{"paper":{"title":"The equivariant Milnor-Witt motive of $\\overline{\\mathcal{M}}_{1,2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The equivariant Milnor-Witt motive of the moduli space of stable curves with two marked points admits an explicit decomposition.","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Nanjun Yang","submitted_at":"2026-05-12T06:02:58Z","abstract_excerpt":"We provide a decomposition of the equivariant Milnor-Witt motives for the moduli spaces of stable curves $\\overline{\\mathcal{M}}_{1,2}$."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We provide a decomposition of the equivariant Milnor-Witt motives for the moduli spaces of stable curves overline M_{1,2}.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The category of equivariant Milnor-Witt motives is well-defined and admits a decomposition for this specific moduli space that can be explicitly described.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A decomposition is given for the equivariant Milnor-Witt motive of the moduli space overline M_{1,2}.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The equivariant Milnor-Witt motive of the moduli space of stable curves with two marked points admits an explicit decomposition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"106312b0dc5a513449f78561785ce1a840de331caf15abe839983e54f9003d0a"},"source":{"id":"2605.11576","kind":"arxiv","version":3},"verdict":{"id":"88b2ae7c-4281-4599-9a06-b9b175e8a4af","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:49:46.705203Z","strongest_claim":"We provide a decomposition of the equivariant Milnor-Witt motives for the moduli spaces of stable curves overline M_{1,2}.","one_line_summary":"A decomposition is given for the equivariant Milnor-Witt motive of the moduli space overline M_{1,2}.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The category of equivariant Milnor-Witt motives is well-defined and admits a decomposition for this specific moduli space that can be explicitly described.","pith_extraction_headline":"The equivariant Milnor-Witt motive of the moduli space of stable curves with two marked points admits an explicit decomposition."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11576/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T12:33:39.678590Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T09:31:18.431045Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T08:18:46.669464Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"49f5cf5224ecec391f8c027b886dc7e3c1a6b75b2477ecf6f3a7b12e137f201e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"079959005e431ff9bc2c13740f8ea9cd328a71d5240c87cd6b54e587d50a4acb"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}