{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FHEL6PBWUOGBFCFZMJOM3MML3W","short_pith_number":"pith:FHEL6PBW","canonical_record":{"source":{"id":"1008.5063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-30T12:03:30Z","cross_cats_sorted":[],"title_canon_sha256":"6b7b74f54ae79ec92d1dfec0254f14dd249879e82ff864f9653feda05d220f74","abstract_canon_sha256":"80e62b32f90374e8371100c4d41fc27a07c6be457eefb646b1c8e0633bec2f0f"},"schema_version":"1.0"},"canonical_sha256":"29c8bf3c36a38c1288b9625ccdb18bdda078b6fc8d60c0c578407f432ad69e37","source":{"kind":"arxiv","id":"1008.5063","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.5063","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"1008.5063v2","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.5063","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"FHEL6PBWUOGB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FHEL6PBWUOGBFCFZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FHEL6PBW","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FHEL6PBWUOGBFCFZMJOM3MML3W","target":"record","payload":{"canonical_record":{"source":{"id":"1008.5063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-30T12:03:30Z","cross_cats_sorted":[],"title_canon_sha256":"6b7b74f54ae79ec92d1dfec0254f14dd249879e82ff864f9653feda05d220f74","abstract_canon_sha256":"80e62b32f90374e8371100c4d41fc27a07c6be457eefb646b1c8e0633bec2f0f"},"schema_version":"1.0"},"canonical_sha256":"29c8bf3c36a38c1288b9625ccdb18bdda078b6fc8d60c0c578407f432ad69e37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:06.787570Z","signature_b64":"9uCsJjfKqfGdD3vL9dsdqrpbd9+Mm653arMMN7pirxlQpwsnl2aZE4Fc78dcf1A/xbOu4FzIvtBcUcbC9doUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29c8bf3c36a38c1288b9625ccdb18bdda078b6fc8d60c0c578407f432ad69e37","last_reissued_at":"2026-05-18T04:27:06.786942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:06.786942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.5063","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":"2026-05-18T04:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2AhW9XYLKVAp0fhsPUZF0Iy6yoIwtUmA+iP6MOEbZ1TK0NARzj6dCRYCPu9DV257DtWUsVJdg1DcVI+kX5p5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T17:52:26.400806Z"},"content_sha256":"1e1e8ccbd4cba2c5c7e1fee9881fcd72a2845d7660483b4153822bdc942b7f72","schema_version":"1.0","event_id":"sha256:1e1e8ccbd4cba2c5c7e1fee9881fcd72a2845d7660483b4153822bdc942b7f72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FHEL6PBWUOGBFCFZMJOM3MML3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the pre-lambda ring structure on the Grothendieck ring of stacks and the power structures over it","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Melle Hernandez, I. Luengo, S.M. Gusein-Zade","submitted_at":"2010-08-30T12:03:30Z","abstract_excerpt":"In this note we discuss a generalization (\"extension\") of the pre-lambda structure on the Grothendieck ring of quasi-projective varieties and of the corresponding power structure over it to the Grothendieck ring of stacks, discuss some of their properties and give some explicit formulae for the Kapranov zeta function for some stacks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.5063","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":"2026-05-18T04:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F72fvf2A74leidPEQa8VaUiik9bGEYXz2oqJoAr71MLVHuhMgMt3vRo78MBjVHrrFMl5RmK+5biLdRG1OlnkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T17:52:26.401146Z"},"content_sha256":"7e8507874a6e660cf866d392e6a3e09d5feaa68f67377334b60c5a0c06350660","schema_version":"1.0","event_id":"sha256:7e8507874a6e660cf866d392e6a3e09d5feaa68f67377334b60c5a0c06350660"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHEL6PBWUOGBFCFZMJOM3MML3W/bundle.json","state_url":"https://pith.science/pith/FHEL6PBWUOGBFCFZMJOM3MML3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHEL6PBWUOGBFCFZMJOM3MML3W/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":"2026-07-02T17:52:26Z","links":{"resolver":"https://pith.science/pith/FHEL6PBWUOGBFCFZMJOM3MML3W","bundle":"https://pith.science/pith/FHEL6PBWUOGBFCFZMJOM3MML3W/bundle.json","state":"https://pith.science/pith/FHEL6PBWUOGBFCFZMJOM3MML3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHEL6PBWUOGBFCFZMJOM3MML3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FHEL6PBWUOGBFCFZMJOM3MML3W","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":"80e62b32f90374e8371100c4d41fc27a07c6be457eefb646b1c8e0633bec2f0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-30T12:03:30Z","title_canon_sha256":"6b7b74f54ae79ec92d1dfec0254f14dd249879e82ff864f9653feda05d220f74"},"schema_version":"1.0","source":{"id":"1008.5063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.5063","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"1008.5063v2","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.5063","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"FHEL6PBWUOGB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FHEL6PBWUOGBFCFZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FHEL6PBW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:7e8507874a6e660cf866d392e6a3e09d5feaa68f67377334b60c5a0c06350660","target":"graph","created_at":"2026-05-18T04:27:06Z","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":"In this note we discuss a generalization (\"extension\") of the pre-lambda structure on the Grothendieck ring of quasi-projective varieties and of the corresponding power structure over it to the Grothendieck ring of stacks, discuss some of their properties and give some explicit formulae for the Kapranov zeta function for some stacks.","authors_text":"A. Melle Hernandez, I. Luengo, S.M. Gusein-Zade","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-30T12:03:30Z","title":"On the pre-lambda ring structure on the Grothendieck ring of stacks and the power structures over it"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.5063","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":"sha256:1e1e8ccbd4cba2c5c7e1fee9881fcd72a2845d7660483b4153822bdc942b7f72","target":"record","created_at":"2026-05-18T04:27:06Z","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":"80e62b32f90374e8371100c4d41fc27a07c6be457eefb646b1c8e0633bec2f0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-30T12:03:30Z","title_canon_sha256":"6b7b74f54ae79ec92d1dfec0254f14dd249879e82ff864f9653feda05d220f74"},"schema_version":"1.0","source":{"id":"1008.5063","kind":"arxiv","version":2}},"canonical_sha256":"29c8bf3c36a38c1288b9625ccdb18bdda078b6fc8d60c0c578407f432ad69e37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29c8bf3c36a38c1288b9625ccdb18bdda078b6fc8d60c0c578407f432ad69e37","first_computed_at":"2026-05-18T04:27:06.786942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:06.786942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9uCsJjfKqfGdD3vL9dsdqrpbd9+Mm653arMMN7pirxlQpwsnl2aZE4Fc78dcf1A/xbOu4FzIvtBcUcbC9doUCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:06.787570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.5063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e1e8ccbd4cba2c5c7e1fee9881fcd72a2845d7660483b4153822bdc942b7f72","sha256:7e8507874a6e660cf866d392e6a3e09d5feaa68f67377334b60c5a0c06350660"],"state_sha256":"dd9b8064ac0b32c59d410277b35c96cdca598a9ba622a3a49f0bd6759663b0c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pD4NTleIzNPTCElzbNUzOuKRhiKfFERde3/gza4BX1Il2UKt+nmxYXT9NfGKpXaYZskZWjF7XvMq+3bi78tXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T17:52:26.403134Z","bundle_sha256":"e4fb744131e0bda5a1f3fe8115cb850ece92bcd94ac86879dc18ce370c2aa3e7"}}