{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:PCGLT6HNDMZSTVRPQYXWCC5PIY","short_pith_number":"pith:PCGLT6HN","canonical_record":{"source":{"id":"0906.3109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-17T08:42:18Z","cross_cats_sorted":[],"title_canon_sha256":"27a38f6989e09ee9f1633f1169461fe39f79140b595a71887845c2dd7a682c88","abstract_canon_sha256":"a7781891f005d28bc63b4b0e81a0cf970ba5392b3052329d152b906bd9694657"},"schema_version":"1.0"},"canonical_sha256":"788cb9f8ed1b3329d62f862f610baf462ea02013dc6b9dd68753831f12eedc26","source":{"kind":"arxiv","id":"0906.3109","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3109","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3109v2","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3109","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"PCGLT6HNDMZS","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PCGLT6HNDMZSTVRP","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PCGLT6HN","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:PCGLT6HNDMZSTVRPQYXWCC5PIY","target":"record","payload":{"canonical_record":{"source":{"id":"0906.3109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-17T08:42:18Z","cross_cats_sorted":[],"title_canon_sha256":"27a38f6989e09ee9f1633f1169461fe39f79140b595a71887845c2dd7a682c88","abstract_canon_sha256":"a7781891f005d28bc63b4b0e81a0cf970ba5392b3052329d152b906bd9694657"},"schema_version":"1.0"},"canonical_sha256":"788cb9f8ed1b3329d62f862f610baf462ea02013dc6b9dd68753831f12eedc26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:12.821484Z","signature_b64":"ke97vNJ1njmuRVJ+5HFJFCQ+7enc8wFeG+ZskPS+EqGjXghgqfS+zUNacPBasa0Sp38nqA7RcbMUhxnjaCUPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"788cb9f8ed1b3329d62f862f610baf462ea02013dc6b9dd68753831f12eedc26","last_reissued_at":"2026-05-18T00:56:12.820826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:12.820826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.3109","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":"2026-05-18T00:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElJiNwaLtuGXQA/p9G4nHTXu0L3XqUQjQCJk5PER4iH/Twk6oLh45zSFgXyOvjGio4uQReiiZIOhHL3efT5OAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:05:04.969559Z"},"content_sha256":"eae0bf863b23b259c1b2fa37c9900dd8fcdc2ff5454582003392c91b9197fde6","schema_version":"1.0","event_id":"sha256:eae0bf863b23b259c1b2fa37c9900dd8fcdc2ff5454582003392c91b9197fde6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:PCGLT6HNDMZSTVRPQYXWCC5PIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant K-theory and Higher Chow Groups of Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amalendu Krishna","submitted_at":"2009-06-17T08:42:18Z","abstract_excerpt":"For a smooth quasi-projective scheme $X$ over a field $k$ with an action of a reductive group, we establish a spectral sequence connecting the equivariant and the ordinary higher Chow groups of $X$. For $X$ smooth and projective, we show that this spectral sequence degenerates, leading to an explicit relation between the equivariant and the ordinary higher Chow groups. We obtain several applications to algebraic $K$-theory.\n  We show that for a reductive group $G$ acting on a smooth projective scheme $X$, the forgetful map $K^G_i(X) \\to K_i(X)$ induces an isomorphism $K^G_i(X)/{I_G K^G_i(X)} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3109","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":"2026-05-18T00:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rw7niweGgWVki6pGWrqJSLQgDu2lZ1TUxDnZzu0bFy6WS73afXWeFIOATpWMGQUY7k/8yVrGwDgnOfWyaHOzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:05:04.969906Z"},"content_sha256":"47d8a325b77d60ea2660fe883b7524b339c20c71d59660aae27933419933b526","schema_version":"1.0","event_id":"sha256:47d8a325b77d60ea2660fe883b7524b339c20c71d59660aae27933419933b526"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCGLT6HNDMZSTVRPQYXWCC5PIY/bundle.json","state_url":"https://pith.science/pith/PCGLT6HNDMZSTVRPQYXWCC5PIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCGLT6HNDMZSTVRPQYXWCC5PIY/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":"2026-06-21T22:05:04Z","links":{"resolver":"https://pith.science/pith/PCGLT6HNDMZSTVRPQYXWCC5PIY","bundle":"https://pith.science/pith/PCGLT6HNDMZSTVRPQYXWCC5PIY/bundle.json","state":"https://pith.science/pith/PCGLT6HNDMZSTVRPQYXWCC5PIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCGLT6HNDMZSTVRPQYXWCC5PIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PCGLT6HNDMZSTVRPQYXWCC5PIY","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":"a7781891f005d28bc63b4b0e81a0cf970ba5392b3052329d152b906bd9694657","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-17T08:42:18Z","title_canon_sha256":"27a38f6989e09ee9f1633f1169461fe39f79140b595a71887845c2dd7a682c88"},"schema_version":"1.0","source":{"id":"0906.3109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3109","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3109v2","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3109","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"PCGLT6HNDMZS","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PCGLT6HNDMZSTVRP","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PCGLT6HN","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:47d8a325b77d60ea2660fe883b7524b339c20c71d59660aae27933419933b526","target":"graph","created_at":"2026-05-18T00:56:12Z","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":"For a smooth quasi-projective scheme $X$ over a field $k$ with an action of a reductive group, we establish a spectral sequence connecting the equivariant and the ordinary higher Chow groups of $X$. For $X$ smooth and projective, we show that this spectral sequence degenerates, leading to an explicit relation between the equivariant and the ordinary higher Chow groups. We obtain several applications to algebraic $K$-theory.\n  We show that for a reductive group $G$ acting on a smooth projective scheme $X$, the forgetful map $K^G_i(X) \\to K_i(X)$ induces an isomorphism $K^G_i(X)/{I_G K^G_i(X)} \\","authors_text":"Amalendu Krishna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-17T08:42:18Z","title":"Equivariant K-theory and Higher Chow Groups of Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3109","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:eae0bf863b23b259c1b2fa37c9900dd8fcdc2ff5454582003392c91b9197fde6","target":"record","created_at":"2026-05-18T00:56:12Z","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":"a7781891f005d28bc63b4b0e81a0cf970ba5392b3052329d152b906bd9694657","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-17T08:42:18Z","title_canon_sha256":"27a38f6989e09ee9f1633f1169461fe39f79140b595a71887845c2dd7a682c88"},"schema_version":"1.0","source":{"id":"0906.3109","kind":"arxiv","version":2}},"canonical_sha256":"788cb9f8ed1b3329d62f862f610baf462ea02013dc6b9dd68753831f12eedc26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"788cb9f8ed1b3329d62f862f610baf462ea02013dc6b9dd68753831f12eedc26","first_computed_at":"2026-05-18T00:56:12.820826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:12.820826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ke97vNJ1njmuRVJ+5HFJFCQ+7enc8wFeG+ZskPS+EqGjXghgqfS+zUNacPBasa0Sp38nqA7RcbMUhxnjaCUPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:12.821484Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.3109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eae0bf863b23b259c1b2fa37c9900dd8fcdc2ff5454582003392c91b9197fde6","sha256:47d8a325b77d60ea2660fe883b7524b339c20c71d59660aae27933419933b526"],"state_sha256":"74bc67c0201aa7187b76c482648063850dfed99c7a2f15d25036e15cbb329078"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sw+367C8hDD6JAQgbOBulFkFEu+JE4bTtbcZMH1s7PEmWd3ilPKMyAB8gyd1rkyWQsdpb8T+zhnBwTrQ9IjqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:05:04.971865Z","bundle_sha256":"9a12f9cbbb58b076f3cf02df134c0ca7dc78cabba25e2b015c03ad137e12eaa6"}}