{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZX5374P32YRYXD725HSAOFJ45L","short_pith_number":"pith:ZX5374P3","canonical_record":{"source":{"id":"1710.05532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-16T06:40:02Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"77f9743ae33831672deb177684de03142062893e23c0972797cdb6118c90530a","abstract_canon_sha256":"d2d5bc976b9904dba608ff674b72442d5a865fbbedb94647d81767693b9aef20"},"schema_version":"1.0"},"canonical_sha256":"cdfbbff1fbd6238b8ffae9e407153ceafaab0c3f64f8c3c2253749e323f89e11","source":{"kind":"arxiv","id":"1710.05532","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05532","created_at":"2026-05-18T00:32:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05532v1","created_at":"2026-05-18T00:32:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05532","created_at":"2026-05-18T00:32:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZX5374P32YRY","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZX5374P32YRYXD72","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZX5374P3","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZX5374P32YRYXD725HSAOFJ45L","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-16T06:40:02Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"77f9743ae33831672deb177684de03142062893e23c0972797cdb6118c90530a","abstract_canon_sha256":"d2d5bc976b9904dba608ff674b72442d5a865fbbedb94647d81767693b9aef20"},"schema_version":"1.0"},"canonical_sha256":"cdfbbff1fbd6238b8ffae9e407153ceafaab0c3f64f8c3c2253749e323f89e11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:49.038515Z","signature_b64":"5xVynyio8/U6EdIDZo+4HMAVAiARWdFPvQLXYQU0qGvx2cLqzKDZLwoUrStCODsBq1UGaZgjiNhYBGBFZc5OAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdfbbff1fbd6238b8ffae9e407153ceafaab0c3f64f8c3c2253749e323f89e11","last_reissued_at":"2026-05-18T00:32:49.037841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:49.037841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05532","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":"2026-05-18T00:32:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5dAq5BlYuTafW3F+BPj0NTUFLyjXNs0N2gc7yE4jhraOCWH9HDVKShppZ0dAqsD0uObWHyViDI5Y8Usgicv8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:01:35.816356Z"},"content_sha256":"336ecd92e93f58c23e834b1e557fab50733cafc7abc304e9fd234d69b25cd693","schema_version":"1.0","event_id":"sha256:336ecd92e93f58c23e834b1e557fab50733cafc7abc304e9fd234d69b25cd693"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZX5374P32YRYXD725HSAOFJ45L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic monodromy actions on pro-metabelian fundamental groups of once-punctured elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.AG","authors_text":"Pierre Deligne, William Yun Chen","submitted_at":"2017-10-16T06:40:02Z","abstract_excerpt":"We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $H\\le GL_2(\\mathbb{Z}/e)$ such that $G$-structures on elliptic curves $E$ are equivalent to \"congruence structures of level $H$\". Our methods are almost entirely group theoretic. Let $\\widehat{M}$ denote the free profinite metabelian group of rank 2, then along the way we prove a decomposition of $Out(\\widehat{M})$ as an internal semi-direct product of the subgroup of \""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05532","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AuS+hgX3qyGL07krYkY6Jz6xqAFjuZdxYEK5mE9VgZNcS3qalSWaV82OWMUpzlYNAit7GDFYKwFWvVKUyvnQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:01:35.817063Z"},"content_sha256":"db057cf8514e1de9143318e0973cb30a593f374339c6012dabc4f01b539d6c29","schema_version":"1.0","event_id":"sha256:db057cf8514e1de9143318e0973cb30a593f374339c6012dabc4f01b539d6c29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZX5374P32YRYXD725HSAOFJ45L/bundle.json","state_url":"https://pith.science/pith/ZX5374P32YRYXD725HSAOFJ45L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZX5374P32YRYXD725HSAOFJ45L/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":"2026-06-11T01:01:35Z","links":{"resolver":"https://pith.science/pith/ZX5374P32YRYXD725HSAOFJ45L","bundle":"https://pith.science/pith/ZX5374P32YRYXD725HSAOFJ45L/bundle.json","state":"https://pith.science/pith/ZX5374P32YRYXD725HSAOFJ45L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZX5374P32YRYXD725HSAOFJ45L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZX5374P32YRYXD725HSAOFJ45L","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":"d2d5bc976b9904dba608ff674b72442d5a865fbbedb94647d81767693b9aef20","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-16T06:40:02Z","title_canon_sha256":"77f9743ae33831672deb177684de03142062893e23c0972797cdb6118c90530a"},"schema_version":"1.0","source":{"id":"1710.05532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05532","created_at":"2026-05-18T00:32:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05532v1","created_at":"2026-05-18T00:32:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05532","created_at":"2026-05-18T00:32:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZX5374P32YRY","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZX5374P32YRYXD72","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZX5374P3","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:db057cf8514e1de9143318e0973cb30a593f374339c6012dabc4f01b539d6c29","target":"graph","created_at":"2026-05-18T00:32:49Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $H\\le GL_2(\\mathbb{Z}/e)$ such that $G$-structures on elliptic curves $E$ are equivalent to \"congruence structures of level $H$\". Our methods are almost entirely group theoretic. Let $\\widehat{M}$ denote the free profinite metabelian group of rank 2, then along the way we prove a decomposition of $Out(\\widehat{M})$ as an internal semi-direct product of the subgroup of \"","authors_text":"Pierre Deligne, William Yun Chen","cross_cats":["math.GR","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-16T06:40:02Z","title":"Arithmetic monodromy actions on pro-metabelian fundamental groups of once-punctured elliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05532","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:336ecd92e93f58c23e834b1e557fab50733cafc7abc304e9fd234d69b25cd693","target":"record","created_at":"2026-05-18T00:32:49Z","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":"d2d5bc976b9904dba608ff674b72442d5a865fbbedb94647d81767693b9aef20","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-16T06:40:02Z","title_canon_sha256":"77f9743ae33831672deb177684de03142062893e23c0972797cdb6118c90530a"},"schema_version":"1.0","source":{"id":"1710.05532","kind":"arxiv","version":1}},"canonical_sha256":"cdfbbff1fbd6238b8ffae9e407153ceafaab0c3f64f8c3c2253749e323f89e11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdfbbff1fbd6238b8ffae9e407153ceafaab0c3f64f8c3c2253749e323f89e11","first_computed_at":"2026-05-18T00:32:49.037841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:49.037841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xVynyio8/U6EdIDZo+4HMAVAiARWdFPvQLXYQU0qGvx2cLqzKDZLwoUrStCODsBq1UGaZgjiNhYBGBFZc5OAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:49.038515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:336ecd92e93f58c23e834b1e557fab50733cafc7abc304e9fd234d69b25cd693","sha256:db057cf8514e1de9143318e0973cb30a593f374339c6012dabc4f01b539d6c29"],"state_sha256":"874be9e24dfd07783561c4ea01598a1297aaf4663669b60a8d98264146538790"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"om9w5SvLQNaI8VPMSyRiwPZu/lwHgGXMidplp0jn1Ly3DbrVpaXjsTfBnB4KS8R0HxETxIs4lgFYq7TdZkGHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:01:35.821760Z","bundle_sha256":"f88eee63345e913f1a55a68057f583f344be2244d489e59ad5adf0307a8a327a"}}