{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Z4ZFRIDN6LLHVFDYH52YPHYQZN","short_pith_number":"pith:Z4ZFRIDN","canonical_record":{"source":{"id":"1207.4458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-18T19:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"67f671836899472db60ac1b9e5f3eaa1b7341aa2a16f8f2ad5b513de665a226b","abstract_canon_sha256":"4e579fa43e77831166c2b326c80a5d4ff788eac2252efab22610811f57aff37f"},"schema_version":"1.0"},"canonical_sha256":"cf3258a06df2d67a94783f75879f10cb7faecf24ce2dde94b3333378166db11c","source":{"kind":"arxiv","id":"1207.4458","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4458","created_at":"2026-05-18T01:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4458v2","created_at":"2026-05-18T01:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4458","created_at":"2026-05-18T01:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"Z4ZFRIDN6LLH","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z4ZFRIDN6LLHVFDY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z4ZFRIDN","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Z4ZFRIDN6LLHVFDYH52YPHYQZN","target":"record","payload":{"canonical_record":{"source":{"id":"1207.4458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-18T19:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"67f671836899472db60ac1b9e5f3eaa1b7341aa2a16f8f2ad5b513de665a226b","abstract_canon_sha256":"4e579fa43e77831166c2b326c80a5d4ff788eac2252efab22610811f57aff37f"},"schema_version":"1.0"},"canonical_sha256":"cf3258a06df2d67a94783f75879f10cb7faecf24ce2dde94b3333378166db11c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:16.717611Z","signature_b64":"nKztPuI3K6f8l9WHWLXYBQrQwj4Cg8fUt4w3PdVGFgnIIKdMrJtDNZiWaKPkHs0ydxq0TSE7gQpfuKtUuZ/XAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf3258a06df2d67a94783f75879f10cb7faecf24ce2dde94b3333378166db11c","last_reissued_at":"2026-05-18T01:56:16.716929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:16.716929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.4458","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ig1TlixkzKyYv4SMmvkL1uxs5JgPiu4+i6nnWbc9Fn42ERPLV/VG0CkItiMbJO/XrHJ4FQJ2KGFfnq7QoIWXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:59:50.085990Z"},"content_sha256":"912e6d01fae6fd8c09ecf394fa52a9fed871631679c126494e096ac1a81da78b","schema_version":"1.0","event_id":"sha256:912e6d01fae6fd8c09ecf394fa52a9fed871631679c126494e096ac1a81da78b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Z4ZFRIDN6LLHVFDYH52YPHYQZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravity Amplitudes from n-Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Clifford Cheung","submitted_at":"2012-07-18T19:27:45Z","abstract_excerpt":"We identify a hidden GL(n,C) symmetry of the tree level n-point MHV gravity amplitude. Representations of this symmetry reside in an auxiliary n-space whose indices are external particle labels. Spinor helicity variables transform non-linearly under GL(n,C), but linearly under its notable subgroups, the little group and the permutation group S_n. Using GL(n,C) covariant variables, we present a new and simple formula for the MHV amplitude which can be derived solely from geometric constraints. This expression carries a huge intrinsic redundancy which can be parameterized by a pair of reference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4458","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1Yd3Ogxsoy0p+olhuLFv8Jr93arGYD1+LaXgtexUQLOU0TOF+ZgMR5sOgKH3h92m5RcYxqon+sm8uNDQ3MVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:59:50.086660Z"},"content_sha256":"0f2a8fe5f7db59fc8d6415c7e4e627b0b5aa71a93eb2b00063f8450e504fc506","schema_version":"1.0","event_id":"sha256:0f2a8fe5f7db59fc8d6415c7e4e627b0b5aa71a93eb2b00063f8450e504fc506"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4ZFRIDN6LLHVFDYH52YPHYQZN/bundle.json","state_url":"https://pith.science/pith/Z4ZFRIDN6LLHVFDYH52YPHYQZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4ZFRIDN6LLHVFDYH52YPHYQZN/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":"2026-06-05T22:59:50Z","links":{"resolver":"https://pith.science/pith/Z4ZFRIDN6LLHVFDYH52YPHYQZN","bundle":"https://pith.science/pith/Z4ZFRIDN6LLHVFDYH52YPHYQZN/bundle.json","state":"https://pith.science/pith/Z4ZFRIDN6LLHVFDYH52YPHYQZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4ZFRIDN6LLHVFDYH52YPHYQZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z4ZFRIDN6LLHVFDYH52YPHYQZN","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":"4e579fa43e77831166c2b326c80a5d4ff788eac2252efab22610811f57aff37f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-18T19:27:45Z","title_canon_sha256":"67f671836899472db60ac1b9e5f3eaa1b7341aa2a16f8f2ad5b513de665a226b"},"schema_version":"1.0","source":{"id":"1207.4458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4458","created_at":"2026-05-18T01:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4458v2","created_at":"2026-05-18T01:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4458","created_at":"2026-05-18T01:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"Z4ZFRIDN6LLH","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z4ZFRIDN6LLHVFDY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z4ZFRIDN","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:0f2a8fe5f7db59fc8d6415c7e4e627b0b5aa71a93eb2b00063f8450e504fc506","target":"graph","created_at":"2026-05-18T01:56:16Z","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 identify a hidden GL(n,C) symmetry of the tree level n-point MHV gravity amplitude. Representations of this symmetry reside in an auxiliary n-space whose indices are external particle labels. Spinor helicity variables transform non-linearly under GL(n,C), but linearly under its notable subgroups, the little group and the permutation group S_n. Using GL(n,C) covariant variables, we present a new and simple formula for the MHV amplitude which can be derived solely from geometric constraints. This expression carries a huge intrinsic redundancy which can be parameterized by a pair of reference ","authors_text":"Clifford Cheung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-18T19:27:45Z","title":"Gravity Amplitudes from n-Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4458","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":"sha256:912e6d01fae6fd8c09ecf394fa52a9fed871631679c126494e096ac1a81da78b","target":"record","created_at":"2026-05-18T01:56:16Z","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":"4e579fa43e77831166c2b326c80a5d4ff788eac2252efab22610811f57aff37f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-18T19:27:45Z","title_canon_sha256":"67f671836899472db60ac1b9e5f3eaa1b7341aa2a16f8f2ad5b513de665a226b"},"schema_version":"1.0","source":{"id":"1207.4458","kind":"arxiv","version":2}},"canonical_sha256":"cf3258a06df2d67a94783f75879f10cb7faecf24ce2dde94b3333378166db11c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf3258a06df2d67a94783f75879f10cb7faecf24ce2dde94b3333378166db11c","first_computed_at":"2026-05-18T01:56:16.716929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:16.716929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nKztPuI3K6f8l9WHWLXYBQrQwj4Cg8fUt4w3PdVGFgnIIKdMrJtDNZiWaKPkHs0ydxq0TSE7gQpfuKtUuZ/XAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:16.717611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:912e6d01fae6fd8c09ecf394fa52a9fed871631679c126494e096ac1a81da78b","sha256:0f2a8fe5f7db59fc8d6415c7e4e627b0b5aa71a93eb2b00063f8450e504fc506"],"state_sha256":"ea575e1362405821c99835554401f035a9708818b86cc9b1acda2bbe78c8c0ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3aAsPgVVIN/PEfl4ATb4DV74Fd706vJQdImL+bvHVTKCm2JGOKDwsyaJ3yi69RJD8UKkwjB0QoDf69Nt1f8gCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:59:50.090893Z","bundle_sha256":"1378b8687a3fab9a84398cfa49be139385cbefdb9517bd64850e4ff607cf2d25"}}