{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7ISMYQKGLUA462KHD6P2TYTYJL","short_pith_number":"pith:7ISMYQKG","schema_version":"1.0","canonical_sha256":"fa24cc41465d01cf69471f9fa9e2784af910e4a4600d72761ca5601a3a0eed0c","source":{"kind":"arxiv","id":"2607.29368","version":1},"attestation_state":"computed","paper":{"title":"Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Andreas Koutsogiannis, Borys Kuca, Wenbo Sun","submitted_at":"2026-07-31T12:52:49Z","abstract_excerpt":"We investigate manifestations of the Nilpotent Heuristic, which posits that recurrence and convergence phenomena known for measure-preserving $\\mathbb{Z}^D$-systems extend to nilpotent group actions. Our main results establish seminorm estimates and limiting formulas for multiple ergodic averages arising from actions of 2-step nilpotent groups. In particular, if $T_1,\\ldots,T_\\ell$ are totally ergodic and generate a 2-step nilpotent group, then \\[ \\lim_{N\\to\\infty}\\frac{1}{N}\\sum_{n=1}^N T_1^n f_1 \\cdots T_\\ell^{n^\\ell}f_\\ell = \\prod_{j=1}^{\\ell}\\int f_j\\,d\\mu \\] in the $L^{2}$ norm for all bo"},"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":"2607.29368","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-07-31T12:52:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"87f9ed6d3a2af11346b398f9974d7aa107cddfc21c8518d457b422ad721b2a14","abstract_canon_sha256":"c1f43ae5830730ca57732eabb1d712bee2d5bbc521a89e43dbfd4fbb2585da9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:33:21.465741Z","signature_b64":"kwNn/18HdGrlnfsy906YE0Qvw84Iq53OHGOSZtej2X+gJJGzscUS9wcpd2/itIB7lc37e+43D693r+TLdlhTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa24cc41465d01cf69471f9fa9e2784af910e4a4600d72761ca5601a3a0eed0c","last_reissued_at":"2026-08-03T01:33:21.463799Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:33:21.463799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Andreas Koutsogiannis, Borys Kuca, Wenbo Sun","submitted_at":"2026-07-31T12:52:49Z","abstract_excerpt":"We investigate manifestations of the Nilpotent Heuristic, which posits that recurrence and convergence phenomena known for measure-preserving $\\mathbb{Z}^D$-systems extend to nilpotent group actions. Our main results establish seminorm estimates and limiting formulas for multiple ergodic averages arising from actions of 2-step nilpotent groups. In particular, if $T_1,\\ldots,T_\\ell$ are totally ergodic and generate a 2-step nilpotent group, then \\[ \\lim_{N\\to\\infty}\\frac{1}{N}\\sum_{n=1}^N T_1^n f_1 \\cdots T_\\ell^{n^\\ell}f_\\ell = \\prod_{j=1}^{\\ell}\\int f_j\\,d\\mu \\] in the $L^{2}$ norm for all bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29368","kind":"arxiv","version":1},"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/2607.29368/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":"2607.29368","created_at":"2026-08-03T01:33:21.464863+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.29368v1","created_at":"2026-08-03T01:33:21.464863+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29368","created_at":"2026-08-03T01:33:21.464863+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ISMYQKGLUA4","created_at":"2026-08-03T01:33:21.464863+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ISMYQKGLUA462KH","created_at":"2026-08-03T01:33:21.464863+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ISMYQKG","created_at":"2026-08-03T01:33:21.464863+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/7ISMYQKGLUA462KHD6P2TYTYJL","json":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL.json","graph_json":"https://pith.science/api/pith-number/7ISMYQKGLUA462KHD6P2TYTYJL/graph.json","events_json":"https://pith.science/api/pith-number/7ISMYQKGLUA462KHD6P2TYTYJL/events.json","paper":"https://pith.science/paper/7ISMYQKG"},"agent_actions":{"view_html":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL","download_json":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL.json","view_paper":"https://pith.science/paper/7ISMYQKG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.29368&json=true","fetch_graph":"https://pith.science/api/pith-number/7ISMYQKGLUA462KHD6P2TYTYJL/graph.json","fetch_events":"https://pith.science/api/pith-number/7ISMYQKGLUA462KHD6P2TYTYJL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL/action/storage_attestation","attest_author":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL/action/author_attestation","sign_citation":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL/action/citation_signature","submit_replication":"https://pith.science/pith/7ISMYQKGLUA462KHD6P2TYTYJL/action/replication_record"}},"created_at":"2026-08-03T01:33:21.464863+00:00","updated_at":"2026-08-03T01:33:21.464863+00:00"}