{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HRO6VOLPQIS2PRBGCH2SMWCIYW","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":"5ca31a4e0dfc671c64e4096774303aa71667422f2a07f5233984136b010fd9c6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-25T11:03:23Z","title_canon_sha256":"d110484e7afab4ef757c6c1f6c4dca6cacaffbbc48d52b8753f04c1bfd82a9f0"},"schema_version":"1.0","source":{"id":"1307.6697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6697","created_at":"2026-05-18T03:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6697v2","created_at":"2026-05-18T03:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6697","created_at":"2026-05-18T03:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"HRO6VOLPQIS2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HRO6VOLPQIS2PRBG","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HRO6VOLP","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:e6d37d231aecd5d3b7ce5569fe47befc9b42cb4a54f6d5e6cd19733d1f2ed4c1","target":"graph","created_at":"2026-05-18T03:05:37Z","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":"In this paper we are interested in computing representations of the fundamental group of a 3-manifold into PSL(3;C) (in particular in PSL(2;C); PSL(3;R) and PU(2; 1)). The representations are obtained by gluing decorated tetrahedra of flags. We list complete computations (giving 0-dimensional or 1-dimensional solution sets) for the first complete hyperbolic non-compact manifolds with finite volume which are obtained gluing less than three tetrahedra with a description of the computer methods used to find them.","authors_text":"E. Falbel, F. Rouillier, P. -V. Koseleff","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-25T11:03:23Z","title":"Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6697","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:eaaf731e4803ee20859c6b3339e7abe112fc990aaf4c52ccfee5d8a338fd4fdc","target":"record","created_at":"2026-05-18T03:05:37Z","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":"5ca31a4e0dfc671c64e4096774303aa71667422f2a07f5233984136b010fd9c6","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-25T11:03:23Z","title_canon_sha256":"d110484e7afab4ef757c6c1f6c4dca6cacaffbbc48d52b8753f04c1bfd82a9f0"},"schema_version":"1.0","source":{"id":"1307.6697","kind":"arxiv","version":2}},"canonical_sha256":"3c5deab96f8225a7c42611f5265848c593f2ac6aaca46bf2099ba448239d8c4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c5deab96f8225a7c42611f5265848c593f2ac6aaca46bf2099ba448239d8c4f","first_computed_at":"2026-05-18T03:05:37.814310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:37.814310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Pmm+tOK/FlHbdtW17kPpSQJJJzbFlW6/VR/Uh8PVtMhcCFUoDp3pnY8osaJMQ3gGWUTtuGKotfqlrAOlT0IBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:37.814884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eaaf731e4803ee20859c6b3339e7abe112fc990aaf4c52ccfee5d8a338fd4fdc","sha256:e6d37d231aecd5d3b7ce5569fe47befc9b42cb4a54f6d5e6cd19733d1f2ed4c1"],"state_sha256":"ac8dfe1740cde6b1a7e8dfe9685369ae6924b6ea0fba176b34c831961ca03bac"}