{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HZHF4BJRKLVWHE5KOVE7PO55MJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a0d1d63736ba2464a30a2a77d66d0a6a8824131d9aac524e7e7429b3bddab5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-01-17T17:50:16Z","title_canon_sha256":"03491f8ce1edd4a0bcab0f48410a76575827a90e383e9024fb6222e2e6ba4974"},"schema_version":"1.0","source":{"id":"1101.3279","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3279","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3279v5","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3279","created_at":"2026-05-18T02:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"HZHF4BJRKLVW","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HZHF4BJRKLVWHE5K","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HZHF4BJR","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:e44afb2013c32b163660d9b594c67939bdc15448cbcc65144bc3ba889f60c8b1","target":"graph","created_at":"2026-05-18T02:22:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We use the properties of the refined Bloch group of a field to prove that H_3 of SL_2 of a global field is never finitely generated, and to calculate - up to some 2-torsion - H_3 of SL_2 of local fields with finite residue field of odd characteristic. We also give lower bounds for the 3-torsion in the H_3 of SL_2 of rings of S-integers.","authors_text":"Kevin Hutchinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-01-17T17:50:16Z","title":"A refined Bloch group and the third homology of SL_2 of a field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3279","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:54ea985507b63c30eb3ffb48743c1c40c50f1276fe4339d7a0a7c236254d7721","target":"record","created_at":"2026-05-18T02:22:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a0d1d63736ba2464a30a2a77d66d0a6a8824131d9aac524e7e7429b3bddab5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-01-17T17:50:16Z","title_canon_sha256":"03491f8ce1edd4a0bcab0f48410a76575827a90e383e9024fb6222e2e6ba4974"},"schema_version":"1.0","source":{"id":"1101.3279","kind":"arxiv","version":5}},"canonical_sha256":"3e4e5e053152eb6393aa7549f7bbbd62789f7c6b9fc6275a445433279f79ed46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e4e5e053152eb6393aa7549f7bbbd62789f7c6b9fc6275a445433279f79ed46","first_computed_at":"2026-05-18T02:22:51.965633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:51.965633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8QtLK8k/0Yh56bfYlNkapT8ehgzs7+oZQiJ9m6LeWZmI7wdIWI0pU3Axu7R4JeQce83noJMEdySj7+4RFCztBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:51.966101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3279","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54ea985507b63c30eb3ffb48743c1c40c50f1276fe4339d7a0a7c236254d7721","sha256:e44afb2013c32b163660d9b594c67939bdc15448cbcc65144bc3ba889f60c8b1"],"state_sha256":"fbe55f5ee09d1f533ef39e5dfb6e42e32e74a8d786d7a9346c7187d0341f5f66"}