{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:PLJO2TY6VWXJRVD73NB2JZUC65","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":"8a0589aecf95d6ce002d7c5eaf6ca7d20cefd45c9f1ce1865a62388cc53876fe","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2004-08-25T12:11:14Z","title_canon_sha256":"dd9bb72167c4a8dea546415509f63b554285c69c9aa0639aa06d01bb9b544ec9"},"schema_version":"1.0","source":{"id":"gr-qc/0408082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0408082","created_at":"2026-05-18T00:59:50Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0408082v1","created_at":"2026-05-18T00:59:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0408082","created_at":"2026-05-18T00:59:50Z"},{"alias_kind":"pith_short_12","alias_value":"PLJO2TY6VWXJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"PLJO2TY6VWXJRVD7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"PLJO2TY6","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:534bab55bd8d13c7daf6d851e0a86ec94e69ae0fbd7b2dceba57f55cb03202bf","target":"graph","created_at":"2026-05-18T00:59:50Z","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 describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and upper--triangular form are constructed, which in the latter case exhibit additional, non--trivial internal relations for each holonomy matrix. This leads to the notion of quantum matrix pairs. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are ","authors_text":"Italy), J. E. Nelson (University of Turin, Lisbon, Portugal), R. F. Picken (Instituto Superior Tecnico","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2004-08-25T12:11:14Z","title":"Quantum Holonomies in (2+1)-Dimensional Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0408082","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:ad54a465556a4a33a4cc8bbcaf87955f0a74d17cc2249034b6641dbf3fd4e140","target":"record","created_at":"2026-05-18T00:59:50Z","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":"8a0589aecf95d6ce002d7c5eaf6ca7d20cefd45c9f1ce1865a62388cc53876fe","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2004-08-25T12:11:14Z","title_canon_sha256":"dd9bb72167c4a8dea546415509f63b554285c69c9aa0639aa06d01bb9b544ec9"},"schema_version":"1.0","source":{"id":"gr-qc/0408082","kind":"arxiv","version":1}},"canonical_sha256":"7ad2ed4f1eadae98d47fdb43a4e682f762d5fb43d796cfc47a1e065902c2f10e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ad2ed4f1eadae98d47fdb43a4e682f762d5fb43d796cfc47a1e065902c2f10e","first_computed_at":"2026-05-18T00:59:50.338400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:50.338400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E/N7Mwpiw46R0mCQ2V8jv4cOWweqC5peBsTw+Al8j+qMMEkvmhc1NwfAJdGVkYrC6Gw+eK4jtpZ7lSSOjlLNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:50.339124Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0408082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad54a465556a4a33a4cc8bbcaf87955f0a74d17cc2249034b6641dbf3fd4e140","sha256:534bab55bd8d13c7daf6d851e0a86ec94e69ae0fbd7b2dceba57f55cb03202bf"],"state_sha256":"84ebf9d85f71804d19abda32cb09632f06acdae769b03160c4113743e42004d7"}