{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ZYYJJX63AKJ3DQOKOP27GQ3D26","short_pith_number":"pith:ZYYJJX63","canonical_record":{"source":{"id":"0707.1144","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-07-08T15:49:00Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"75ccd38313485a369d4ebb75e405e0a26810b1310c39a9260709700cbe391379","abstract_canon_sha256":"766fe1b8d47321b1d2b98a34bb301bcef0bfed90f58ce541b3da35a2fc74febb"},"schema_version":"1.0"},"canonical_sha256":"ce3094dfdb0293b1c1ca73f5f34363d794f102a843ba7e1d8cdd85145dd386bf","source":{"kind":"arxiv","id":"0707.1144","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.1144","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0707.1144v2","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.1144","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZYYJJX63AKJ3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZYYJJX63AKJ3DQOK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZYYJJX63","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ZYYJJX63AKJ3DQOKOP27GQ3D26","target":"record","payload":{"canonical_record":{"source":{"id":"0707.1144","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-07-08T15:49:00Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"75ccd38313485a369d4ebb75e405e0a26810b1310c39a9260709700cbe391379","abstract_canon_sha256":"766fe1b8d47321b1d2b98a34bb301bcef0bfed90f58ce541b3da35a2fc74febb"},"schema_version":"1.0"},"canonical_sha256":"ce3094dfdb0293b1c1ca73f5f34363d794f102a843ba7e1d8cdd85145dd386bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:15.706826Z","signature_b64":"nZpy3gsDzW1/7N4BwOIBdkvt4DAxsWDGlZwyRBap+7GcZzfYC1c3bymgWItpKQn6fh0brcOBWcWPeMHUpMjsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce3094dfdb0293b1c1ca73f5f34363d794f102a843ba7e1d8cdd85145dd386bf","last_reissued_at":"2026-05-18T04:09:15.706241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:15.706241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.1144","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":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wIrV1fadl9PTCx2n3hL43vZcbwj+N7oKSjBmmk0vSZ1fUAI5UXL77+VOTVdJvj+BR6t+wAA8mtKqI7DxMt9XBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:30:13.920693Z"},"content_sha256":"6fbe5ba3840ff1120e65245e421e534e2ccb8a941c24fe42dd5c09170730f47f","schema_version":"1.0","event_id":"sha256:6fbe5ba3840ff1120e65245e421e534e2ccb8a941c24fe42dd5c09170730f47f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ZYYJJX63AKJ3DQOKOP27GQ3D26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surface subgroups of right-angled Artin groups","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"John Crisp, Mark Sapir, Michah Sageev","submitted_at":"2007-07-08T15:49:00Z","abstract_excerpt":"We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group $A(K)$ has such a subgroup if its defining graph $K$ contains an $n$-hole (i.e. an induced cycle of length $n$) with $n\\geq 5$. We construct another eight \"forbidden\" graphs and show that every graph $K$ on $\\le 8$ vertices either contains one of our examples, or contains a hole of length $\\ge 5$, or has the property that $A(K)$ does not contain hyperbolic closed surface subgroups. We also provide several sufficient conditions for a \\RAAG to conta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.1144","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":""},"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":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3nfRYXbp/R98ToADLF22/jjUQm8QifgHVKbw9J8Mx7NX6cLii7jWQo2YOrwB8dJUZonZf2glcsGtR+o8ogmfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:30:13.921370Z"},"content_sha256":"ff23937974c0afc9832030bd0dfce9475a834510d869584a3579dcb1cd75e69f","schema_version":"1.0","event_id":"sha256:ff23937974c0afc9832030bd0dfce9475a834510d869584a3579dcb1cd75e69f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYYJJX63AKJ3DQOKOP27GQ3D26/bundle.json","state_url":"https://pith.science/pith/ZYYJJX63AKJ3DQOKOP27GQ3D26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYYJJX63AKJ3DQOKOP27GQ3D26/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":"2026-06-07T16:30:13Z","links":{"resolver":"https://pith.science/pith/ZYYJJX63AKJ3DQOKOP27GQ3D26","bundle":"https://pith.science/pith/ZYYJJX63AKJ3DQOKOP27GQ3D26/bundle.json","state":"https://pith.science/pith/ZYYJJX63AKJ3DQOKOP27GQ3D26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYYJJX63AKJ3DQOKOP27GQ3D26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ZYYJJX63AKJ3DQOKOP27GQ3D26","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":"766fe1b8d47321b1d2b98a34bb301bcef0bfed90f58ce541b3da35a2fc74febb","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-07-08T15:49:00Z","title_canon_sha256":"75ccd38313485a369d4ebb75e405e0a26810b1310c39a9260709700cbe391379"},"schema_version":"1.0","source":{"id":"0707.1144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.1144","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0707.1144v2","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.1144","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZYYJJX63AKJ3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZYYJJX63AKJ3DQOK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZYYJJX63","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:ff23937974c0afc9832030bd0dfce9475a834510d869584a3579dcb1cd75e69f","target":"graph","created_at":"2026-05-18T04:09:15Z","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"},"paper":{"abstract_excerpt":"We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group $A(K)$ has such a subgroup if its defining graph $K$ contains an $n$-hole (i.e. an induced cycle of length $n$) with $n\\geq 5$. We construct another eight \"forbidden\" graphs and show that every graph $K$ on $\\le 8$ vertices either contains one of our examples, or contains a hole of length $\\ge 5$, or has the property that $A(K)$ does not contain hyperbolic closed surface subgroups. We also provide several sufficient conditions for a \\RAAG to conta","authors_text":"John Crisp, Mark Sapir, Michah Sageev","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2007-07-08T15:49:00Z","title":"Surface subgroups of right-angled Artin groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.1144","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":"sha256:6fbe5ba3840ff1120e65245e421e534e2ccb8a941c24fe42dd5c09170730f47f","target":"record","created_at":"2026-05-18T04:09:15Z","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":"766fe1b8d47321b1d2b98a34bb301bcef0bfed90f58ce541b3da35a2fc74febb","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-07-08T15:49:00Z","title_canon_sha256":"75ccd38313485a369d4ebb75e405e0a26810b1310c39a9260709700cbe391379"},"schema_version":"1.0","source":{"id":"0707.1144","kind":"arxiv","version":2}},"canonical_sha256":"ce3094dfdb0293b1c1ca73f5f34363d794f102a843ba7e1d8cdd85145dd386bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce3094dfdb0293b1c1ca73f5f34363d794f102a843ba7e1d8cdd85145dd386bf","first_computed_at":"2026-05-18T04:09:15.706241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:15.706241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nZpy3gsDzW1/7N4BwOIBdkvt4DAxsWDGlZwyRBap+7GcZzfYC1c3bymgWItpKQn6fh0brcOBWcWPeMHUpMjsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:15.706826Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.1144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fbe5ba3840ff1120e65245e421e534e2ccb8a941c24fe42dd5c09170730f47f","sha256:ff23937974c0afc9832030bd0dfce9475a834510d869584a3579dcb1cd75e69f"],"state_sha256":"3a5add78397b54eae1c853f43e0361f24a36683a7bc122b342bd016cd29b4db5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3GiGe3mlP2Bwitm/oFRPqt1yJM0zTLPpGF50O8qVU/LwzmB77g3cHF691BEVk3WvKpICH//p2be45BzsO7AvDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:30:13.925099Z","bundle_sha256":"c3785883d00fd94d562d1da1c91ab5d75ea659f8606305a6a3dcba31d5d72a43"}}