{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:45IQWMLR223V4S3B7V4MDU2QEB","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":"adf022c708da2cc553c0b9ed5d8df8676747a1a0bb05274eea188e6532f9f399","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-07-07T20:00:56Z","title_canon_sha256":"fd22dfd845dad8b491cd88ef0e0a2c4a13a236b0f4bfbb8373dcae5beaf62600"},"schema_version":"1.0","source":{"id":"1507.01950","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01950","created_at":"2026-05-18T01:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01950v2","created_at":"2026-05-18T01:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01950","created_at":"2026-05-18T01:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"45IQWMLR223V","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"45IQWMLR223V4S3B","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"45IQWMLR","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:26e2ae8b474e789ef76e69a722d88a5c5c93cf3e3f228a49f1ab8af2f5fa5378","target":"graph","created_at":"2026-05-18T01:22:39Z","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":"Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the $A_n$ cluster algebra. Using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.","authors_text":"Adam Scherlis, Anastasia Volovich, Daniel E. Parker, Marcus Spradlin","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-07-07T20:00:56Z","title":"Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01950","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:ada3a7911afd83e4cd0dfb47e12e5108a536bdd1ce2446e2819787306e0033bf","target":"record","created_at":"2026-05-18T01:22:39Z","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":"adf022c708da2cc553c0b9ed5d8df8676747a1a0bb05274eea188e6532f9f399","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-07-07T20:00:56Z","title_canon_sha256":"fd22dfd845dad8b491cd88ef0e0a2c4a13a236b0f4bfbb8373dcae5beaf62600"},"schema_version":"1.0","source":{"id":"1507.01950","kind":"arxiv","version":2}},"canonical_sha256":"e7510b3171d6b75e4b61fd78c1d350207a894e22dfa28ea50a12d4d78b59735c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7510b3171d6b75e4b61fd78c1d350207a894e22dfa28ea50a12d4d78b59735c","first_computed_at":"2026-05-18T01:22:39.336123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:39.336123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qh9H6rh8JXFTVqg9oQILy0Rss0JWeA1NmJiAdSEm5ZBhEEn+FGVL0eM5ONqRtsGKhNQ6ZGGE47dZUicYCMXmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:39.336738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01950","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ada3a7911afd83e4cd0dfb47e12e5108a536bdd1ce2446e2819787306e0033bf","sha256:26e2ae8b474e789ef76e69a722d88a5c5c93cf3e3f228a49f1ab8af2f5fa5378"],"state_sha256":"51f8a5be0569f32775a9b3506c9b320dfaf1d91d582c738c10fb529f4bb0b412"}