{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HHF7LD7W2AQOC2RY6XN7AIMPSJ","short_pith_number":"pith:HHF7LD7W","canonical_record":{"source":{"id":"1101.4803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-01-25T13:07:59Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"4bb690e81b7eac9f1588a56bcfa7769eb8572b01da39209801ec206d267b7e1c","abstract_canon_sha256":"9494804bd4f34fe8fc4fe27779c68dde75ee8a66b4d46f7320ee2c41647278ec"},"schema_version":"1.0"},"canonical_sha256":"39cbf58ff6d020e16a38f5dbf0218f926c0245081cc7ff47e3c9b560e87224fe","source":{"kind":"arxiv","id":"1101.4803","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4803","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4803v2","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4803","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"HHF7LD7W2AQO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HHF7LD7W2AQOC2RY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HHF7LD7W","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HHF7LD7W2AQOC2RY6XN7AIMPSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-01-25T13:07:59Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"4bb690e81b7eac9f1588a56bcfa7769eb8572b01da39209801ec206d267b7e1c","abstract_canon_sha256":"9494804bd4f34fe8fc4fe27779c68dde75ee8a66b4d46f7320ee2c41647278ec"},"schema_version":"1.0"},"canonical_sha256":"39cbf58ff6d020e16a38f5dbf0218f926c0245081cc7ff47e3c9b560e87224fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:37.848615Z","signature_b64":"nJVOCBAJvZhB/AlO/Aj1rUHaLdfKsD4vtvsFRFRUFOqsZ7Vi3T99IuZHX2X4opr+okD8Fx0iab2dAKhW5o5ZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39cbf58ff6d020e16a38f5dbf0218f926c0245081cc7ff47e3c9b560e87224fe","last_reissued_at":"2026-05-18T03:29:37.847817Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:37.847817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4803","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":"2026-05-18T03:29:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1kk+poazJjRQWHXYFKNc7+MysGQv7ZRcYMpZuSkhKtvWZIoI7CIAkfkyGCPdO4sjuShmJasxpyuJT76kywkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:20:43.306750Z"},"content_sha256":"2d9f0a344641fe37b40815083eb6cf5119b6f94c4d6c37ce6669adf0ced38231","schema_version":"1.0","event_id":"sha256:2d9f0a344641fe37b40815083eb6cf5119b6f94c4d6c37ce6669adf0ced38231"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HHF7LD7W2AQOC2RY6XN7AIMPSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lifting defects for nonstable K_0-theory of exchange rings and C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.OA","authors_text":"Friedrich Wehrung (LMNO)","submitted_at":"2011-01-25T13:07:59Z","abstract_excerpt":"The assignment (nonstable K_0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: (1) There is no functor F, from simplicial monoids with order-unit with normalized positive homomorphisms to exchange rings, such that VF is equivalent to the identity. (2) There is no functor F, from simplicial monoids with order-unit with normalized positive embeddings to C*-algebras of real rank 0 (resp.,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4803","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":"2026-05-18T03:29:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kb7G9a6MS0sLyT37TG9J+EeBfomqClK746dJ+yJO+Gn83Hrtms3GsLNSnQfYB+gM818e+CNljCZhqXvGLSp/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:20:43.307432Z"},"content_sha256":"ae630b397576b2d62caf8e9bebc1f9efe70d2c4a7c61a2b29eb2eab44f9be235","schema_version":"1.0","event_id":"sha256:ae630b397576b2d62caf8e9bebc1f9efe70d2c4a7c61a2b29eb2eab44f9be235"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HHF7LD7W2AQOC2RY6XN7AIMPSJ/bundle.json","state_url":"https://pith.science/pith/HHF7LD7W2AQOC2RY6XN7AIMPSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HHF7LD7W2AQOC2RY6XN7AIMPSJ/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":"2026-05-26T20:20:43Z","links":{"resolver":"https://pith.science/pith/HHF7LD7W2AQOC2RY6XN7AIMPSJ","bundle":"https://pith.science/pith/HHF7LD7W2AQOC2RY6XN7AIMPSJ/bundle.json","state":"https://pith.science/pith/HHF7LD7W2AQOC2RY6XN7AIMPSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HHF7LD7W2AQOC2RY6XN7AIMPSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HHF7LD7W2AQOC2RY6XN7AIMPSJ","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":"9494804bd4f34fe8fc4fe27779c68dde75ee8a66b4d46f7320ee2c41647278ec","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-01-25T13:07:59Z","title_canon_sha256":"4bb690e81b7eac9f1588a56bcfa7769eb8572b01da39209801ec206d267b7e1c"},"schema_version":"1.0","source":{"id":"1101.4803","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4803","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4803v2","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4803","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"HHF7LD7W2AQO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HHF7LD7W2AQOC2RY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HHF7LD7W","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:ae630b397576b2d62caf8e9bebc1f9efe70d2c4a7c61a2b29eb2eab44f9be235","target":"graph","created_at":"2026-05-18T03:29:37Z","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":"The assignment (nonstable K_0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: (1) There is no functor F, from simplicial monoids with order-unit with normalized positive homomorphisms to exchange rings, such that VF is equivalent to the identity. (2) There is no functor F, from simplicial monoids with order-unit with normalized positive embeddings to C*-algebras of real rank 0 (resp.,","authors_text":"Friedrich Wehrung (LMNO)","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-01-25T13:07:59Z","title":"Lifting defects for nonstable K_0-theory of exchange rings and C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4803","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":"sha256:2d9f0a344641fe37b40815083eb6cf5119b6f94c4d6c37ce6669adf0ced38231","target":"record","created_at":"2026-05-18T03:29:37Z","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":"9494804bd4f34fe8fc4fe27779c68dde75ee8a66b4d46f7320ee2c41647278ec","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-01-25T13:07:59Z","title_canon_sha256":"4bb690e81b7eac9f1588a56bcfa7769eb8572b01da39209801ec206d267b7e1c"},"schema_version":"1.0","source":{"id":"1101.4803","kind":"arxiv","version":2}},"canonical_sha256":"39cbf58ff6d020e16a38f5dbf0218f926c0245081cc7ff47e3c9b560e87224fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39cbf58ff6d020e16a38f5dbf0218f926c0245081cc7ff47e3c9b560e87224fe","first_computed_at":"2026-05-18T03:29:37.847817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:37.847817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nJVOCBAJvZhB/AlO/Aj1rUHaLdfKsD4vtvsFRFRUFOqsZ7Vi3T99IuZHX2X4opr+okD8Fx0iab2dAKhW5o5ZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:37.848615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4803","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d9f0a344641fe37b40815083eb6cf5119b6f94c4d6c37ce6669adf0ced38231","sha256:ae630b397576b2d62caf8e9bebc1f9efe70d2c4a7c61a2b29eb2eab44f9be235"],"state_sha256":"d781574b09bd4eedb6c2635d9def965663d7af3cf578d37eeb62a5f85d68d112"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x8/BsTBdrUVIXqhAfqUr4dwYX0s+zZZNnp3JQaTeyccvqX7pR9hU1bjeHpmRYeSpbgNJjDr3LVrgYp+Vt2gkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:20:43.310677Z","bundle_sha256":"0ed488359a76cb58e7df640788507a35419fa14fba46735a3aa159da49214370"}}