5i3fS6LrsrK5ZmPcKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:47:41.071666Z"},"content_sha256":"2e4313a0c3f823c5ca400407cdd93b87461bde336254259dad5ec679af4ed1c1","schema_version":"1.0","event_id":"sha256:2e4313a0c3f823c5ca400407cdd93b87461bde336254259dad5ec679af4ed1c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YT6LKM72OB63CFWTYKNZ7UK2D4/bundle.json","state_url":"https://pith.science/pith/YT6LKM72OB63CFWTYKNZ7UK2D4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YT6LKM72OB63CFWTYKNZ7UK2D4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T17:47:41Z","links":{"resolver":"https://pith.science/pith/YT6LKM72OB63CFWTYKNZ7UK2D4","bundle":"https://pith.science/pith/YT6LKM72OB63CFWTYKNZ7UK2D4/bundle.json","state":"https://pith.science/pith/YT6LKM72OB63CFWTYKNZ7UK2D4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YT6LKM72OB63CFWTYKNZ7UK2D4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YT6LKM72OB63CFWTYKNZ7UK2D4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"45c53f09fcd6fc1303888c4b34b48f6d728fdb632e4fb5c799f2270f4838f68e","cross_cats_sorted":["math.GR","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-15T21:54:13Z","title_canon_sha256":"556076b848477cd5735e14086083fd85e15446db6a1d14a5fc06a47a418a6059"},"schema_version":"1.0","source":{"id":"2605.16658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16658","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16658v1","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16658","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"YT6LKM72OB63","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"YT6LKM72OB63CFWT","created_at":"2026-05-20T00:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"YT6LKM72","created_at":"2026-05-20T00:02:34Z"}],"graph_snapshots":[{"event_id":"sha256:2e4313a0c3f823c5ca400407cdd93b87461bde336254259dad5ec679af4ed1c1","target":"graph","created_at":"2026-05-20T00:02:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove that the ``divisor subgroup'' of π₁(C) is characteristic. This can be interpreted as saying that the group theory of π₁(C) ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that C has no nontrivial biholomorphic automorphisms as complex analytic orbifold."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The deduction that the characteristic property of the divisor subgroup, together with basic complex analysis, suffices to rule out all nontrivial biholomorphic automorphisms of C as an orbifold; this relies on an unstated but load-bearing identification of what constitutes a biholomorphic automorphism in the orbifold category and on the precise definition of the divisor subgroup being invariant under the relevant group actions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic."}],"snapshot_sha256":"76c457db597cbc5dcfa6fe4abc0107d3b566cf9287ba7655b2db69284c5a53d1"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"ea64dc2f5611a18303a17153cac9d1d526e345fdb291b12108602d2b96ede072"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T21:01:19.303010Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T20:51:13.496580Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.399967Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.519602Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.16658/integrity.json","findings":[],"snapshot_sha256":"ad24176442b57fa83908058f84137615c0ea34f3da23e137ee38e96f5fff8ba2","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{C}$ be the moduli space of smooth complex cubic surfaces and let $\\pi_1(\\mathcal{C})$ be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $\\pi_1(\\mathcal{C})$ is characteristic. This can be interpreted as saying that the group theory of $\\pi_1(\\mathcal{C})$ ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that $\\mathcal{C}$ has no nontrivial biholomorphic automorphisms as complex analytic orbifold.","authors_text":"Ariyan Javanpeykar, Benson Farb, Gregorio Baldi, Matthew Stover","cross_cats":["math.GR","math.GT"],"headline":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-15T21:54:13Z","title":"Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group"},"references":{"count":15,"internal_anchors":0,"resolved_work":15,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"D. Allcock, J. A. Carlson, and D. Toledo. The complex hyperbolic geometry of the moduli space of cubic surfaces. J. Algebr. Geom., 11(4):659–724, 2002","work_id":"87ea9e12-dd7c-4a94-8033-ed273a8761a9","year":2002},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"D. Allcock, J. A. Carlson, and D. Toledo. Orthogonal complex hyperbolic arrangements. In Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000) , volume 312 of Contemp. Math. , pages 1–8. Amer","work_id":"a1f4ed53-0023-4d8d-a9b7-bc43927f9467","year":2000},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"W. L. Baily, Jr. and A. Borel. On the compactification of arithmetically defined quotients of bounded symmetric domains. Bull. Amer. Math. Soc. , 70:588–593, 1964","work_id":"b1c33ebc-fe3d-4440-a1d9-0d829b062477","year":1964},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"W. Bosma, J. Cannon, and C. Playoust. The Magma algebra system. I. The user language. J. Symbolic Comput., 24(3-4):235–265, 1997. Computational algebra and number theory (London, 1993)","work_id":"02d7e853-bfbd-441a-b7bb-7cc80b92a035","year":1997},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"M. R. Bridson and A. Haefliger. Metric spaces of non-positive curvature, volume 319 of Grundlehren Math. Wiss. Berlin: Springer, 1999","work_id":"392c47f9-e253-4727-a9be-ace2c78a2eb4","year":1999}],"snapshot_sha256":"f9639b6b71acee0754b86fd0970b00cc455647dcd0f46b20922b692d5d39434c"},"source":{"id":"2605.16658","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T20:40:52.839112Z","id":"7984d9d6-9ef4-435e-94ae-c7dc688ad142","model_set":{"reader":"grok-4.3"},"one_line_summary":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic.","strongest_claim":"We prove that the ``divisor subgroup'' of π₁(C) is characteristic. This can be interpreted as saying that the group theory of π₁(C) ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that C has no nontrivial biholomorphic automorphisms as complex analytic orbifold.","weakest_assumption":"The deduction that the characteristic property of the divisor subgroup, together with basic complex analysis, suffices to rule out all nontrivial biholomorphic automorphisms of C as an orbifold; this relies on an unstated but load-bearing identification of what constitutes a biholomorphic automorphism in the orbifold category and on the precise definition of the divisor subgroup being invariant under the relevant group actions."}},"verdict_id":"7984d9d6-9ef4-435e-94ae-c7dc688ad142"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:302ef832b05eda206720e57f88d0861437cdd83808861dfa7e6a277a98f1b923","target":"record","created_at":"2026-05-20T00:02:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"45c53f09fcd6fc1303888c4b34b48f6d728fdb632e4fb5c799f2270f4838f68e","cross_cats_sorted":["math.GR","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-15T21:54:13Z","title_canon_sha256":"556076b848477cd5735e14086083fd85e15446db6a1d14a5fc06a47a418a6059"},"schema_version":"1.0","source":{"id":"2605.16658","kind":"arxiv","version":1}},"canonical_sha256":"c4fcb533fa707db116d3c29b9fd15a1f3e25dcf8e590d53f8de09681559e5138","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4fcb533fa707db116d3c29b9fd15a1f3e25dcf8e590d53f8de09681559e5138","first_computed_at":"2026-05-20T00:02:34.838309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:34.838309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SLqCAoxisbUW2dH8EYgxSLUqVFs212dDUBROtN8kkR56XtJrltBoUqEG5MD7ZRxSIrKA3AerJkPxYVsBnbwVBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:34.839164Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:302ef832b05eda206720e57f88d0861437cdd83808861dfa7e6a277a98f1b923","sha256:2e4313a0c3f823c5ca400407cdd93b87461bde336254259dad5ec679af4ed1c1"],"state_sha256":"913870107717bd440cd3f7ab16d6c7f485f841fb359636e873a09a6cc23fcf16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvOXt7h/nfeN5SC4kFVdbdSXsSUGZTfMOw81rbH7Cwx8VRoABQmmzCpEmXVgVZppdgc7VIcmSbqiSEDI/kR6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:47:41.078279Z","bundle_sha256":"f051b0aaa079b47807a16a6b75d369dc3e08847a4484a77a01f78e6cc68c72e9"}}