{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:LVUPWA2FLW3AC5JDTYSU4RWQS4","short_pith_number":"pith:LVUPWA2F","schema_version":"1.0","canonical_sha256":"5d68fb03455db60175239e254e46d097171f22d5f2c2973a676cdcc4c0b5e5d0","source":{"kind":"arxiv","id":"2501.01609","version":1},"attestation_state":"computed","paper":{"title":"A stable rank filtration on direct sum $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Alexander Kupers, Inna Zakharevich, Jonathan Campbell","submitted_at":"2025-01-03T03:06:30Z","abstract_excerpt":"In the literature, there are two standard rank filtrations on $K$-theory: an ``unstable'' one which is traditionally defined through the homology of $GL_n$, and a ``stable'' one which was defined by Rognes using the simplicial structure on Waldhausen's $S_\\bullet$-construction. In this paper we give an alternate stable rank filtration, which uses the simplicial structure present in a $\\Gamma$-space construction of $K$-theory; we investigate this in the case of ``convenient addition categories,'' and show that in good situtations where a notion of ``rank'' is present, the filtration quotients w"},"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":"2501.01609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-01-03T03:06:30Z","cross_cats_sorted":[],"title_canon_sha256":"b22cfd63e26bb86fb0c607304841ea39e58a286f3f0cefe235caa82d78dfa795","abstract_canon_sha256":"08077fb257b74cd2514d721fcfb9b0a4b7b817bb04a12e2abb7d8423faa9d873"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:27.466265Z","signature_b64":"CuKu83OyKJKJzzELXmREEqJj2R3Mm2qdTKmpwtsl+SzdgR45C1JXXxOdDbcRsEYs50qocU0W8rDrVqumD/qGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d68fb03455db60175239e254e46d097171f22d5f2c2973a676cdcc4c0b5e5d0","last_reissued_at":"2026-07-05T09:56:27.465875Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:27.465875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stable rank filtration on direct sum $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Alexander Kupers, Inna Zakharevich, Jonathan Campbell","submitted_at":"2025-01-03T03:06:30Z","abstract_excerpt":"In the literature, there are two standard rank filtrations on $K$-theory: an ``unstable'' one which is traditionally defined through the homology of $GL_n$, and a ``stable'' one which was defined by Rognes using the simplicial structure on Waldhausen's $S_\\bullet$-construction. In this paper we give an alternate stable rank filtration, which uses the simplicial structure present in a $\\Gamma$-space construction of $K$-theory; we investigate this in the case of ``convenient addition categories,'' and show that in good situtations where a notion of ``rank'' is present, the filtration quotients w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01609","kind":"arxiv","version":1},"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/2501.01609/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":"2501.01609","created_at":"2026-07-05T09:56:27.465933+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.01609v1","created_at":"2026-07-05T09:56:27.465933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01609","created_at":"2026-07-05T09:56:27.465933+00:00"},{"alias_kind":"pith_short_12","alias_value":"LVUPWA2FLW3A","created_at":"2026-07-05T09:56:27.465933+00:00"},{"alias_kind":"pith_short_16","alias_value":"LVUPWA2FLW3AC5JD","created_at":"2026-07-05T09:56:27.465933+00:00"},{"alias_kind":"pith_short_8","alias_value":"LVUPWA2F","created_at":"2026-07-05T09:56:27.465933+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/LVUPWA2FLW3AC5JDTYSU4RWQS4","json":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4.json","graph_json":"https://pith.science/api/pith-number/LVUPWA2FLW3AC5JDTYSU4RWQS4/graph.json","events_json":"https://pith.science/api/pith-number/LVUPWA2FLW3AC5JDTYSU4RWQS4/events.json","paper":"https://pith.science/paper/LVUPWA2F"},"agent_actions":{"view_html":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4","download_json":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4.json","view_paper":"https://pith.science/paper/LVUPWA2F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.01609&json=true","fetch_graph":"https://pith.science/api/pith-number/LVUPWA2FLW3AC5JDTYSU4RWQS4/graph.json","fetch_events":"https://pith.science/api/pith-number/LVUPWA2FLW3AC5JDTYSU4RWQS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/action/storage_attestation","attest_author":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/action/author_attestation","sign_citation":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/action/citation_signature","submit_replication":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/action/replication_record"}},"created_at":"2026-07-05T09:56:27.465933+00:00","updated_at":"2026-07-05T09:56:27.465933+00:00"}