{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:X24SABKQRTOBICS5AMAQJY75EK","short_pith_number":"pith:X24SABKQ","canonical_record":{"source":{"id":"2012.15780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-31T17:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"4bf40ea17abd4185c85e991fc3a9aeaf8bf5f04fb3b6a5e9dddd7052c6af3bbd","abstract_canon_sha256":"faccfe0d664c9279ac573929d15114968ec9273a56b069391df11b7dc3c2c393"},"schema_version":"1.0"},"canonical_sha256":"beb92005508cdc140a5d030104e3fd22be904f4da4d1f52ec5ba037e3646ef86","source":{"kind":"arxiv","id":"2012.15780","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.15780","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"2012.15780v1","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.15780","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"X24SABKQRTOB","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"pith_short_16","alias_value":"X24SABKQRTOBICS5","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"pith_short_8","alias_value":"X24SABKQ","created_at":"2026-07-05T02:39:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:X24SABKQRTOBICS5AMAQJY75EK","target":"record","payload":{"canonical_record":{"source":{"id":"2012.15780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-31T17:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"4bf40ea17abd4185c85e991fc3a9aeaf8bf5f04fb3b6a5e9dddd7052c6af3bbd","abstract_canon_sha256":"faccfe0d664c9279ac573929d15114968ec9273a56b069391df11b7dc3c2c393"},"schema_version":"1.0"},"canonical_sha256":"beb92005508cdc140a5d030104e3fd22be904f4da4d1f52ec5ba037e3646ef86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:39:10.044903Z","signature_b64":"9lQ/lv0gK/297yEoT5O963/UOZCXYJaGR3S0PU+aUXZBinUo0Sm3t+9SyEkHq6OfYPx/Dw5QukNnWu0kst7sBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beb92005508cdc140a5d030104e3fd22be904f4da4d1f52ec5ba037e3646ef86","last_reissued_at":"2026-07-05T02:39:10.044397Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:39:10.044397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.15780","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:39:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GqdrKaz+5KUkVZlDB4XvGb0qmnbyBlRwtJDZ2mXRWl/JSPZa6KjHgrSHe7WTUkbYaqGyfvKI1iIQkgOrEIG3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:28:50.072459Z"},"content_sha256":"2494ee1d1c29a113cd2abfac0b8b55e1fd532dfa31e869d517778b5ac5c82bdc","schema_version":"1.0","event_id":"sha256:2494ee1d1c29a113cd2abfac0b8b55e1fd532dfa31e869d517778b5ac5c82bdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:X24SABKQRTOBICS5AMAQJY75EK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Jaroslav Trnka","submitted_at":"2020-12-31T17:59:34Z","abstract_excerpt":"In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity analogues which we call G-invariants, and expand the NMHV gravity amplitudes in terms of these objects. We provide explicit formulas of NMHV gravity amplitudes up to eight points in terms of G-invariants, and give the general definition for any number of points. We discuss the connection to BCFW representation, special behavior under large momentum shift, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.15780","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.15780/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:39:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZR93hEGKK1iDQA2H4RD+/FiaMFQeb6qwTIE+n2I0K4Zrw9/A3CLgjFhWr5n0AdYG68j9QgN/VQWlPnbBNTECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:28:50.072959Z"},"content_sha256":"f3e9f263b4901f85e153f9db35c9bd8fc7626b9d225d803ab3dde83475d4d62d","schema_version":"1.0","event_id":"sha256:f3e9f263b4901f85e153f9db35c9bd8fc7626b9d225d803ab3dde83475d4d62d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X24SABKQRTOBICS5AMAQJY75EK/bundle.json","state_url":"https://pith.science/pith/X24SABKQRTOBICS5AMAQJY75EK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X24SABKQRTOBICS5AMAQJY75EK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T04:28:50Z","links":{"resolver":"https://pith.science/pith/X24SABKQRTOBICS5AMAQJY75EK","bundle":"https://pith.science/pith/X24SABKQRTOBICS5AMAQJY75EK/bundle.json","state":"https://pith.science/pith/X24SABKQRTOBICS5AMAQJY75EK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X24SABKQRTOBICS5AMAQJY75EK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:X24SABKQRTOBICS5AMAQJY75EK","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":"faccfe0d664c9279ac573929d15114968ec9273a56b069391df11b7dc3c2c393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-31T17:59:34Z","title_canon_sha256":"4bf40ea17abd4185c85e991fc3a9aeaf8bf5f04fb3b6a5e9dddd7052c6af3bbd"},"schema_version":"1.0","source":{"id":"2012.15780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.15780","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"2012.15780v1","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.15780","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"X24SABKQRTOB","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"pith_short_16","alias_value":"X24SABKQRTOBICS5","created_at":"2026-07-05T02:39:10Z"},{"alias_kind":"pith_short_8","alias_value":"X24SABKQ","created_at":"2026-07-05T02:39:10Z"}],"graph_snapshots":[{"event_id":"sha256:f3e9f263b4901f85e153f9db35c9bd8fc7626b9d225d803ab3dde83475d4d62d","target":"graph","created_at":"2026-07-05T02:39:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.15780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity analogues which we call G-invariants, and expand the NMHV gravity amplitudes in terms of these objects. We provide explicit formulas of NMHV gravity amplitudes up to eight points in terms of G-invariants, and give the general definition for any number of points. We discuss the connection to BCFW representation, special behavior under large momentum shift, t","authors_text":"Jaroslav Trnka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-31T17:59:34Z","title":"Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.15780","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":"sha256:2494ee1d1c29a113cd2abfac0b8b55e1fd532dfa31e869d517778b5ac5c82bdc","target":"record","created_at":"2026-07-05T02:39:10Z","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":"faccfe0d664c9279ac573929d15114968ec9273a56b069391df11b7dc3c2c393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-31T17:59:34Z","title_canon_sha256":"4bf40ea17abd4185c85e991fc3a9aeaf8bf5f04fb3b6a5e9dddd7052c6af3bbd"},"schema_version":"1.0","source":{"id":"2012.15780","kind":"arxiv","version":1}},"canonical_sha256":"beb92005508cdc140a5d030104e3fd22be904f4da4d1f52ec5ba037e3646ef86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"beb92005508cdc140a5d030104e3fd22be904f4da4d1f52ec5ba037e3646ef86","first_computed_at":"2026-07-05T02:39:10.044397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:39:10.044397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9lQ/lv0gK/297yEoT5O963/UOZCXYJaGR3S0PU+aUXZBinUo0Sm3t+9SyEkHq6OfYPx/Dw5QukNnWu0kst7sBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:39:10.044903Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.15780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2494ee1d1c29a113cd2abfac0b8b55e1fd532dfa31e869d517778b5ac5c82bdc","sha256:f3e9f263b4901f85e153f9db35c9bd8fc7626b9d225d803ab3dde83475d4d62d"],"state_sha256":"8b616d8e234f008fa680506818eab95c899b60da7e95a788f158a239c40f1f9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LeAyLppPQFNsgNuF+tGjeNeRcWTxz1kN2CrzofnZ4noMf5UKrinjtcMXQ8zBIFF/qVL/4rpkRas6mhs8JPIEBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:28:50.076815Z","bundle_sha256":"328e958a7a836b673e0209eeff7c6e75e1eb9b7e2472bfb35f07bdae0978e420"}}