{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:RNUCUY5NQQMO5YLDUAXI5FX6TM","short_pith_number":"pith:RNUCUY5N","canonical_record":{"source":{"id":"0912.0563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-03T01:30:18Z","cross_cats_sorted":[],"title_canon_sha256":"946c707c497d17563c1553ba5c6321596f36ac4b6e78525ab96d5df2f5a4bc66","abstract_canon_sha256":"ff18af58089f69c6d11994794b3ba502a3a2251eb53398bdffd81b92507bb2c6"},"schema_version":"1.0"},"canonical_sha256":"8b682a63ad8418eee163a02e8e96fe9b02e3d807b4488ae3e77d689b197e8014","source":{"kind":"arxiv","id":"0912.0563","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0563","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0563v2","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0563","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"pith_short_12","alias_value":"RNUCUY5NQQMO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RNUCUY5NQQMO5YLD","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RNUCUY5N","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:RNUCUY5NQQMO5YLDUAXI5FX6TM","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-03T01:30:18Z","cross_cats_sorted":[],"title_canon_sha256":"946c707c497d17563c1553ba5c6321596f36ac4b6e78525ab96d5df2f5a4bc66","abstract_canon_sha256":"ff18af58089f69c6d11994794b3ba502a3a2251eb53398bdffd81b92507bb2c6"},"schema_version":"1.0"},"canonical_sha256":"8b682a63ad8418eee163a02e8e96fe9b02e3d807b4488ae3e77d689b197e8014","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:48.573703Z","signature_b64":"M2kBjML1TRBJVrgmgurVfky6LqVJDCzqslsDNml8477Knh12hOMRBF+ZcbzgFpzCTwwLFfcQ8awh+Rr26RFDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b682a63ad8418eee163a02e8e96fe9b02e3d807b4488ae3e77d689b197e8014","last_reissued_at":"2026-05-18T04:38:48.573170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:48.573170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0563","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":"2026-05-18T04:38:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CrJilSMc6s3ZfAa4bDsvUa2o2usxFgonXpdAmhfIwzIc/nWaFkbSMMc9Quv1IgrYMHMbUxURWiSvDW85qi0IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T15:20:41.944131Z"},"content_sha256":"d1c48a26c9b192025410e7d80962855f90574fe11b5a7647d6f49ee025d3543b","schema_version":"1.0","event_id":"sha256:d1c48a26c9b192025410e7d80962855f90574fe11b5a7647d6f49ee025d3543b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:RNUCUY5NQQMO5YLDUAXI5FX6TM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Additive invariants of actions of additive and multiplicative groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Wenchuan Hu","submitted_at":"2009-12-03T01:30:18Z","abstract_excerpt":"The additive invariants of an algebraic variety is calculated in terms of those of the fixed point set under the action of additive and multiplicative groups, by using Bialynicki-Birula's fixed point formula for a projective algebraicset with a G_m-action or G_a-action.\n  The method is also generalized to calculate certain additive invariants for Chow varieties. As applications, we obtain the Hodge polynomial of Chow varieties in characteristic zero and the number of points for Chow varieties over finite fields.\n  As applications, we obtain the l-adic Euler-Poincare characteristic for the Chow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0563","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":"2026-05-18T04:38:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOHxx8DWix4sq3Gbs5O2ZvhYLsbSKOpVVuNhtYMB2f/UWOUlFWpQUNlYg7lagIa+3SQWObcedGW7/Tf1iqlkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T15:20:41.944610Z"},"content_sha256":"84cc89595dce2ee6733f95a4d1d6fce77eae873c02482a60ede51b3830bf0ea4","schema_version":"1.0","event_id":"sha256:84cc89595dce2ee6733f95a4d1d6fce77eae873c02482a60ede51b3830bf0ea4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RNUCUY5NQQMO5YLDUAXI5FX6TM/bundle.json","state_url":"https://pith.science/pith/RNUCUY5NQQMO5YLDUAXI5FX6TM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RNUCUY5NQQMO5YLDUAXI5FX6TM/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":"2026-08-19T15:20:41Z","links":{"resolver":"https://pith.science/pith/RNUCUY5NQQMO5YLDUAXI5FX6TM","bundle":"https://pith.science/pith/RNUCUY5NQQMO5YLDUAXI5FX6TM/bundle.json","state":"https://pith.science/pith/RNUCUY5NQQMO5YLDUAXI5FX6TM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RNUCUY5NQQMO5YLDUAXI5FX6TM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RNUCUY5NQQMO5YLDUAXI5FX6TM","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":"ff18af58089f69c6d11994794b3ba502a3a2251eb53398bdffd81b92507bb2c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-03T01:30:18Z","title_canon_sha256":"946c707c497d17563c1553ba5c6321596f36ac4b6e78525ab96d5df2f5a4bc66"},"schema_version":"1.0","source":{"id":"0912.0563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0563","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0563v2","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0563","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"pith_short_12","alias_value":"RNUCUY5NQQMO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RNUCUY5NQQMO5YLD","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RNUCUY5N","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:84cc89595dce2ee6733f95a4d1d6fce77eae873c02482a60ede51b3830bf0ea4","target":"graph","created_at":"2026-05-18T04:38:48Z","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 additive invariants of an algebraic variety is calculated in terms of those of the fixed point set under the action of additive and multiplicative groups, by using Bialynicki-Birula's fixed point formula for a projective algebraicset with a G_m-action or G_a-action.\n  The method is also generalized to calculate certain additive invariants for Chow varieties. As applications, we obtain the Hodge polynomial of Chow varieties in characteristic zero and the number of points for Chow varieties over finite fields.\n  As applications, we obtain the l-adic Euler-Poincare characteristic for the Chow","authors_text":"Wenchuan Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-03T01:30:18Z","title":"On Additive invariants of actions of additive and multiplicative groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0563","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:d1c48a26c9b192025410e7d80962855f90574fe11b5a7647d6f49ee025d3543b","target":"record","created_at":"2026-05-18T04:38:48Z","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":"ff18af58089f69c6d11994794b3ba502a3a2251eb53398bdffd81b92507bb2c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-03T01:30:18Z","title_canon_sha256":"946c707c497d17563c1553ba5c6321596f36ac4b6e78525ab96d5df2f5a4bc66"},"schema_version":"1.0","source":{"id":"0912.0563","kind":"arxiv","version":2}},"canonical_sha256":"8b682a63ad8418eee163a02e8e96fe9b02e3d807b4488ae3e77d689b197e8014","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b682a63ad8418eee163a02e8e96fe9b02e3d807b4488ae3e77d689b197e8014","first_computed_at":"2026-05-18T04:38:48.573170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:48.573170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2kBjML1TRBJVrgmgurVfky6LqVJDCzqslsDNml8477Knh12hOMRBF+ZcbzgFpzCTwwLFfcQ8awh+Rr26RFDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:48.573703Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1c48a26c9b192025410e7d80962855f90574fe11b5a7647d6f49ee025d3543b","sha256:84cc89595dce2ee6733f95a4d1d6fce77eae873c02482a60ede51b3830bf0ea4"],"state_sha256":"15cf36b3bcc11b431cd63f7d19e89d62a50f26bed4fa989c3a266aab4c44a00d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SlKOkflXUwPNlF7jCs8s+xEToskHMmFxv9VDSfpTVdOXQ6iBIc0mmeaxboQ2PBvQVs8ymggsm6KEnImsARo6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T15:20:41.948805Z","bundle_sha256":"32f3594678b2ca6c67b9df9c756d23fbb89bbe23f84388d83c9fd4687d1d1407"}}