{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:BUMVQ653ZC3FLLHUK3DRLN5XGQ","short_pith_number":"pith:BUMVQ653","schema_version":"1.0","canonical_sha256":"0d19587bbbc8b655acf456c715b7b73439ce1be1bb0c6bb5a657250e4e6e2ccb","source":{"kind":"arxiv","id":"2106.01405","version":2},"attestation_state":"computed","paper":{"title":"Symbol Alphabets from Tensor Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Anastasia Volovich, Lecheng Ren, Marcus Spradlin","submitted_at":"2021-06-02T18:19:06Z","abstract_excerpt":"We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of $n$-particle amplitudes in planar $\\mathcal{N}=4$ Yang-Mills theory and certain polytopes associated to the Grassmannian G(4, $n$). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner "},"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":"2106.01405","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-06-02T18:19:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b375971f698327f3d4fb999441be200322c4af3449e75ebdd1cb4e88177735de","abstract_canon_sha256":"be4d6456136d00613acdcb00776cdef92c262ef96cc867ab59e6dd6359c305ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:45:33.248227Z","signature_b64":"5VUnzkDTuFtvojvuS3sKEwhacJMM12mX9N2CJEagLG1Yzi/j7pm8MO8SI0b1i20hnoIPDAafIJMbi+rrokeVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d19587bbbc8b655acf456c715b7b73439ce1be1bb0c6bb5a657250e4e6e2ccb","last_reissued_at":"2026-07-05T03:45:33.247796Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:45:33.247796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symbol Alphabets from Tensor Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Anastasia Volovich, Lecheng Ren, Marcus Spradlin","submitted_at":"2021-06-02T18:19:06Z","abstract_excerpt":"We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of $n$-particle amplitudes in planar $\\mathcal{N}=4$ Yang-Mills theory and certain polytopes associated to the Grassmannian G(4, $n$). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.01405","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/2106.01405/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":"2106.01405","created_at":"2026-07-05T03:45:33.247853+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.01405v2","created_at":"2026-07-05T03:45:33.247853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.01405","created_at":"2026-07-05T03:45:33.247853+00:00"},{"alias_kind":"pith_short_12","alias_value":"BUMVQ653ZC3F","created_at":"2026-07-05T03:45:33.247853+00:00"},{"alias_kind":"pith_short_16","alias_value":"BUMVQ653ZC3FLLHU","created_at":"2026-07-05T03:45:33.247853+00:00"},{"alias_kind":"pith_short_8","alias_value":"BUMVQ653","created_at":"2026-07-05T03:45:33.247853+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ","json":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ.json","graph_json":"https://pith.science/api/pith-number/BUMVQ653ZC3FLLHUK3DRLN5XGQ/graph.json","events_json":"https://pith.science/api/pith-number/BUMVQ653ZC3FLLHUK3DRLN5XGQ/events.json","paper":"https://pith.science/paper/BUMVQ653"},"agent_actions":{"view_html":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ","download_json":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ.json","view_paper":"https://pith.science/paper/BUMVQ653","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.01405&json=true","fetch_graph":"https://pith.science/api/pith-number/BUMVQ653ZC3FLLHUK3DRLN5XGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/BUMVQ653ZC3FLLHUK3DRLN5XGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ/action/storage_attestation","attest_author":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ/action/author_attestation","sign_citation":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ/action/citation_signature","submit_replication":"https://pith.science/pith/BUMVQ653ZC3FLLHUK3DRLN5XGQ/action/replication_record"}},"created_at":"2026-07-05T03:45:33.247853+00:00","updated_at":"2026-07-05T03:45:33.247853+00:00"}