{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:U5NJFMJ36VQKV3FYQ45YW5RCQ5","short_pith_number":"pith:U5NJFMJ3","schema_version":"1.0","canonical_sha256":"a75a92b13bf560aaecb8873b8b762287450f840a96a5cb9cc7233a300d760fc4","source":{"kind":"arxiv","id":"0908.2238","version":4},"attestation_state":"computed","paper":{"title":"A simple construction of Grassmannian polylogarithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"A.B. Goncharov","submitted_at":"2009-08-16T13:19:28Z","abstract_excerpt":"We give a simple explicit construction of the Grassmannian n-logarithm, which is a multivalued analytic function on the quotient of the Grassmannian of generic n-dimensional subspaces in 2n-dimensional coordinate complex vector space by the action of the 2n-dimensional coordinate torus.\n  We study Tate iterated integrals, which are homotopy invariant integrals of 1-forms dlog(rational functions). We introduce the Hopf algebra of integrable symbols related to an algebraic variety, which controls the Tate iterated integrals We give a simple explicit formula for the Tate iterated integrals relate"},"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":"0908.2238","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-16T13:19:28Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"c9a6df849286ae4d99b2c73b0836e239fbf2274bf86b48467bec25d19aca5598","abstract_canon_sha256":"65eb1034fcabdbc3e23a903c74c75acd5a84a2a948f78dd2d9c635b3e3c3f5d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:48.797529Z","signature_b64":"UJkMUSuaMiA7Sd5Jn1OEA3k6oQugKIupSqBOgdE9rKI2Uvi7kaevh/gqMwfqyIHhlwVnliRivZF68qB1xqKwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a75a92b13bf560aaecb8873b8b762287450f840a96a5cb9cc7233a300d760fc4","last_reissued_at":"2026-05-18T03:29:48.797004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:48.797004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A simple construction of Grassmannian polylogarithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"A.B. Goncharov","submitted_at":"2009-08-16T13:19:28Z","abstract_excerpt":"We give a simple explicit construction of the Grassmannian n-logarithm, which is a multivalued analytic function on the quotient of the Grassmannian of generic n-dimensional subspaces in 2n-dimensional coordinate complex vector space by the action of the 2n-dimensional coordinate torus.\n  We study Tate iterated integrals, which are homotopy invariant integrals of 1-forms dlog(rational functions). We introduce the Hopf algebra of integrable symbols related to an algebraic variety, which controls the Tate iterated integrals We give a simple explicit formula for the Tate iterated integrals relate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2238","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0908.2238","created_at":"2026-05-18T03:29:48.797078+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.2238v4","created_at":"2026-05-18T03:29:48.797078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2238","created_at":"2026-05-18T03:29:48.797078+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5NJFMJ36VQK","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5NJFMJ36VQKV3FY","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5NJFMJ3","created_at":"2026-05-18T12:26:02.257875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2505.10406","citing_title":"One-loop amplitudes for $t\\bar{t}j$ and $t\\bar{t}\\gamma$ productions at the LHC through $\\mathcal{O}(\\epsilon^2)$","ref_index":105,"is_internal_anchor":true},{"citing_arxiv_id":"2605.16034","citing_title":"Walking Sudakov: From Cusp to Octagon","ref_index":87,"is_internal_anchor":true},{"citing_arxiv_id":"2512.21210","citing_title":"Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics","ref_index":110,"is_internal_anchor":true},{"citing_arxiv_id":"2604.08658","citing_title":"Differential Equations for Massive Correlators","ref_index":43,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5","json":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5.json","graph_json":"https://pith.science/api/pith-number/U5NJFMJ36VQKV3FYQ45YW5RCQ5/graph.json","events_json":"https://pith.science/api/pith-number/U5NJFMJ36VQKV3FYQ45YW5RCQ5/events.json","paper":"https://pith.science/paper/U5NJFMJ3"},"agent_actions":{"view_html":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5","download_json":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5.json","view_paper":"https://pith.science/paper/U5NJFMJ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.2238&json=true","fetch_graph":"https://pith.science/api/pith-number/U5NJFMJ36VQKV3FYQ45YW5RCQ5/graph.json","fetch_events":"https://pith.science/api/pith-number/U5NJFMJ36VQKV3FYQ45YW5RCQ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5/action/storage_attestation","attest_author":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5/action/author_attestation","sign_citation":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5/action/citation_signature","submit_replication":"https://pith.science/pith/U5NJFMJ36VQKV3FYQ45YW5RCQ5/action/replication_record"}},"created_at":"2026-05-18T03:29:48.797078+00:00","updated_at":"2026-05-18T03:29:48.797078+00:00"}