{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:X5J6X4TRALD233U4FLBE6X5FCJ","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":"65df49861c892f2246b9c81250257a71c50064e65adebe290de32277dbeebe39","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-15T10:11:27Z","title_canon_sha256":"ff4f8653b7351a552bb44a74dfd579cd90504e40d260b3b743482592a477c5e0"},"schema_version":"1.0","source":{"id":"1012.3263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3263","created_at":"2026-05-18T04:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3263v2","created_at":"2026-05-18T04:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3263","created_at":"2026-05-18T04:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"X5J6X4TRALD2","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"X5J6X4TRALD233U4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"X5J6X4TR","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d0fd04ed24b3e76df1e5bcc48a86ae9b47e2f1634984313e3692ae2aa41484f3","target":"graph","created_at":"2026-05-18T04:13:05Z","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 present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the ","authors_text":"M. Ciafaloni, S. Munier","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-15T10:11:27Z","title":"Hamiltonian solutions of the 3-body problem in (2+1)-gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3263","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:f4e0af55fb6a84a28655d1e263a66189ba7d6c426acbe9158fe6c67543103cab","target":"record","created_at":"2026-05-18T04:13:05Z","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":"65df49861c892f2246b9c81250257a71c50064e65adebe290de32277dbeebe39","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-15T10:11:27Z","title_canon_sha256":"ff4f8653b7351a552bb44a74dfd579cd90504e40d260b3b743482592a477c5e0"},"schema_version":"1.0","source":{"id":"1012.3263","kind":"arxiv","version":2}},"canonical_sha256":"bf53ebf27102c7adee9c2ac24f5fa5125519bbcf66162bf3d596458b341f6303","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf53ebf27102c7adee9c2ac24f5fa5125519bbcf66162bf3d596458b341f6303","first_computed_at":"2026-05-18T04:13:05.657360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:05.657360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXOSBJYD4ynsearLFZpoFPSgViTFg1MGeBCQliEC5GBixSlyNWd/bN+eYBYvxFa107XH3WMgaGYB8VX6pd+iAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:05.657842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4e0af55fb6a84a28655d1e263a66189ba7d6c426acbe9158fe6c67543103cab","sha256:d0fd04ed24b3e76df1e5bcc48a86ae9b47e2f1634984313e3692ae2aa41484f3"],"state_sha256":"a2825ef6c718baa0fc844e3f9b0c20321c32e70b7a01670758b25d0ce2d68bce"}