{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:LBGTU33BNZOQMZH4K3EZ7K47OC","short_pith_number":"pith:LBGTU33B","schema_version":"1.0","canonical_sha256":"584d3a6f616e5d0664fc56c99fab9f70b244751865cea39043a8d7700ffd2cb2","source":{"kind":"arxiv","id":"1912.11764","version":2},"attestation_state":"computed","paper":{"title":"Binary Geometries, Generalized Particles and Strings, and Cluster Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Hugh Thomas, Nima Arkani-Hamed, Song He, Thomas Lam","submitted_at":"2019-12-26T03:28:14Z","abstract_excerpt":"We introduce the notion of \"binary\" positive and complex geometries, giving a completely rigid geometric realization of the combinatorics of generalized associahedra attached to any Dynkin diagram. We also define open and closed \"cluster string integrals\" associated with these \"cluster configuration spaces\". The binary geometry of type ${\\cal A}$ gives a gauge-invariant description of the usual open and closed string moduli spaces for tree scattering, making no explicit reference to a worldsheet. The binary geometries and cluster string integrals for other Dynkin types provide a generalization"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1912.11764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-26T03:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"e48c5afbb93e9ec2ab38fcea58cf8d9bdcbc3e2dd9caec05819f170a1c05e46c","abstract_canon_sha256":"0886e490121f5c228025dfe196227598e48478558f3ea473eab9dcbe7a8d3a18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:41:01.918820Z","signature_b64":"GWzRaE7MJgqcrumI8qu4hWNM2r0DOhBpId10/+A5hSa9dp05O9mzggYNzCBCFaxRrvJNfmalnp/MGL8KOy3eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"584d3a6f616e5d0664fc56c99fab9f70b244751865cea39043a8d7700ffd2cb2","last_reissued_at":"2026-07-05T00:41:01.918325Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:41:01.918325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Binary Geometries, Generalized Particles and Strings, and Cluster Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Hugh Thomas, Nima Arkani-Hamed, Song He, Thomas Lam","submitted_at":"2019-12-26T03:28:14Z","abstract_excerpt":"We introduce the notion of \"binary\" positive and complex geometries, giving a completely rigid geometric realization of the combinatorics of generalized associahedra attached to any Dynkin diagram. We also define open and closed \"cluster string integrals\" associated with these \"cluster configuration spaces\". The binary geometry of type ${\\cal A}$ gives a gauge-invariant description of the usual open and closed string moduli spaces for tree scattering, making no explicit reference to a worldsheet. The binary geometries and cluster string integrals for other Dynkin types provide a generalization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.11764","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.11764/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1912.11764","created_at":"2026-07-05T00:41:01.918386+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.11764v2","created_at":"2026-07-05T00:41:01.918386+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.11764","created_at":"2026-07-05T00:41:01.918386+00:00"},{"alias_kind":"pith_short_12","alias_value":"LBGTU33BNZOQ","created_at":"2026-07-05T00:41:01.918386+00:00"},{"alias_kind":"pith_short_16","alias_value":"LBGTU33BNZOQMZH4","created_at":"2026-07-05T00:41:01.918386+00:00"},{"alias_kind":"pith_short_8","alias_value":"LBGTU33B","created_at":"2026-07-05T00:41:01.918386+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.09246","citing_title":"Strings from Almost Nothing","ref_index":128,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC","json":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC.json","graph_json":"https://pith.science/api/pith-number/LBGTU33BNZOQMZH4K3EZ7K47OC/graph.json","events_json":"https://pith.science/api/pith-number/LBGTU33BNZOQMZH4K3EZ7K47OC/events.json","paper":"https://pith.science/paper/LBGTU33B"},"agent_actions":{"view_html":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC","download_json":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC.json","view_paper":"https://pith.science/paper/LBGTU33B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.11764&json=true","fetch_graph":"https://pith.science/api/pith-number/LBGTU33BNZOQMZH4K3EZ7K47OC/graph.json","fetch_events":"https://pith.science/api/pith-number/LBGTU33BNZOQMZH4K3EZ7K47OC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC/action/storage_attestation","attest_author":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC/action/author_attestation","sign_citation":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC/action/citation_signature","submit_replication":"https://pith.science/pith/LBGTU33BNZOQMZH4K3EZ7K47OC/action/replication_record"}},"created_at":"2026-07-05T00:41:01.918386+00:00","updated_at":"2026-07-05T00:41:01.918386+00:00"}