{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DILIES3EXIM55XT46EQBUCLK3J","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":"503a0a453a7af22b43c572cc97c4af74b943fe69bd6278783abbc377f84e68db","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-04-20T16:36:25Z","title_canon_sha256":"a89bc55adfc4f4442a68972d696b97e3e9721c603a8c9fa9da7de567020ef148"},"schema_version":"1.0","source":{"id":"1004.3498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3498","created_at":"2026-05-18T04:26:43Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3498v1","created_at":"2026-05-18T04:26:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3498","created_at":"2026-05-18T04:26:43Z"},{"alias_kind":"pith_short_12","alias_value":"DILIES3EXIM5","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DILIES3EXIM55XT4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DILIES3E","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:cdc00d06895fa3fbffee39311868d31c71a01597c4df7ed5bb059e70eea33983","target":"graph","created_at":"2026-05-18T04:26:43Z","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 show that one-loop scalar box functions can be interpreted as volumes of geodesic tetrahedra embedded in a copy of AdS_5 that has dual conformal space-time as boundary.  When the tetrahedron is space-like, it lies in a totally geodesic hyperbolic three-space inside AdS_5, with its four vertices on the boundary. It is a classical result that the volume of such a tetrahedron is given by the Bloch-Wigner dilogarithm and this agrees with the standard physics formulae for such box functions. The combinations of box functions that arise in the n-particle one-loop MHV amplitude in N=4 super Yang-M","authors_text":"David Skinner, Lionel Mason","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-04-20T16:36:25Z","title":"Amplitudes at Weak Coupling as Polytopes in AdS_5"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3498","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":"sha256:7a4299b81c9d0f6fd3ce2d75e7e534158964d4a9fad0dbdb900a9d978d5592f4","target":"record","created_at":"2026-05-18T04:26:43Z","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":"503a0a453a7af22b43c572cc97c4af74b943fe69bd6278783abbc377f84e68db","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-04-20T16:36:25Z","title_canon_sha256":"a89bc55adfc4f4442a68972d696b97e3e9721c603a8c9fa9da7de567020ef148"},"schema_version":"1.0","source":{"id":"1004.3498","kind":"arxiv","version":1}},"canonical_sha256":"1a16824b64ba19dede7cf1201a096ada793ae0dee5b42b575d437f76ecd6e99b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a16824b64ba19dede7cf1201a096ada793ae0dee5b42b575d437f76ecd6e99b","first_computed_at":"2026-05-18T04:26:43.611062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:43.611062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4fdmWLC8GflZaz6sLcUd/t3HQQJ+uy5WYT7H3Vl7BYQgFRv1nPdVW/qWryIB7o5tcO85aCT0SZnZzyqTn0gCBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:43.611813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a4299b81c9d0f6fd3ce2d75e7e534158964d4a9fad0dbdb900a9d978d5592f4","sha256:cdc00d06895fa3fbffee39311868d31c71a01597c4df7ed5bb059e70eea33983"],"state_sha256":"f85153c7aac56ae86a37ddf1d7ec1cd4311bc1a764389451e099d54fb0f575fc"}