{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:WUDSAP2POQBZ3U2SZFC3D6TXGG","short_pith_number":"pith:WUDSAP2P","canonical_record":{"source":{"id":"0811.3624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-11-21T20:00:30Z","cross_cats_sorted":[],"title_canon_sha256":"ca26890345917b5d0532460f35e84a064b5401e44e23f844870d6faa16df42cd","abstract_canon_sha256":"e5af75aaa8403198b810a4c6dee56a9c975af372dbbf00d875f8204c3aa6ad13"},"schema_version":"1.0"},"canonical_sha256":"b507203f4f74039dd352c945b1fa7731a2a8e48e71c95016b04beef10e2bde56","source":{"kind":"arxiv","id":"0811.3624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.3624","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"0811.3624v1","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.3624","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"WUDSAP2POQBZ","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"pith_short_16","alias_value":"WUDSAP2POQBZ3U2S","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"pith_short_8","alias_value":"WUDSAP2P","created_at":"2026-07-04T15:46:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:WUDSAP2POQBZ3U2SZFC3D6TXGG","target":"record","payload":{"canonical_record":{"source":{"id":"0811.3624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-11-21T20:00:30Z","cross_cats_sorted":[],"title_canon_sha256":"ca26890345917b5d0532460f35e84a064b5401e44e23f844870d6faa16df42cd","abstract_canon_sha256":"e5af75aaa8403198b810a4c6dee56a9c975af372dbbf00d875f8204c3aa6ad13"},"schema_version":"1.0"},"canonical_sha256":"b507203f4f74039dd352c945b1fa7731a2a8e48e71c95016b04beef10e2bde56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:46:23.079212Z","signature_b64":"XtYQ82+0T+p/z2ncxHrkReb+U4R2RRCfAmpc920zLpfIBfvBmXP4AzJYs3OGYgaGg6qwh4LTW49j9JDuiJx7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b507203f4f74039dd352c945b1fa7731a2a8e48e71c95016b04beef10e2bde56","last_reissued_at":"2026-07-04T15:46:23.078826Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:46:23.078826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.3624","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":"2026-07-04T15:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dE2zQj5BwRs+H1sQIOj+nTtlfx/TmT3B3PwGQRw0O8DkGcJxrXzw29LxhhepyeYDvGKs59rx3zshVFbclgHzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T23:02:24.955282Z"},"content_sha256":"d639e95d621cf496a6ba6cf0694fdee6f9264e9b07fe6b5a9425a17f706a952c","schema_version":"1.0","event_id":"sha256:d639e95d621cf496a6ba6cf0694fdee6f9264e9b07fe6b5a9425a17f706a952c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:WUDSAP2POQBZ3U2SZFC3D6TXGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Daniel Z. Freedman (MIT), Henriette Elvang (IAS), Michael Kiermaier (MIT)","submitted_at":"2008-11-21T20:00:30Z","abstract_excerpt":"We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory. The proof uses a shift acting on all external momenta, and we show that every N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this shift. The MHV vertex expansion allows us to derive compact and efficient generating functions for all N^kMHV tree amplitudes of the theory. We also derive an improved form of the anti-NMHV generating function. The proof leads to a curious set of sum rules for the diagrams of the MHV vertex expansion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3624","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/0811.3624/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":"2026-07-04T15:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5cpKcsAgLOZSr2vnE2X7CApRHQsVPGLlFyy/fYXA4zDMFoTCvOGn7Ht0WKYl4VEfytQcTLmMhqO/avxzYHeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T23:02:24.955901Z"},"content_sha256":"629c9942d981afec1c1c514879b2f98834c454ac8ba7d49e974d76a7c78bf0f6","schema_version":"1.0","event_id":"sha256:629c9942d981afec1c1c514879b2f98834c454ac8ba7d49e974d76a7c78bf0f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUDSAP2POQBZ3U2SZFC3D6TXGG/bundle.json","state_url":"https://pith.science/pith/WUDSAP2POQBZ3U2SZFC3D6TXGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUDSAP2POQBZ3U2SZFC3D6TXGG/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":"2026-08-18T23:02:24Z","links":{"resolver":"https://pith.science/pith/WUDSAP2POQBZ3U2SZFC3D6TXGG","bundle":"https://pith.science/pith/WUDSAP2POQBZ3U2SZFC3D6TXGG/bundle.json","state":"https://pith.science/pith/WUDSAP2POQBZ3U2SZFC3D6TXGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUDSAP2POQBZ3U2SZFC3D6TXGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WUDSAP2POQBZ3U2SZFC3D6TXGG","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":"e5af75aaa8403198b810a4c6dee56a9c975af372dbbf00d875f8204c3aa6ad13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-11-21T20:00:30Z","title_canon_sha256":"ca26890345917b5d0532460f35e84a064b5401e44e23f844870d6faa16df42cd"},"schema_version":"1.0","source":{"id":"0811.3624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.3624","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"0811.3624v1","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.3624","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"WUDSAP2POQBZ","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"pith_short_16","alias_value":"WUDSAP2POQBZ3U2S","created_at":"2026-07-04T15:46:23Z"},{"alias_kind":"pith_short_8","alias_value":"WUDSAP2P","created_at":"2026-07-04T15:46:23Z"}],"graph_snapshots":[{"event_id":"sha256:629c9942d981afec1c1c514879b2f98834c454ac8ba7d49e974d76a7c78bf0f6","target":"graph","created_at":"2026-07-04T15:46:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0811.3624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory. The proof uses a shift acting on all external momenta, and we show that every N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this shift. The MHV vertex expansion allows us to derive compact and efficient generating functions for all N^kMHV tree amplitudes of the theory. We also derive an improved form of the anti-NMHV generating function. The proof leads to a curious set of sum rules for the diagrams of the MHV vertex expansion.","authors_text":"Daniel Z. Freedman (MIT), Henriette Elvang (IAS), Michael Kiermaier (MIT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-11-21T20:00:30Z","title":"Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3624","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:d639e95d621cf496a6ba6cf0694fdee6f9264e9b07fe6b5a9425a17f706a952c","target":"record","created_at":"2026-07-04T15:46:23Z","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":"e5af75aaa8403198b810a4c6dee56a9c975af372dbbf00d875f8204c3aa6ad13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-11-21T20:00:30Z","title_canon_sha256":"ca26890345917b5d0532460f35e84a064b5401e44e23f844870d6faa16df42cd"},"schema_version":"1.0","source":{"id":"0811.3624","kind":"arxiv","version":1}},"canonical_sha256":"b507203f4f74039dd352c945b1fa7731a2a8e48e71c95016b04beef10e2bde56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b507203f4f74039dd352c945b1fa7731a2a8e48e71c95016b04beef10e2bde56","first_computed_at":"2026-07-04T15:46:23.078826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:46:23.078826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XtYQ82+0T+p/z2ncxHrkReb+U4R2RRCfAmpc920zLpfIBfvBmXP4AzJYs3OGYgaGg6qwh4LTW49j9JDuiJx7BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:46:23.079212Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.3624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d639e95d621cf496a6ba6cf0694fdee6f9264e9b07fe6b5a9425a17f706a952c","sha256:629c9942d981afec1c1c514879b2f98834c454ac8ba7d49e974d76a7c78bf0f6"],"state_sha256":"65238156a34a208755ad56a7b363fc1946f2ca0bfaed5c4440e9333b9fbb6ad9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9i3iBJc9x5WXz9qU+br14T8doyhRCpjBupmCIksIt7xfsWozD/WwNJy62CpgYf+7IJAnRQnGlK+eHrmxwERgDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T23:02:24.961825Z","bundle_sha256":"4d41ec9bb60cd17baf4b80c88712c840eb39c5e4a0036e6c7b1aa08937382fb7"}}