{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VVAPLKFVHDSKICTWSJTJ2PBRXZ","short_pith_number":"pith:VVAPLKFV","canonical_record":{"source":{"id":"2501.13234","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-01-22T21:35:15Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e4d80e8eda28417b519acc1ace467daae34e5989b944497592824bafb20ff8c1","abstract_canon_sha256":"e68377e12dfd644e1f6f89f01299d6c94894c1692a0860824b97e8b1d1033998"},"schema_version":"1.0"},"canonical_sha256":"ad40f5a8b538e4a40a7692669d3c31be7ed5b52483b43c2f7c1132e9beebfb7d","source":{"kind":"arxiv","id":"2501.13234","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13234","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13234v2","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13234","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_12","alias_value":"VVAPLKFVHDSK","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_16","alias_value":"VVAPLKFVHDSKICTW","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_8","alias_value":"VVAPLKFV","created_at":"2026-07-05T12:11:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VVAPLKFVHDSKICTWSJTJ2PBRXZ","target":"record","payload":{"canonical_record":{"source":{"id":"2501.13234","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-01-22T21:35:15Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e4d80e8eda28417b519acc1ace467daae34e5989b944497592824bafb20ff8c1","abstract_canon_sha256":"e68377e12dfd644e1f6f89f01299d6c94894c1692a0860824b97e8b1d1033998"},"schema_version":"1.0"},"canonical_sha256":"ad40f5a8b538e4a40a7692669d3c31be7ed5b52483b43c2f7c1132e9beebfb7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:11:15.204132Z","signature_b64":"7b6kRg8vLwtmhBAtOIaDWx8pJfv69avvSS1PCsTaEUHKTfnYPClxKSS2aEltnSVBW7wrxuxT+wRm8ZRgcfIjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad40f5a8b538e4a40a7692669d3c31be7ed5b52483b43c2f7c1132e9beebfb7d","last_reissued_at":"2026-07-05T12:11:15.203604Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:11:15.203604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.13234","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:11:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qZcNcnB4EHJdSJkuG03QEyRLiIVHJ5Ss5M+vR6r2FnirYMUksouf7KTROD8NPjFT0KNgNqdeCJ9B+kdPqWXqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:27:58.879466Z"},"content_sha256":"df0199fd701a7d99f9cd2793205de53157a0cb7e774c24629d97438bb816f618","schema_version":"1.0","event_id":"sha256:df0199fd701a7d99f9cd2793205de53157a0cb7e774c24629d97438bb816f618"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VVAPLKFVHDSKICTWSJTJ2PBRXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructing reducibly geometrically finite subgroups of the mapping class group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Brandis Whitfield, Hannah Hoganson, Harrison Bray, Sara Maloni, Spencer Dowdall, Tarik Aougab","submitted_at":"2025-01-22T21:35:15Z","abstract_excerpt":"In this article, we consider qualified notions of geometric finiteness in mapping class groups called parabolically geometrically finite (PGF) and reducibly geometrically finite (RGF). We examine several constructions of subgroups and determine when they produce a PGF or RGF subgroup. These results provide a variety of new examples of PGF and RGF subgroups. Firstly, we consider the right-angled Artin subgroups constructed by Koberda and Clay--Leininger--Mangahas, which are generated by high powers of given elements of the mapping class group. We give conditions on the supports of these element"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13234","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.13234/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T12:11:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61Is9PNrcqEFIxf+71l3feBCz4Bu92H3rui9wX9jMJGYriPR+ungrj7K+j5HNpfW+WlUAZRqeOfPkwdtrWndBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:27:58.880170Z"},"content_sha256":"a432eabc80afa7bc6c6f37b136a2b48077301de63846476599b45786efd34b99","schema_version":"1.0","event_id":"sha256:a432eabc80afa7bc6c6f37b136a2b48077301de63846476599b45786efd34b99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVAPLKFVHDSKICTWSJTJ2PBRXZ/bundle.json","state_url":"https://pith.science/pith/VVAPLKFVHDSKICTWSJTJ2PBRXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVAPLKFVHDSKICTWSJTJ2PBRXZ/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":"2026-08-16T19:27:58Z","links":{"resolver":"https://pith.science/pith/VVAPLKFVHDSKICTWSJTJ2PBRXZ","bundle":"https://pith.science/pith/VVAPLKFVHDSKICTWSJTJ2PBRXZ/bundle.json","state":"https://pith.science/pith/VVAPLKFVHDSKICTWSJTJ2PBRXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVAPLKFVHDSKICTWSJTJ2PBRXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VVAPLKFVHDSKICTWSJTJ2PBRXZ","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":"e68377e12dfd644e1f6f89f01299d6c94894c1692a0860824b97e8b1d1033998","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-01-22T21:35:15Z","title_canon_sha256":"e4d80e8eda28417b519acc1ace467daae34e5989b944497592824bafb20ff8c1"},"schema_version":"1.0","source":{"id":"2501.13234","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13234","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13234v2","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13234","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_12","alias_value":"VVAPLKFVHDSK","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_16","alias_value":"VVAPLKFVHDSKICTW","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_8","alias_value":"VVAPLKFV","created_at":"2026-07-05T12:11:15Z"}],"graph_snapshots":[{"event_id":"sha256:a432eabc80afa7bc6c6f37b136a2b48077301de63846476599b45786efd34b99","target":"graph","created_at":"2026-07-05T12:11:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.13234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we consider qualified notions of geometric finiteness in mapping class groups called parabolically geometrically finite (PGF) and reducibly geometrically finite (RGF). We examine several constructions of subgroups and determine when they produce a PGF or RGF subgroup. These results provide a variety of new examples of PGF and RGF subgroups. Firstly, we consider the right-angled Artin subgroups constructed by Koberda and Clay--Leininger--Mangahas, which are generated by high powers of given elements of the mapping class group. We give conditions on the supports of these element","authors_text":"Brandis Whitfield, Hannah Hoganson, Harrison Bray, Sara Maloni, Spencer Dowdall, Tarik Aougab","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-01-22T21:35:15Z","title":"Constructing reducibly geometrically finite subgroups of the mapping class group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13234","kind":"arxiv","version":2},"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:df0199fd701a7d99f9cd2793205de53157a0cb7e774c24629d97438bb816f618","target":"record","created_at":"2026-07-05T12:11:15Z","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":"e68377e12dfd644e1f6f89f01299d6c94894c1692a0860824b97e8b1d1033998","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-01-22T21:35:15Z","title_canon_sha256":"e4d80e8eda28417b519acc1ace467daae34e5989b944497592824bafb20ff8c1"},"schema_version":"1.0","source":{"id":"2501.13234","kind":"arxiv","version":2}},"canonical_sha256":"ad40f5a8b538e4a40a7692669d3c31be7ed5b52483b43c2f7c1132e9beebfb7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad40f5a8b538e4a40a7692669d3c31be7ed5b52483b43c2f7c1132e9beebfb7d","first_computed_at":"2026-07-05T12:11:15.203604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:11:15.203604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7b6kRg8vLwtmhBAtOIaDWx8pJfv69avvSS1PCsTaEUHKTfnYPClxKSS2aEltnSVBW7wrxuxT+wRm8ZRgcfIjCA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:11:15.204132Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13234","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df0199fd701a7d99f9cd2793205de53157a0cb7e774c24629d97438bb816f618","sha256:a432eabc80afa7bc6c6f37b136a2b48077301de63846476599b45786efd34b99"],"state_sha256":"cd95a953686d30174ec31452632c4fc754f93befd99b9717d893b68d5fb68fcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IbuumdTEMyZFTUySM5IBJYhoRd2jmbfBLd89vKLtZsto5Mk8bA0RCBRZRhcbMdq2sw2lPUP5HDWKxHvTFZcFAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:27:58.883727Z","bundle_sha256":"966bf7d7e92d2636c5f92c984fe4885c647f18dd26e3fb4852187aa84181c8b4"}}