{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:Q6FRQKNAVOM6CHXEVF4QE67Q4B","short_pith_number":"pith:Q6FRQKNA","canonical_record":{"source":{"id":"0809.3544","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2008-09-21T01:13:02Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a70cbce915c38543106f21cbf9c1e42bfff502abcf1902f6dddb78ee689b36b1","abstract_canon_sha256":"04f24f03485d6c55c83c10031fad64540e87ceb2b0a50b399919604be57c1cb0"},"schema_version":"1.0"},"canonical_sha256":"878b1829a0ab99e11ee4a979027bf0e06733504f56c9e9bc98144ce57171de1b","source":{"kind":"arxiv","id":"0809.3544","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.3544","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"0809.3544v2","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.3544","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"Q6FRQKNAVOM6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q6FRQKNAVOM6CHXE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q6FRQKNA","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:Q6FRQKNAVOM6CHXEVF4QE67Q4B","target":"record","payload":{"canonical_record":{"source":{"id":"0809.3544","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2008-09-21T01:13:02Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a70cbce915c38543106f21cbf9c1e42bfff502abcf1902f6dddb78ee689b36b1","abstract_canon_sha256":"04f24f03485d6c55c83c10031fad64540e87ceb2b0a50b399919604be57c1cb0"},"schema_version":"1.0"},"canonical_sha256":"878b1829a0ab99e11ee4a979027bf0e06733504f56c9e9bc98144ce57171de1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:20.812386Z","signature_b64":"W/kIBXnRFPE90loCyInYQxnI5iVkoSywmaxfbwB0fyllWlLemBEW6IB149XEh1Aq334VpxwjM4xnqJ/r58d3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"878b1829a0ab99e11ee4a979027bf0e06733504f56c9e9bc98144ce57171de1b","last_reissued_at":"2026-05-18T02:20:20.811655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:20.811655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.3544","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HeERarc1Y3HHa6DldJFZMlVeZAFh+P3807XmfvZL4Jk3DyqA351vxzclKmhdZGKyVSVmDF5Ydvm/sUcZLx+iCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:36:24.326940Z"},"content_sha256":"8805a7ac5657fbfa1028887cc271bd0d604f1899224003a073ba09b76a4602a3","schema_version":"1.0","event_id":"sha256:8805a7ac5657fbfa1028887cc271bd0d604f1899224003a073ba09b76a4602a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:Q6FRQKNAVOM6CHXEVF4QE67Q4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the K-theory of truncated polynomial algebras over the integers","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AT","authors_text":"Lars Hesselholt, Teena Gerhardt, Vigleik Angeltveit","submitted_at":"2008-09-21T01:13:02Z","abstract_excerpt":"We show that the K_{2i}(Z[x]/(x^m),(x)) is finite of order (mi)!(i!)^{m-2} and that K_{2i+1}(Z[x]/(x^m),(x)) is free abelian of rank m-1. This is accomplished by showing that the equivariant homotopy groups of the topological Hochschild spectrum THH(Z) are finite, in odd degrees, and free abelian, in even degrees, and by evaluating their orders and ranks, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3544","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZfDXPrAmjPX9pSwOaAuvPOpD1oy/yululzld5LbIV2lFiRyTdYzMb4g/FLns4/QJj5tjzMmlDsyeBbWUT+pAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:36:24.327283Z"},"content_sha256":"028e1c3fb351c99d328c212df1f517dd72a27d99a82203cd8e6a2a85cc0ad22a","schema_version":"1.0","event_id":"sha256:028e1c3fb351c99d328c212df1f517dd72a27d99a82203cd8e6a2a85cc0ad22a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6FRQKNAVOM6CHXEVF4QE67Q4B/bundle.json","state_url":"https://pith.science/pith/Q6FRQKNAVOM6CHXEVF4QE67Q4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6FRQKNAVOM6CHXEVF4QE67Q4B/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T16:36:24Z","links":{"resolver":"https://pith.science/pith/Q6FRQKNAVOM6CHXEVF4QE67Q4B","bundle":"https://pith.science/pith/Q6FRQKNAVOM6CHXEVF4QE67Q4B/bundle.json","state":"https://pith.science/pith/Q6FRQKNAVOM6CHXEVF4QE67Q4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6FRQKNAVOM6CHXEVF4QE67Q4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:Q6FRQKNAVOM6CHXEVF4QE67Q4B","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":"04f24f03485d6c55c83c10031fad64540e87ceb2b0a50b399919604be57c1cb0","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2008-09-21T01:13:02Z","title_canon_sha256":"a70cbce915c38543106f21cbf9c1e42bfff502abcf1902f6dddb78ee689b36b1"},"schema_version":"1.0","source":{"id":"0809.3544","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.3544","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"0809.3544v2","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.3544","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"Q6FRQKNAVOM6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q6FRQKNAVOM6CHXE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q6FRQKNA","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:028e1c3fb351c99d328c212df1f517dd72a27d99a82203cd8e6a2a85cc0ad22a","target":"graph","created_at":"2026-05-18T02:20:20Z","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 show that the K_{2i}(Z[x]/(x^m),(x)) is finite of order (mi)!(i!)^{m-2} and that K_{2i+1}(Z[x]/(x^m),(x)) is free abelian of rank m-1. This is accomplished by showing that the equivariant homotopy groups of the topological Hochschild spectrum THH(Z) are finite, in odd degrees, and free abelian, in even degrees, and by evaluating their orders and ranks, respectively.","authors_text":"Lars Hesselholt, Teena Gerhardt, Vigleik Angeltveit","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2008-09-21T01:13:02Z","title":"On the K-theory of truncated polynomial algebras over the integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3544","kind":"arxiv","version":2},"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":"sha256:8805a7ac5657fbfa1028887cc271bd0d604f1899224003a073ba09b76a4602a3","target":"record","created_at":"2026-05-18T02:20:20Z","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":"04f24f03485d6c55c83c10031fad64540e87ceb2b0a50b399919604be57c1cb0","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AT","submitted_at":"2008-09-21T01:13:02Z","title_canon_sha256":"a70cbce915c38543106f21cbf9c1e42bfff502abcf1902f6dddb78ee689b36b1"},"schema_version":"1.0","source":{"id":"0809.3544","kind":"arxiv","version":2}},"canonical_sha256":"878b1829a0ab99e11ee4a979027bf0e06733504f56c9e9bc98144ce57171de1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"878b1829a0ab99e11ee4a979027bf0e06733504f56c9e9bc98144ce57171de1b","first_computed_at":"2026-05-18T02:20:20.811655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:20.811655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W/kIBXnRFPE90loCyInYQxnI5iVkoSywmaxfbwB0fyllWlLemBEW6IB149XEh1Aq334VpxwjM4xnqJ/r58d3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:20.812386Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.3544","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8805a7ac5657fbfa1028887cc271bd0d604f1899224003a073ba09b76a4602a3","sha256:028e1c3fb351c99d328c212df1f517dd72a27d99a82203cd8e6a2a85cc0ad22a"],"state_sha256":"76ee4c9f5ff056eb744ab02c6bf64ce0acbc42e01cc1dfc88a12a33ea8d199f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhUPVIHl3NFgINOiwjOZ4SjK+CqoJvTzYA1lXr55HuOKugSqbxtLFleq4kBZFIDox+atscOZV2DW3APO0hYRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:36:24.329441Z","bundle_sha256":"deedd0dec0e99cd5f028009ce90223b10c0a65d982a707e739c61d105dc6b12d"}}