{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BPBR22OGGDIZHJQUP2GRFBXZGF","short_pith_number":"pith:BPBR22OG","canonical_record":{"source":{"id":"1505.02989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-12T13:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"072253375682e6fc829afd9d8e5d13cf28d636b06d4ba8da22080fc0a9cf1376","abstract_canon_sha256":"3d66bace6400462b468486500d975692a9fe1144952ca54ff0ffdeea976a2c2d"},"schema_version":"1.0"},"canonical_sha256":"0bc31d69c630d193a6147e8d1286f931609bbc2311a9515224c7acd4c678424c","source":{"kind":"arxiv","id":"1505.02989","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02989","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02989v1","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02989","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"BPBR22OGGDIZ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BPBR22OGGDIZHJQU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BPBR22OG","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BPBR22OGGDIZHJQUP2GRFBXZGF","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-12T13:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"072253375682e6fc829afd9d8e5d13cf28d636b06d4ba8da22080fc0a9cf1376","abstract_canon_sha256":"3d66bace6400462b468486500d975692a9fe1144952ca54ff0ffdeea976a2c2d"},"schema_version":"1.0"},"canonical_sha256":"0bc31d69c630d193a6147e8d1286f931609bbc2311a9515224c7acd4c678424c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:15.370770Z","signature_b64":"f+3bCg25NwvIYPqm8wWF8N4m1LjWV/xoNbvnAjq5zwcQt0CEGos2GPPNxxCmyfgugl4b45zk99yUnkTDmHd+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bc31d69c630d193a6147e8d1286f931609bbc2311a9515224c7acd4c678424c","last_reissued_at":"2026-05-18T02:14:15.370022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:15.370022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02989","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XqDhBEsoAF0OgvCJsLfckDwUfrPjFwGdTdfMMKM5wQg6D2AhOmdOio9fb7DE9cSBmOG3loByg+Vv18f/fnh0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:31:57.745685Z"},"content_sha256":"59c0f5dbb9cb3614804ece05faf29a1cd1a032acd351073c4dbf62ffa00317d1","schema_version":"1.0","event_id":"sha256:59c0f5dbb9cb3614804ece05faf29a1cd1a032acd351073c4dbf62ffa00317d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BPBR22OGGDIZHJQUP2GRFBXZGF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Motivic classes of generalized Kummer schemes via relative power structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrew Morrison, Junliang Shen","submitted_at":"2015-05-12T13:03:00Z","abstract_excerpt":"We develop a power structure over the Grothendieck ring of varieties relative to an abelian monoid, which allows us to compute the motivic class of the generalized Kummer scheme. We obtain a generalized version of Cheah's formula for the Hilbert scheme of points, which specializes to Gulbrandsen's conjecture for Euler characteristics. Moreover, in the surface case we prove a conjecture of G\\\"{o}ttsche for geometrically ruled surfaces, and we obtain an explicit formula for the virtual motive of the generalized Kummer scheme in dimension three."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02989","kind":"arxiv","version":1},"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":"2026-05-18T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kh28QHfEBr66iJR8tSQHu1P8f+MnyAHN9dEWc9jSduX6OZ9FL/xBr9LG/ypP95TGM9fSQck4f9UlaL5jf6ObCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:31:57.746364Z"},"content_sha256":"e48f82aa0e02608b1dcb68717cb32d1a2dd0fba0df052cda8aee3ef465e12e76","schema_version":"1.0","event_id":"sha256:e48f82aa0e02608b1dcb68717cb32d1a2dd0fba0df052cda8aee3ef465e12e76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPBR22OGGDIZHJQUP2GRFBXZGF/bundle.json","state_url":"https://pith.science/pith/BPBR22OGGDIZHJQUP2GRFBXZGF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPBR22OGGDIZHJQUP2GRFBXZGF/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":"2026-05-26T08:31:57Z","links":{"resolver":"https://pith.science/pith/BPBR22OGGDIZHJQUP2GRFBXZGF","bundle":"https://pith.science/pith/BPBR22OGGDIZHJQUP2GRFBXZGF/bundle.json","state":"https://pith.science/pith/BPBR22OGGDIZHJQUP2GRFBXZGF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPBR22OGGDIZHJQUP2GRFBXZGF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BPBR22OGGDIZHJQUP2GRFBXZGF","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":"3d66bace6400462b468486500d975692a9fe1144952ca54ff0ffdeea976a2c2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-12T13:03:00Z","title_canon_sha256":"072253375682e6fc829afd9d8e5d13cf28d636b06d4ba8da22080fc0a9cf1376"},"schema_version":"1.0","source":{"id":"1505.02989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02989","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02989v1","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02989","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"BPBR22OGGDIZ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BPBR22OGGDIZHJQU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BPBR22OG","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:e48f82aa0e02608b1dcb68717cb32d1a2dd0fba0df052cda8aee3ef465e12e76","target":"graph","created_at":"2026-05-18T02:14:15Z","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":"We develop a power structure over the Grothendieck ring of varieties relative to an abelian monoid, which allows us to compute the motivic class of the generalized Kummer scheme. We obtain a generalized version of Cheah's formula for the Hilbert scheme of points, which specializes to Gulbrandsen's conjecture for Euler characteristics. Moreover, in the surface case we prove a conjecture of G\\\"{o}ttsche for geometrically ruled surfaces, and we obtain an explicit formula for the virtual motive of the generalized Kummer scheme in dimension three.","authors_text":"Andrew Morrison, Junliang Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-12T13:03:00Z","title":"Motivic classes of generalized Kummer schemes via relative power structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02989","kind":"arxiv","version":1},"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":"sha256:59c0f5dbb9cb3614804ece05faf29a1cd1a032acd351073c4dbf62ffa00317d1","target":"record","created_at":"2026-05-18T02:14:15Z","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":"3d66bace6400462b468486500d975692a9fe1144952ca54ff0ffdeea976a2c2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-12T13:03:00Z","title_canon_sha256":"072253375682e6fc829afd9d8e5d13cf28d636b06d4ba8da22080fc0a9cf1376"},"schema_version":"1.0","source":{"id":"1505.02989","kind":"arxiv","version":1}},"canonical_sha256":"0bc31d69c630d193a6147e8d1286f931609bbc2311a9515224c7acd4c678424c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bc31d69c630d193a6147e8d1286f931609bbc2311a9515224c7acd4c678424c","first_computed_at":"2026-05-18T02:14:15.370022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:15.370022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f+3bCg25NwvIYPqm8wWF8N4m1LjWV/xoNbvnAjq5zwcQt0CEGos2GPPNxxCmyfgugl4b45zk99yUnkTDmHd+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:15.370770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59c0f5dbb9cb3614804ece05faf29a1cd1a032acd351073c4dbf62ffa00317d1","sha256:e48f82aa0e02608b1dcb68717cb32d1a2dd0fba0df052cda8aee3ef465e12e76"],"state_sha256":"42950a760a27b682b347ed54b60c0372ad15652f40c3a0f6194a46d944d86007"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T4OPsg/Mp4IClm/BKhWhn+UmO5l4BghRzsx2K7sEiBHuKRIIyrMzj3mSzByPGyT7575YQDtO3d28BFfxM9BGCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:31:57.749973Z","bundle_sha256":"b5ee25081e0c01317a74f1f4ca182d0ac49a9d74b100f88da9a1889baaaf02bb"}}