{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LVUPWA2FLW3AC5JDTYSU4RWQS4","short_pith_number":"pith:LVUPWA2F","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"},"canonical_sha256":"5d68fb03455db60175239e254e46d097171f22d5f2c2973a676cdcc4c0b5e5d0","source":{"kind":"arxiv","id":"2501.01609","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01609","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01609v1","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01609","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"pith_short_12","alias_value":"LVUPWA2FLW3A","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"pith_short_16","alias_value":"LVUPWA2FLW3AC5JD","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"pith_short_8","alias_value":"LVUPWA2F","created_at":"2026-07-05T09:56:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LVUPWA2FLW3AC5JDTYSU4RWQS4","target":"record","payload":{"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"},"canonical_sha256":"5d68fb03455db60175239e254e46d097171f22d5f2c2973a676cdcc4c0b5e5d0","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"},"source_kind":"arxiv","source_id":"2501.01609","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:56:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQq1RuOV/6biSdKFWSdNQyl71ckoPDoZiwQwNDjjQo/aex+LfkHHWflCXwrAlUVPQaygqhs3ge0kECAjWTE0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:36:18.197431Z"},"content_sha256":"3332a8cd1c9a090a65a65abe5a096a5fae0b9311fc1606e3faafd3eb60e7d537","schema_version":"1.0","event_id":"sha256:3332a8cd1c9a090a65a65abe5a096a5fae0b9311fc1606e3faafd3eb60e7d537"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LVUPWA2FLW3AC5JDTYSU4RWQS4","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:56:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9A80bOkMHS2Vyj6IQ5t2TezJIkO0gUA2P6Wgs1cRT898Mkt16Q2SbPnj5BDpj0TU8zRXsx0tQ4lZjCPDfOS+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:36:18.198319Z"},"content_sha256":"6307595ea87baac32f019b8e45626d8f7b7f20df7b2a2e0f459ac7e69f3f6f78","schema_version":"1.0","event_id":"sha256:6307595ea87baac32f019b8e45626d8f7b7f20df7b2a2e0f459ac7e69f3f6f78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/bundle.json","state_url":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/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":"2026-08-11T20:36:18Z","links":{"resolver":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4","bundle":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/bundle.json","state":"https://pith.science/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVUPWA2FLW3AC5JDTYSU4RWQS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LVUPWA2FLW3AC5JDTYSU4RWQS4","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":"08077fb257b74cd2514d721fcfb9b0a4b7b817bb04a12e2abb7d8423faa9d873","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-01-03T03:06:30Z","title_canon_sha256":"b22cfd63e26bb86fb0c607304841ea39e58a286f3f0cefe235caa82d78dfa795"},"schema_version":"1.0","source":{"id":"2501.01609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01609","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01609v1","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01609","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"pith_short_12","alias_value":"LVUPWA2FLW3A","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"pith_short_16","alias_value":"LVUPWA2FLW3AC5JD","created_at":"2026-07-05T09:56:27Z"},{"alias_kind":"pith_short_8","alias_value":"LVUPWA2F","created_at":"2026-07-05T09:56:27Z"}],"graph_snapshots":[{"event_id":"sha256:6307595ea87baac32f019b8e45626d8f7b7f20df7b2a2e0f459ac7e69f3f6f78","target":"graph","created_at":"2026-07-05T09:56:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.01609/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Alexander Kupers, Inna Zakharevich, Jonathan Campbell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-01-03T03:06:30Z","title":"A stable rank filtration on direct sum $K$-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01609","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":"sha256:3332a8cd1c9a090a65a65abe5a096a5fae0b9311fc1606e3faafd3eb60e7d537","target":"record","created_at":"2026-07-05T09:56:27Z","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":"08077fb257b74cd2514d721fcfb9b0a4b7b817bb04a12e2abb7d8423faa9d873","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2025-01-03T03:06:30Z","title_canon_sha256":"b22cfd63e26bb86fb0c607304841ea39e58a286f3f0cefe235caa82d78dfa795"},"schema_version":"1.0","source":{"id":"2501.01609","kind":"arxiv","version":1}},"canonical_sha256":"5d68fb03455db60175239e254e46d097171f22d5f2c2973a676cdcc4c0b5e5d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d68fb03455db60175239e254e46d097171f22d5f2c2973a676cdcc4c0b5e5d0","first_computed_at":"2026-07-05T09:56:27.465875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:27.465875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CuKu83OyKJKJzzELXmREEqJj2R3Mm2qdTKmpwtsl+SzdgR45C1JXXxOdDbcRsEYs50qocU0W8rDrVqumD/qGAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:27.466265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.01609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3332a8cd1c9a090a65a65abe5a096a5fae0b9311fc1606e3faafd3eb60e7d537","sha256:6307595ea87baac32f019b8e45626d8f7b7f20df7b2a2e0f459ac7e69f3f6f78"],"state_sha256":"c6b8a05247fbb1d97cd1a180f7d555c04fc1b87231166682b98f2b330427ac6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7L7kNNmdH99QS1nPZKdhSzvqQgqc0uCWgRvjsTqXSDJe5A9E3gM6fAY/+jlN6vOAdFGx/fS4tikzmlWJMSHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T20:36:18.205176Z","bundle_sha256":"3977ab14879e5dd76a8ab8c6df2762e71a2eca8e6658db19315ae2c056600678"}}