{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:Y3T22HVMMWX6SMYSTZ7CJQFGTU","short_pith_number":"pith:Y3T22HVM","schema_version":"1.0","canonical_sha256":"c6e7ad1eac65afe933129e7e24c0a69d107606bb162a88bf2c1a9401f216172a","source":{"kind":"arxiv","id":"2102.07392","version":1},"attestation_state":"computed","paper":{"title":"Pluripotential theory for tropical toric varieties and non-archimedean Monge-Amp\\'ere equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Jos\\'e Ignacio Burgos Gil, Klaus K\\\"unnemann, Philipp Jell, Walter Gubler","submitted_at":"2021-02-15T08:24:15Z","abstract_excerpt":"Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions and a Bedford--Taylor product for Lagerberg currents on open subsets of a tropical toric variety. The resulting tropical toric pluripotential theory provides the link to give a canonical correspondence between complex and non-archimedean pluripotential theories of invariant plurisubharmonic functions on toric varieties. We will apply this correspondence to solve invariant non-archimedean Monge--Amp\\`ere equations on to"},"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":"2102.07392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-02-15T08:24:15Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d81cb6aec6f73be47d9c31aa085490e95e5d874cafadac3d9c69abd995649451","abstract_canon_sha256":"772b1e1ce5ac067da9014e6c97e40ba393c4c0640c67ee3e6b01608417e4d201"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:15:15.326060Z","signature_b64":"2cjQ7AyHFFoFVH2rsINaqQ50DvFmCXgombnVlnF0mkgHPXo8jY+W4PfFSVsL5199ya+3h/58mpQ1Ce6k51zNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e7ad1eac65afe933129e7e24c0a69d107606bb162a88bf2c1a9401f216172a","last_reissued_at":"2026-07-05T02:15:15.325638Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:15:15.325638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pluripotential theory for tropical toric varieties and non-archimedean Monge-Amp\\'ere equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Jos\\'e Ignacio Burgos Gil, Klaus K\\\"unnemann, Philipp Jell, Walter Gubler","submitted_at":"2021-02-15T08:24:15Z","abstract_excerpt":"Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions and a Bedford--Taylor product for Lagerberg currents on open subsets of a tropical toric variety. The resulting tropical toric pluripotential theory provides the link to give a canonical correspondence between complex and non-archimedean pluripotential theories of invariant plurisubharmonic functions on toric varieties. We will apply this correspondence to solve invariant non-archimedean Monge--Amp\\`ere equations on to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07392","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.07392/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2102.07392","created_at":"2026-07-05T02:15:15.325698+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.07392v1","created_at":"2026-07-05T02:15:15.325698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.07392","created_at":"2026-07-05T02:15:15.325698+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y3T22HVMMWX6","created_at":"2026-07-05T02:15:15.325698+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y3T22HVMMWX6SMYS","created_at":"2026-07-05T02:15:15.325698+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y3T22HVM","created_at":"2026-07-05T02:15:15.325698+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2409.00611","citing_title":"Abstract divisorial spaces and arithmetic intersection numbers","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU","json":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU.json","graph_json":"https://pith.science/api/pith-number/Y3T22HVMMWX6SMYSTZ7CJQFGTU/graph.json","events_json":"https://pith.science/api/pith-number/Y3T22HVMMWX6SMYSTZ7CJQFGTU/events.json","paper":"https://pith.science/paper/Y3T22HVM"},"agent_actions":{"view_html":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU","download_json":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU.json","view_paper":"https://pith.science/paper/Y3T22HVM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.07392&json=true","fetch_graph":"https://pith.science/api/pith-number/Y3T22HVMMWX6SMYSTZ7CJQFGTU/graph.json","fetch_events":"https://pith.science/api/pith-number/Y3T22HVMMWX6SMYSTZ7CJQFGTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU/action/storage_attestation","attest_author":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU/action/author_attestation","sign_citation":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU/action/citation_signature","submit_replication":"https://pith.science/pith/Y3T22HVMMWX6SMYSTZ7CJQFGTU/action/replication_record"}},"created_at":"2026-07-05T02:15:15.325698+00:00","updated_at":"2026-07-05T02:15:15.325698+00:00"}