{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:S226YS5X324LOGPXMMDAPOBN3J","short_pith_number":"pith:S226YS5X","canonical_record":{"source":{"id":"math/0701493","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-01-17T21:17:07Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"7d72924695fe3ee4496020c3154451d1f0a28bf6a7b98c62e0a5ab13a2c5122f","abstract_canon_sha256":"eef3a5c0807a3daed1a053e74695a0c55fe2dbab810ecaca43a1412aef9a27dd"},"schema_version":"1.0"},"canonical_sha256":"96b5ec4bb7deb8b719f7630607b82dda5761b4cde5e7012fc509cb4c18e394ef","source":{"kind":"arxiv","id":"math/0701493","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701493","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701493v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701493","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"S226YS5X324L","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"S226YS5X324LOGPX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"S226YS5X","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:S226YS5X324LOGPXMMDAPOBN3J","target":"record","payload":{"canonical_record":{"source":{"id":"math/0701493","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-01-17T21:17:07Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"7d72924695fe3ee4496020c3154451d1f0a28bf6a7b98c62e0a5ab13a2c5122f","abstract_canon_sha256":"eef3a5c0807a3daed1a053e74695a0c55fe2dbab810ecaca43a1412aef9a27dd"},"schema_version":"1.0"},"canonical_sha256":"96b5ec4bb7deb8b719f7630607b82dda5761b4cde5e7012fc509cb4c18e394ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:26.619939Z","signature_b64":"oZ4s3xTY0YMkYqXThWrQyDN5fuyg1jwKe+45sOX9HzwVrZDAx2h4c+YS/HjzWgXVxWJvG/SNjOcTj2ValePJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96b5ec4bb7deb8b719f7630607b82dda5761b4cde5e7012fc509cb4c18e394ef","last_reissued_at":"2026-05-18T02:41:26.619480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:26.619480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0701493","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bKXGkhrF5fbMyyM9S5WENQAtX2eVv4Vi0o43hOGbxRF1/bxm3fjeHB2LukGi6TnhQnYxaMTHIDOd1fywwNFBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T00:48:53.885126Z"},"content_sha256":"173587bfa062505bdffef4c76365cd4efbc8cd93f6d127cfe26084e41d7846bb","schema_version":"1.0","event_id":"sha256:173587bfa062505bdffef4c76365cd4efbc8cd93f6d127cfe26084e41d7846bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:S226YS5X324LOGPXMMDAPOBN3J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations of Surface Groups and Right-Angled Artin Groups in Higher Rank","license":"","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.GR","authors_text":"Stephen Wang","submitted_at":"2007-01-17T21:17:07Z","abstract_excerpt":"We give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we find a general criterion for when discrete and faithful representations exist, and show that the criterion is satisfied in particular cases. There are direct applications towards constructing representations of surface groups into higher-rank Lie groups, and, in particular, into lattices in higher-rank Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701493","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kos9cGGmY2XBtiiwl1ndwTijmoBV30YsNfhb1bFzeBtPO1kF3kMEjqDKnwDsF4CWPB8npagrc1wo4iAOvVYnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T00:48:53.885495Z"},"content_sha256":"b62304836485ad6397bf950c4fd760506a471ecbd67537fb05826bfbf42928c4","schema_version":"1.0","event_id":"sha256:b62304836485ad6397bf950c4fd760506a471ecbd67537fb05826bfbf42928c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S226YS5X324LOGPXMMDAPOBN3J/bundle.json","state_url":"https://pith.science/pith/S226YS5X324LOGPXMMDAPOBN3J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S226YS5X324LOGPXMMDAPOBN3J/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":"2026-07-11T00:48:53Z","links":{"resolver":"https://pith.science/pith/S226YS5X324LOGPXMMDAPOBN3J","bundle":"https://pith.science/pith/S226YS5X324LOGPXMMDAPOBN3J/bundle.json","state":"https://pith.science/pith/S226YS5X324LOGPXMMDAPOBN3J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S226YS5X324LOGPXMMDAPOBN3J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:S226YS5X324LOGPXMMDAPOBN3J","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":"eef3a5c0807a3daed1a053e74695a0c55fe2dbab810ecaca43a1412aef9a27dd","cross_cats_sorted":["math.DG","math.GT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-01-17T21:17:07Z","title_canon_sha256":"7d72924695fe3ee4496020c3154451d1f0a28bf6a7b98c62e0a5ab13a2c5122f"},"schema_version":"1.0","source":{"id":"math/0701493","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701493","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701493v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701493","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"S226YS5X324L","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"S226YS5X324LOGPX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"S226YS5X","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:b62304836485ad6397bf950c4fd760506a471ecbd67537fb05826bfbf42928c4","target":"graph","created_at":"2026-05-18T02:41:26Z","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 give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we find a general criterion for when discrete and faithful representations exist, and show that the criterion is satisfied in particular cases. There are direct applications towards constructing representations of surface groups into higher-rank Lie groups, and, in particular, into lattices in higher-rank Lie groups.","authors_text":"Stephen Wang","cross_cats":["math.DG","math.GT"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2007-01-17T21:17:07Z","title":"Representations of Surface Groups and Right-Angled Artin Groups in Higher Rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701493","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":"sha256:173587bfa062505bdffef4c76365cd4efbc8cd93f6d127cfe26084e41d7846bb","target":"record","created_at":"2026-05-18T02:41:26Z","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":"eef3a5c0807a3daed1a053e74695a0c55fe2dbab810ecaca43a1412aef9a27dd","cross_cats_sorted":["math.DG","math.GT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-01-17T21:17:07Z","title_canon_sha256":"7d72924695fe3ee4496020c3154451d1f0a28bf6a7b98c62e0a5ab13a2c5122f"},"schema_version":"1.0","source":{"id":"math/0701493","kind":"arxiv","version":2}},"canonical_sha256":"96b5ec4bb7deb8b719f7630607b82dda5761b4cde5e7012fc509cb4c18e394ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96b5ec4bb7deb8b719f7630607b82dda5761b4cde5e7012fc509cb4c18e394ef","first_computed_at":"2026-05-18T02:41:26.619480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:26.619480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oZ4s3xTY0YMkYqXThWrQyDN5fuyg1jwKe+45sOX9HzwVrZDAx2h4c+YS/HjzWgXVxWJvG/SNjOcTj2ValePJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:26.619939Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701493","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:173587bfa062505bdffef4c76365cd4efbc8cd93f6d127cfe26084e41d7846bb","sha256:b62304836485ad6397bf950c4fd760506a471ecbd67537fb05826bfbf42928c4"],"state_sha256":"a4380c4efb5eec74c8d1423eb6c499ee15a27b976e22660b230ed244685211db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TngWcoX9DMVgFIKoluONM4/7hK1hEjHyi/WkabBVlZ3H0xWlls+EvnJs5thHHYUc8NDdbqARcmMrI0YWsQlXAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T00:48:53.887531Z","bundle_sha256":"358147a12c01878ddeec6d77c2b7ab1947183deee499cff0e8c802c2a93e78ee"}}