{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Y3WP4X7SBDTVHP4JFZIXMEWAIU","short_pith_number":"pith:Y3WP4X7S","canonical_record":{"source":{"id":"1811.07849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T18:09:07Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"96afe9bc601f3bb1570d30ec716793e5f225ebee05b1b3e5f49877a498712ec8","abstract_canon_sha256":"f67ef974a2411b61126d27d70248546a44a084795b3edf544a14fd7a4e24c511"},"schema_version":"1.0"},"canonical_sha256":"c6ecfe5ff208e753bf892e517612c0451f766d295eb74d170eff5eaf3d23ab6d","source":{"kind":"arxiv","id":"1811.07849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07849","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07849v1","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07849","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"Y3WP4X7SBDTV","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y3WP4X7SBDTVHP4J","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y3WP4X7S","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Y3WP4X7SBDTVHP4JFZIXMEWAIU","target":"record","payload":{"canonical_record":{"source":{"id":"1811.07849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T18:09:07Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"96afe9bc601f3bb1570d30ec716793e5f225ebee05b1b3e5f49877a498712ec8","abstract_canon_sha256":"f67ef974a2411b61126d27d70248546a44a084795b3edf544a14fd7a4e24c511"},"schema_version":"1.0"},"canonical_sha256":"c6ecfe5ff208e753bf892e517612c0451f766d295eb74d170eff5eaf3d23ab6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:23.296681Z","signature_b64":"pJ/MLu1LgXD77qctUE+1xDoVDa/p102co7gL2RguLMncDPLwTfan7IIul9r2KJslNV6yf7qegtBnROGNb3PVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6ecfe5ff208e753bf892e517612c0451f766d295eb74d170eff5eaf3d23ab6d","last_reissued_at":"2026-05-18T00:00:23.296140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:23.296140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.07849","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":"2026-05-18T00:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0tuCGjGoQr66YwZeUYjdTSwemAg0bR4xDl6FCtNmZn+aDmXlAflzyB2xeYPS2cjIP6sGS/eOpvoa6rdVwBMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:47:43.478671Z"},"content_sha256":"94aae46a7a70c565be470c449e2ed67c4b4ca634a7c15bf2c15dccb38995bf7b","schema_version":"1.0","event_id":"sha256:94aae46a7a70c565be470c449e2ed67c4b4ca634a7c15bf2c15dccb38995bf7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Y3WP4X7SBDTVHP4JFZIXMEWAIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphism groups of dessins d'enfants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CV","authors_text":"Ruben A. Hidalgo","submitted_at":"2018-11-19T18:09:07Z","abstract_excerpt":"Recently, Gareth Jones observed that every finite group $G$ can be realized as the group of automorphisms of some dessin d'enfant ${\\mathcal D}$. In this paper, complementing Gareth's result, we prove that for every possible action of $G$ as a group of orientation-preserving homeomorphisms on a closed orientable surface of genus $g \\geq 2$, there is a dessin d'enfant ${\\mathcal D}$ admitting $G$ as its group of automorphisms and realizing the given topological action. In particular, this asserts that the strong symmetric genus of $G$ is also the minimum genus action for it to acts as the group"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07849","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":"2026-05-18T00:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+yPwJLTtZx4b3NSry7poI8bz76CALE4xa7nLLOVsqCwQ04PkWjuH2Cxh7gQQRFWwrhjIDUwMjBoLzZmk0/lrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:47:43.479030Z"},"content_sha256":"439e5d061f9556f1395225bd18515fb9a983e53f324280129f334afdf66e4e40","schema_version":"1.0","event_id":"sha256:439e5d061f9556f1395225bd18515fb9a983e53f324280129f334afdf66e4e40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3WP4X7SBDTVHP4JFZIXMEWAIU/bundle.json","state_url":"https://pith.science/pith/Y3WP4X7SBDTVHP4JFZIXMEWAIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3WP4X7SBDTVHP4JFZIXMEWAIU/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":"2026-06-09T13:47:43Z","links":{"resolver":"https://pith.science/pith/Y3WP4X7SBDTVHP4JFZIXMEWAIU","bundle":"https://pith.science/pith/Y3WP4X7SBDTVHP4JFZIXMEWAIU/bundle.json","state":"https://pith.science/pith/Y3WP4X7SBDTVHP4JFZIXMEWAIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3WP4X7SBDTVHP4JFZIXMEWAIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y3WP4X7SBDTVHP4JFZIXMEWAIU","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":"f67ef974a2411b61126d27d70248546a44a084795b3edf544a14fd7a4e24c511","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T18:09:07Z","title_canon_sha256":"96afe9bc601f3bb1570d30ec716793e5f225ebee05b1b3e5f49877a498712ec8"},"schema_version":"1.0","source":{"id":"1811.07849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07849","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07849v1","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07849","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"Y3WP4X7SBDTV","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y3WP4X7SBDTVHP4J","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y3WP4X7S","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:439e5d061f9556f1395225bd18515fb9a983e53f324280129f334afdf66e4e40","target":"graph","created_at":"2026-05-18T00:00:23Z","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":"Recently, Gareth Jones observed that every finite group $G$ can be realized as the group of automorphisms of some dessin d'enfant ${\\mathcal D}$. In this paper, complementing Gareth's result, we prove that for every possible action of $G$ as a group of orientation-preserving homeomorphisms on a closed orientable surface of genus $g \\geq 2$, there is a dessin d'enfant ${\\mathcal D}$ admitting $G$ as its group of automorphisms and realizing the given topological action. In particular, this asserts that the strong symmetric genus of $G$ is also the minimum genus action for it to acts as the group","authors_text":"Ruben A. Hidalgo","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T18:09:07Z","title":"Automorphism groups of dessins d'enfants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07849","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":"sha256:94aae46a7a70c565be470c449e2ed67c4b4ca634a7c15bf2c15dccb38995bf7b","target":"record","created_at":"2026-05-18T00:00:23Z","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":"f67ef974a2411b61126d27d70248546a44a084795b3edf544a14fd7a4e24c511","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T18:09:07Z","title_canon_sha256":"96afe9bc601f3bb1570d30ec716793e5f225ebee05b1b3e5f49877a498712ec8"},"schema_version":"1.0","source":{"id":"1811.07849","kind":"arxiv","version":1}},"canonical_sha256":"c6ecfe5ff208e753bf892e517612c0451f766d295eb74d170eff5eaf3d23ab6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6ecfe5ff208e753bf892e517612c0451f766d295eb74d170eff5eaf3d23ab6d","first_computed_at":"2026-05-18T00:00:23.296140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:23.296140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pJ/MLu1LgXD77qctUE+1xDoVDa/p102co7gL2RguLMncDPLwTfan7IIul9r2KJslNV6yf7qegtBnROGNb3PVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:23.296681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94aae46a7a70c565be470c449e2ed67c4b4ca634a7c15bf2c15dccb38995bf7b","sha256:439e5d061f9556f1395225bd18515fb9a983e53f324280129f334afdf66e4e40"],"state_sha256":"1ea6045be0257bd526e0cf7786c0531b94d341d0c0efdcdb88d0620f61815ff1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ewfHj41RFeQzgHQnjfPW/Z+ZK9Ce1IqGP/m0HBkfFBtFrGARK3i9qHDyKnM6j1pR4Z7wfUhyU5PcvkBBvZcVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:47:43.481990Z","bundle_sha256":"7a193e276a91f1516369de175fd3c4170fff5a8f3613fa3d4b4e17ccde78b4dc"}}