{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:P2PXQ3VRPQCNDZFKQGAAPUKIBD","short_pith_number":"pith:P2PXQ3VR","canonical_record":{"source":{"id":"1503.08742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-30T17:03:27Z","cross_cats_sorted":[],"title_canon_sha256":"5c1f1f189d03ddc614fc64e6f1d4cfb4f688fbac7f6b16dcf51a33662a4064ba","abstract_canon_sha256":"a048be411e16c04f09ad598847b14caab9f7a7449ba734d40b06c60443ab62e2"},"schema_version":"1.0"},"canonical_sha256":"7e9f786eb17c04d1e4aa818007d14808fe18491fda74e4777dd757173b75e242","source":{"kind":"arxiv","id":"1503.08742","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08742","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08742v2","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08742","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"P2PXQ3VRPQCN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P2PXQ3VRPQCNDZFK","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P2PXQ3VR","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:P2PXQ3VRPQCNDZFKQGAAPUKIBD","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-30T17:03:27Z","cross_cats_sorted":[],"title_canon_sha256":"5c1f1f189d03ddc614fc64e6f1d4cfb4f688fbac7f6b16dcf51a33662a4064ba","abstract_canon_sha256":"a048be411e16c04f09ad598847b14caab9f7a7449ba734d40b06c60443ab62e2"},"schema_version":"1.0"},"canonical_sha256":"7e9f786eb17c04d1e4aa818007d14808fe18491fda74e4777dd757173b75e242","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:27.420888Z","signature_b64":"X63BIcj66ramNbe2AgmCAogh2uIJhUgxGx2V5T6vGcwSvi0aC6Y0/0rRYw3H92fpSvC10GD2hMG1FfHPZ9bAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e9f786eb17c04d1e4aa818007d14808fe18491fda74e4777dd757173b75e242","last_reissued_at":"2026-05-18T00:17:27.420173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:27.420173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08742","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":"2026-05-18T00:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WRfGdbbpmf+i/AsOp92CfMHqbS11+RsaKEmnqm8kVH62qSAY01sOjdWKaH1UpKCcBTGi9SfXU5tYl1sGNITDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:43:17.002167Z"},"content_sha256":"7eb8ffbfa470c692789c223d4c89492b18325396c013d86b40469fcc7e0ebf83","schema_version":"1.0","event_id":"sha256:7eb8ffbfa470c692789c223d4c89492b18325396c013d86b40469fcc7e0ebf83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:P2PXQ3VRPQCNDZFKQGAAPUKIBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity theorems for K- and H-cohomology and other functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Uwe Jannsen","submitted_at":"2015-03-30T17:03:27Z","abstract_excerpt":"Suslin proved that for an extension K/k of algebraically closed fields the induced maps K_m(k)[n] --> K_m(K)[n] and K_m(k)/n ---> K_m(K)/n for the higher K-groups are isomorphisms, where A[n] is the subgroup of n-torsion in an abelien group, and A/n = A/nA, by definition. In this paper we generalize this to other functors and other field extensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08742","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":"2026-05-18T00:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDAIUXCXMonmm9bMxx7K2rydSyuqQkZXS17BebcdQYHdSi9931pMigazkaiB75n4th/waapXzZYkeRJKIP5zBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:43:17.002525Z"},"content_sha256":"b8e27a36297f5634bdeab486ffe0eda310c66102daeacfe5b629f32d97a280a3","schema_version":"1.0","event_id":"sha256:b8e27a36297f5634bdeab486ffe0eda310c66102daeacfe5b629f32d97a280a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2PXQ3VRPQCNDZFKQGAAPUKIBD/bundle.json","state_url":"https://pith.science/pith/P2PXQ3VRPQCNDZFKQGAAPUKIBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2PXQ3VRPQCNDZFKQGAAPUKIBD/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":"2026-06-24T18:43:17Z","links":{"resolver":"https://pith.science/pith/P2PXQ3VRPQCNDZFKQGAAPUKIBD","bundle":"https://pith.science/pith/P2PXQ3VRPQCNDZFKQGAAPUKIBD/bundle.json","state":"https://pith.science/pith/P2PXQ3VRPQCNDZFKQGAAPUKIBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2PXQ3VRPQCNDZFKQGAAPUKIBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P2PXQ3VRPQCNDZFKQGAAPUKIBD","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":"a048be411e16c04f09ad598847b14caab9f7a7449ba734d40b06c60443ab62e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-30T17:03:27Z","title_canon_sha256":"5c1f1f189d03ddc614fc64e6f1d4cfb4f688fbac7f6b16dcf51a33662a4064ba"},"schema_version":"1.0","source":{"id":"1503.08742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08742","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08742v2","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08742","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"P2PXQ3VRPQCN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P2PXQ3VRPQCNDZFK","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P2PXQ3VR","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:b8e27a36297f5634bdeab486ffe0eda310c66102daeacfe5b629f32d97a280a3","target":"graph","created_at":"2026-05-18T00:17:27Z","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":"Suslin proved that for an extension K/k of algebraically closed fields the induced maps K_m(k)[n] --> K_m(K)[n] and K_m(k)/n ---> K_m(K)/n for the higher K-groups are isomorphisms, where A[n] is the subgroup of n-torsion in an abelien group, and A/n = A/nA, by definition. In this paper we generalize this to other functors and other field extensions.","authors_text":"Uwe Jannsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-30T17:03:27Z","title":"Rigidity theorems for K- and H-cohomology and other functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08742","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":"sha256:7eb8ffbfa470c692789c223d4c89492b18325396c013d86b40469fcc7e0ebf83","target":"record","created_at":"2026-05-18T00:17:27Z","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":"a048be411e16c04f09ad598847b14caab9f7a7449ba734d40b06c60443ab62e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-30T17:03:27Z","title_canon_sha256":"5c1f1f189d03ddc614fc64e6f1d4cfb4f688fbac7f6b16dcf51a33662a4064ba"},"schema_version":"1.0","source":{"id":"1503.08742","kind":"arxiv","version":2}},"canonical_sha256":"7e9f786eb17c04d1e4aa818007d14808fe18491fda74e4777dd757173b75e242","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e9f786eb17c04d1e4aa818007d14808fe18491fda74e4777dd757173b75e242","first_computed_at":"2026-05-18T00:17:27.420173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:27.420173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X63BIcj66ramNbe2AgmCAogh2uIJhUgxGx2V5T6vGcwSvi0aC6Y0/0rRYw3H92fpSvC10GD2hMG1FfHPZ9bAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:27.420888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7eb8ffbfa470c692789c223d4c89492b18325396c013d86b40469fcc7e0ebf83","sha256:b8e27a36297f5634bdeab486ffe0eda310c66102daeacfe5b629f32d97a280a3"],"state_sha256":"cf24077c7664aac03049cab2da2b10f64be208d50fcc298cf548ac53f9baa923"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGNne2gEORpSraHSCK7D2i7WUB+RMLLdV+HShWyQHGWVXg1b+2g/TSaYABeEtzM1VgTbo7H4f3MISj4K8CoMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:43:17.004389Z","bundle_sha256":"4c63247c2cdb49c9bbad36fdefe5d97c72680c40f9f6dc5f4a236ffed29d8764"}}