{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6HNXQ24FS4XS35AUWLNRVTXYCT","short_pith_number":"pith:6HNXQ24F","schema_version":"1.0","canonical_sha256":"f1db786b85972f2df414b2db1acef814c65cb7cf5b31655bc63ee09400f5cec1","source":{"kind":"arxiv","id":"1605.08758","version":3},"attestation_state":"computed","paper":{"title":"Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Michael Zlotnikov","submitted_at":"2016-05-27T19:15:54Z","abstract_excerpt":"We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\\sigma$-moduli multivariate polynomial of what we call the $\\textit{standard form}$. We show that a standard form polynomial must have a specific $\\textit{ladder type}$ monomial structure, which has finite size at any $n$, with highest multivariate degree given by $(n-3)(n-4)/2$. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop l"},"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":"1605.08758","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-27T19:15:54Z","cross_cats_sorted":[],"title_canon_sha256":"b349742d4c4796bfec5d273a0ce818030a9b6d3264a26af3e328942a91b5a26b","abstract_canon_sha256":"8c72570cd704a0dcbbc1e40b195cac62c835e0cf0690e787ad24b954408ef86c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:24.200845Z","signature_b64":"6atYzcFCksRedhueWBX9OfQvcBKomsB8zln/PFtccLxLy5MSdwGDQzg/XiQVhGnpp4nP9C2mQ+qzATH5uTTwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1db786b85972f2df414b2db1acef814c65cb7cf5b31655bc63ee09400f5cec1","last_reissued_at":"2026-05-18T01:06:24.200459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:24.200459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Michael Zlotnikov","submitted_at":"2016-05-27T19:15:54Z","abstract_excerpt":"We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\\sigma$-moduli multivariate polynomial of what we call the $\\textit{standard form}$. We show that a standard form polynomial must have a specific $\\textit{ladder type}$ monomial structure, which has finite size at any $n$, with highest multivariate degree given by $(n-3)(n-4)/2$. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08758","kind":"arxiv","version":3},"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":"1605.08758","created_at":"2026-05-18T01:06:24.200519+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.08758v3","created_at":"2026-05-18T01:06:24.200519+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08758","created_at":"2026-05-18T01:06:24.200519+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HNXQ24FS4XS","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HNXQ24FS4XS35AU","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HNXQ24F","created_at":"2026-05-18T12:30:01.593930+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/6HNXQ24FS4XS35AUWLNRVTXYCT","json":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT.json","graph_json":"https://pith.science/api/pith-number/6HNXQ24FS4XS35AUWLNRVTXYCT/graph.json","events_json":"https://pith.science/api/pith-number/6HNXQ24FS4XS35AUWLNRVTXYCT/events.json","paper":"https://pith.science/paper/6HNXQ24F"},"agent_actions":{"view_html":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT","download_json":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT.json","view_paper":"https://pith.science/paper/6HNXQ24F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.08758&json=true","fetch_graph":"https://pith.science/api/pith-number/6HNXQ24FS4XS35AUWLNRVTXYCT/graph.json","fetch_events":"https://pith.science/api/pith-number/6HNXQ24FS4XS35AUWLNRVTXYCT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT/action/storage_attestation","attest_author":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT/action/author_attestation","sign_citation":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT/action/citation_signature","submit_replication":"https://pith.science/pith/6HNXQ24FS4XS35AUWLNRVTXYCT/action/replication_record"}},"created_at":"2026-05-18T01:06:24.200519+00:00","updated_at":"2026-05-18T01:06:24.200519+00:00"}