{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FGTBW6BLZ3HBXX77JRW3MZXSVY","short_pith_number":"pith:FGTBW6BL","schema_version":"1.0","canonical_sha256":"29a61b782bcece1bdfff4c6db666f2ae36571ff56db43c92b37a5b5f8020d6a2","source":{"kind":"arxiv","id":"1609.08452","version":2},"attestation_state":"computed","paper":{"title":"Power structure over the Grothendieck ring of maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alejandro Melle-Hern\\'andez, Ignacio Luengo, Sabir M. Gusein-Zade","submitted_at":"2016-09-27T14:03:30Z","abstract_excerpt":"A power structure over a ring is a method to give sense to expressions of the form $(1+a_1t+a_2t^2+\\ldots)^m$, where $a_i$, $i=1, 2,\\ldots$, and $m$ are elements of the ring. The (natural) power structure over the Grothendieck ring of complex quasi-projective varieties appeared to be useful for a number of applications. We discuss new examples of $\\lambda$- and power structures over some Grothendieck rings of varieties. The main example is for the Grothendieck ring of maps of complex quasi-projective varieties. We describe two natural $\\lambda$-structures on it which lead to the same power str"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.08452","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-27T14:03:30Z","cross_cats_sorted":[],"title_canon_sha256":"dff964211dd23373c9af31fdb7b62dacdff4ba0940391b994a9d7c32846047e1","abstract_canon_sha256":"146fd21ba7df87b207e3b9a7380695a3c88d99872ee9cee370677f6ea86c0fe8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:15.873513Z","signature_b64":"+/csPKboBbFBAmM9/HFR/QyYJ90a687QKuEhY5+OVu+HMqUeHiM3VJgGlwVIFvLCXHCi/6GXHJI0stHlJ8+YDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29a61b782bcece1bdfff4c6db666f2ae36571ff56db43c92b37a5b5f8020d6a2","last_reissued_at":"2026-05-18T00:44:15.872990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:15.872990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Power structure over the Grothendieck ring of maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alejandro Melle-Hern\\'andez, Ignacio Luengo, Sabir M. Gusein-Zade","submitted_at":"2016-09-27T14:03:30Z","abstract_excerpt":"A power structure over a ring is a method to give sense to expressions of the form $(1+a_1t+a_2t^2+\\ldots)^m$, where $a_i$, $i=1, 2,\\ldots$, and $m$ are elements of the ring. The (natural) power structure over the Grothendieck ring of complex quasi-projective varieties appeared to be useful for a number of applications. We discuss new examples of $\\lambda$- and power structures over some Grothendieck rings of varieties. The main example is for the Grothendieck ring of maps of complex quasi-projective varieties. We describe two natural $\\lambda$-structures on it which lead to the same power str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08452","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.08452","created_at":"2026-05-18T00:44:15.873080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.08452v2","created_at":"2026-05-18T00:44:15.873080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08452","created_at":"2026-05-18T00:44:15.873080+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGTBW6BLZ3HB","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGTBW6BLZ3HBXX77","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGTBW6BL","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY","json":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY.json","graph_json":"https://pith.science/api/pith-number/FGTBW6BLZ3HBXX77JRW3MZXSVY/graph.json","events_json":"https://pith.science/api/pith-number/FGTBW6BLZ3HBXX77JRW3MZXSVY/events.json","paper":"https://pith.science/paper/FGTBW6BL"},"agent_actions":{"view_html":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY","download_json":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY.json","view_paper":"https://pith.science/paper/FGTBW6BL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.08452&json=true","fetch_graph":"https://pith.science/api/pith-number/FGTBW6BLZ3HBXX77JRW3MZXSVY/graph.json","fetch_events":"https://pith.science/api/pith-number/FGTBW6BLZ3HBXX77JRW3MZXSVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY/action/storage_attestation","attest_author":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY/action/author_attestation","sign_citation":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY/action/citation_signature","submit_replication":"https://pith.science/pith/FGTBW6BLZ3HBXX77JRW3MZXSVY/action/replication_record"}},"created_at":"2026-05-18T00:44:15.873080+00:00","updated_at":"2026-05-18T00:44:15.873080+00:00"}