{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WPD7L7BUCS4GFSGC3ET5ZRNFVH","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":"3a8ae267522fc08d995d7a28221eabcf07802c4475f0515ad3ae5b46976f81d9","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-20T19:35:21Z","title_canon_sha256":"afe4c38a4f22e782191f37329c2ea84ffa1b109c7f11f591a75ce643af05451d"},"schema_version":"1.0","source":{"id":"2505.14857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.14857","created_at":"2026-07-05T11:06:36Z"},{"alias_kind":"arxiv_version","alias_value":"2505.14857v1","created_at":"2026-07-05T11:06:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.14857","created_at":"2026-07-05T11:06:36Z"},{"alias_kind":"pith_short_12","alias_value":"WPD7L7BUCS4G","created_at":"2026-07-05T11:06:36Z"},{"alias_kind":"pith_short_16","alias_value":"WPD7L7BUCS4GFSGC","created_at":"2026-07-05T11:06:36Z"},{"alias_kind":"pith_short_8","alias_value":"WPD7L7BU","created_at":"2026-07-05T11:06:36Z"}],"graph_snapshots":[{"event_id":"sha256:da99c05429572a4760fc0b3b3fecb87e206d26cabe807394be44561807b25f7e","target":"graph","created_at":"2026-07-05T11:06:36Z","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/2505.14857/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study linear relations between color-ordered all-plus amplitudes at one loop in Yang--Mills theory. We show that on general grounds, there are $(n-1)!/2-2$ relations for $n\\ge 5$, leaving only two independent color-ordered amplitudes. We present two complementary approaches to finding such relations: one using numerical linear algebra and the other using syzygies in computational algebraic geometry. We obtain explicit forms for all relations through $n=7$. We also study relations for the tree-level MHV amplitudes through $n=8$. The latter relations include the well-known color and Bern--Car","authors_text":"David A. Kosower, Sebastian P\\\"ogel","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-20T19:35:21Z","title":"Serendipitous Syzygies of Scattering Amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14857","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":"sha256:256115924e219ce029d2be8220afb18381b37d071b5acea5db6a6af4518f70f1","target":"record","created_at":"2026-07-05T11:06:36Z","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":"3a8ae267522fc08d995d7a28221eabcf07802c4475f0515ad3ae5b46976f81d9","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-20T19:35:21Z","title_canon_sha256":"afe4c38a4f22e782191f37329c2ea84ffa1b109c7f11f591a75ce643af05451d"},"schema_version":"1.0","source":{"id":"2505.14857","kind":"arxiv","version":1}},"canonical_sha256":"b3c7f5fc3414b862c8c2d927dcc5a5a9f390bcc40db037be6ce555784f24781d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3c7f5fc3414b862c8c2d927dcc5a5a9f390bcc40db037be6ce555784f24781d","first_computed_at":"2026-07-05T11:06:36.543220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:36.543220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5UfjUGP7ZZIv+ifDav0n+f33DRpQtg9tMJsNsLjj686lSTWIFbg3wcdCSUC3gwlptdeKaMVvk+qXGt3RIwoiCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:36.543714Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.14857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:256115924e219ce029d2be8220afb18381b37d071b5acea5db6a6af4518f70f1","sha256:da99c05429572a4760fc0b3b3fecb87e206d26cabe807394be44561807b25f7e"],"state_sha256":"3a97db2fa470cdc59d9fc533a1eb65083940332c7f63354eb40eb4335c847b23"}