{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:47IZ23CHMUSDIX5JQU76PUKQZG","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":"bb79adab1171c62d0d75bdde47e23592de957f672d2db1679d9e36b45a648727","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-23T17:14:51Z","title_canon_sha256":"6c0abe359ef2c5d9b3f21ad0bffc327db37851d616be9ec54b18bf03c9365a56"},"schema_version":"1.0","source":{"id":"1404.5896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5896","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5896v1","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5896","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"pith_short_12","alias_value":"47IZ23CHMUSD","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"47IZ23CHMUSDIX5J","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"47IZ23CH","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:c3daa7751ffdca2e417c808b18bdbe851d1dd11e471baef47dc39071f48ee8bc","target":"graph","created_at":"2026-05-18T02:53:27Z","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 prove analogues of the fundamental theorem of algebraic K-theory for the second and third homology of SL_2 over an infinite field k. The statements involve Milnor-Witt K-theory and scissors congruence groups. We use these results to calculate the low-dimensional homology of SL_2 of Laurent polynomials over certain fields.","authors_text":"Kevin Hutchinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-23T17:14:51Z","title":"Low-dimensional Homology of SL_2(k[t,1/t])"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5896","kind":"arxiv","version":1},"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:fb9370d6963da0af34da827a2ff3a76dab2bd552c136b913ac7b3ef20965cec9","target":"record","created_at":"2026-05-18T02:53:27Z","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":"bb79adab1171c62d0d75bdde47e23592de957f672d2db1679d9e36b45a648727","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-23T17:14:51Z","title_canon_sha256":"6c0abe359ef2c5d9b3f21ad0bffc327db37851d616be9ec54b18bf03c9365a56"},"schema_version":"1.0","source":{"id":"1404.5896","kind":"arxiv","version":1}},"canonical_sha256":"e7d19d6c476524345fa9853fe7d150c98e409f9cc983c96f3673d4a70b9e9144","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7d19d6c476524345fa9853fe7d150c98e409f9cc983c96f3673d4a70b9e9144","first_computed_at":"2026-05-18T02:53:27.609128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:27.609128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z/OwnATdJvIztFfU6ERmclYO4zAeU5bTQa0fs+6JQMSCiiox2Fl1yjDEGVfrbLaJdEiB+Ntm7Hi4U6BiNXEpDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:27.610065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb9370d6963da0af34da827a2ff3a76dab2bd552c136b913ac7b3ef20965cec9","sha256:c3daa7751ffdca2e417c808b18bdbe851d1dd11e471baef47dc39071f48ee8bc"],"state_sha256":"9ca7833373deda10b4bacb6c423225155ed4344474a41cf5bbc305b0b5d8ce4d"}