{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QWYVCK3GH4PG74PPS6JZ2U7CYW","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":"e2227aee64710aa519f3601783373672f331b387d76c0e74cb72c70b73b21348","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-13T12:34:06Z","title_canon_sha256":"8a7a9858433ab03a78c8625ea0e9f8f5bcfad3bd22d5951ad38d29084fe01965"},"schema_version":"1.0","source":{"id":"1207.3220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3220","created_at":"2026-05-18T01:56:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3220v1","created_at":"2026-05-18T01:56:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3220","created_at":"2026-05-18T01:56:23Z"},{"alias_kind":"pith_short_12","alias_value":"QWYVCK3GH4PG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QWYVCK3GH4PG74PP","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QWYVCK3G","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:25988f85f837adbdf48c5d8cc08f4f16272a6d20f5c8972d2263c8879088fd2e","target":"graph","created_at":"2026-05-18T01:56:23Z","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 apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general graph-theoretical formulation for the tree-level maximally-helicity-violated gravity amplitudes. Furthermore, we use the link to prove two identities for half-soft functions of gravity amplitudes. Finally we recast the diagrammatic formulation of one-loop rational part of $\\mathcal{N}=4$ supergravity into a matrix form.","authors_text":"Bo Feng, Song He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-13T12:34:06Z","title":"Graphs, determinants and gravity amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3220","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":"sha256:73eafd042cc262cd47117b1a899aa64bf71bc75fb5f591c5ea81321623becb72","target":"record","created_at":"2026-05-18T01:56:23Z","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":"e2227aee64710aa519f3601783373672f331b387d76c0e74cb72c70b73b21348","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-13T12:34:06Z","title_canon_sha256":"8a7a9858433ab03a78c8625ea0e9f8f5bcfad3bd22d5951ad38d29084fe01965"},"schema_version":"1.0","source":{"id":"1207.3220","kind":"arxiv","version":1}},"canonical_sha256":"85b1512b663f1e6ff1ef97939d53e2c58e1ccfb1bfb6276e488c67e43fa09e1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85b1512b663f1e6ff1ef97939d53e2c58e1ccfb1bfb6276e488c67e43fa09e1b","first_computed_at":"2026-05-18T01:56:23.999363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:23.999363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ypQHPD2fdhztjGO24F/IvhH4fxhHGVNdMz+HWPsXhbcVlZ1qcseNaPEagL6rXp+mYqgNKDj/ndLB8QRmwTeJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:24.000021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73eafd042cc262cd47117b1a899aa64bf71bc75fb5f591c5ea81321623becb72","sha256:25988f85f837adbdf48c5d8cc08f4f16272a6d20f5c8972d2263c8879088fd2e"],"state_sha256":"36ea929e1729cc519207151e5425c744d45be32f6004fa1da909d90e2f23b6df"}