{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XVQUHBIRUM4OFQ7AVSJSSGP4NJ","short_pith_number":"pith:XVQUHBIR","schema_version":"1.0","canonical_sha256":"bd61438511a338e2c3e0ac932919fc6a683bbd4fc9399aecb7736379fc8354e5","source":{"kind":"arxiv","id":"1609.05220","version":1},"attestation_state":"computed","paper":{"title":"Constructing the Hyperbolic Plane as the reduction of a three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.DS","authors_text":"Richard Montgomery","submitted_at":"2016-09-16T20:10:43Z","abstract_excerpt":"We construct the hyperbolic plane with its geodesic flow as the scale plus symmetry reduction of a three-body problem in the Euclidean plane. The potential is $-I/\\Delta^2$ where $I$ is the triangle's moment of inertia and $\\Delta$ its area. The reduction method uses the Jacobi-Maupertuis metric, following the author's earlier paper \"Putting Hyperbolic Pants on a Three-body Problem\"."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.05220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-16T20:10:43Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"96e1a62d417a062d00f4056bcccd580dc643300e54da77d12a7f380b29b69b71","abstract_canon_sha256":"9d917d85c3ed4461fc4ab6d0f0202e120052b32981cedf40dc78d83e4616bfd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:30.848575Z","signature_b64":"Aoclr2Y/P9Ja1qjNi+HuPrcovZ66g/UNobton/I/MHAYAjtgGam+trC6hEve9vcQt4d+/gMI+W98T0qkcMlcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd61438511a338e2c3e0ac932919fc6a683bbd4fc9399aecb7736379fc8354e5","last_reissued_at":"2026-05-18T01:04:30.847942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:30.847942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing the Hyperbolic Plane as the reduction of a three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.DS","authors_text":"Richard Montgomery","submitted_at":"2016-09-16T20:10:43Z","abstract_excerpt":"We construct the hyperbolic plane with its geodesic flow as the scale plus symmetry reduction of a three-body problem in the Euclidean plane. The potential is $-I/\\Delta^2$ where $I$ is the triangle's moment of inertia and $\\Delta$ its area. The reduction method uses the Jacobi-Maupertuis metric, following the author's earlier paper \"Putting Hyperbolic Pants on a Three-body Problem\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05220","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.05220","created_at":"2026-05-18T01:04:30.848025+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.05220v1","created_at":"2026-05-18T01:04:30.848025+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05220","created_at":"2026-05-18T01:04:30.848025+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVQUHBIRUM4O","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVQUHBIRUM4OFQ7A","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVQUHBIR","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ","json":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ.json","graph_json":"https://pith.science/api/pith-number/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/graph.json","events_json":"https://pith.science/api/pith-number/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/events.json","paper":"https://pith.science/paper/XVQUHBIR"},"agent_actions":{"view_html":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ","download_json":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ.json","view_paper":"https://pith.science/paper/XVQUHBIR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.05220&json=true","fetch_graph":"https://pith.science/api/pith-number/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/graph.json","fetch_events":"https://pith.science/api/pith-number/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/action/storage_attestation","attest_author":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/action/author_attestation","sign_citation":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/action/citation_signature","submit_replication":"https://pith.science/pith/XVQUHBIRUM4OFQ7AVSJSSGP4NJ/action/replication_record"}},"created_at":"2026-05-18T01:04:30.848025+00:00","updated_at":"2026-05-18T01:04:30.848025+00:00"}