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For any collection of pairwise disjoint, separating simple closed curves on $S_g$, the corresponding Dehn twists pairwise commute and determine a homology class in $H_k(\\mathcal{I}_g)$, which is called an abelian cycle. We prove that the subgroup of $H_k(\\mathcal{I}_g)$ generated by such abelian cycles is a $\\mathbb{Z}/2\\mathbb{Z}$-vec"},"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":"2510.25728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-10-29T17:33:46Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"72c73893d91fea193cf0e2d8a4f085e97a29de1cdd91f4277199eb5a20384e9f","abstract_canon_sha256":"61ca83568e5af976415000f969cd6dd31757f7a596fdfc95cfe36047cc46f54d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:18.227072Z","signature_b64":"H93sEqHX2FMZXmNrNNgnEFDFJEW0zO20c7ks8rITC/wtLv0dHc0zAIAYYfQI7DRukxkmEk/dN3XUMf5h25GPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f2464afb9dc8cd42e834dd78243c7132a3d34bea671353dbb7313575e7aeb7f","last_reissued_at":"2026-05-26T01:03:18.226548Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:18.226548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On torsion in the homology of the Torelli group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Andrei Vladimirov","submitted_at":"2025-10-29T17:33:46Z","abstract_excerpt":"Let $S_g$ be a closed, oriented surface of genus $g$, and let $\\operatorname{Mod}(S_g)$ denote its mapping class group. The Torelli group $\\mathcal{I}_g$ is the subgroup of $\\operatorname{Mod}(S_g)$ consisting of mapping classes that act trivially on $H_1(S_g)$. For any collection of pairwise disjoint, separating simple closed curves on $S_g$, the corresponding Dehn twists pairwise commute and determine a homology class in $H_k(\\mathcal{I}_g)$, which is called an abelian cycle. We prove that the subgroup of $H_k(\\mathcal{I}_g)$ generated by such abelian cycles is a $\\mathbb{Z}/2\\mathbb{Z}$-vec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.25728","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/2510.25728/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":"2510.25728","created_at":"2026-05-26T01:03:18.226616+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.25728v2","created_at":"2026-05-26T01:03:18.226616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.25728","created_at":"2026-05-26T01:03:18.226616+00:00"},{"alias_kind":"pith_short_12","alias_value":"N4SGJL5Z3SGN","created_at":"2026-05-26T01:03:18.226616+00:00"},{"alias_kind":"pith_short_16","alias_value":"N4SGJL5Z3SGNILUD","created_at":"2026-05-26T01:03:18.226616+00:00"},{"alias_kind":"pith_short_8","alias_value":"N4SGJL5Z","created_at":"2026-05-26T01:03:18.226616+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/N4SGJL5Z3SGNILUDJXLYEQ6HCM","json":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM.json","graph_json":"https://pith.science/api/pith-number/N4SGJL5Z3SGNILUDJXLYEQ6HCM/graph.json","events_json":"https://pith.science/api/pith-number/N4SGJL5Z3SGNILUDJXLYEQ6HCM/events.json","paper":"https://pith.science/paper/N4SGJL5Z"},"agent_actions":{"view_html":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM","download_json":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM.json","view_paper":"https://pith.science/paper/N4SGJL5Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.25728&json=true","fetch_graph":"https://pith.science/api/pith-number/N4SGJL5Z3SGNILUDJXLYEQ6HCM/graph.json","fetch_events":"https://pith.science/api/pith-number/N4SGJL5Z3SGNILUDJXLYEQ6HCM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM/action/storage_attestation","attest_author":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM/action/author_attestation","sign_citation":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM/action/citation_signature","submit_replication":"https://pith.science/pith/N4SGJL5Z3SGNILUDJXLYEQ6HCM/action/replication_record"}},"created_at":"2026-05-26T01:03:18.226616+00:00","updated_at":"2026-05-26T01:03:18.226616+00:00"}