{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NXJR7UQM6EIRONLMVKEBWVQYON","short_pith_number":"pith:NXJR7UQM","schema_version":"1.0","canonical_sha256":"6dd31fd20cf11117356caa881b5618734a2d67035042fad8b20d4c32187cbae5","source":{"kind":"arxiv","id":"1108.0519","version":1},"attestation_state":"computed","paper":{"title":"On a tropical dual Nullstellensatz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Dima Grigoriev","submitted_at":"2011-08-02T08:56:53Z","abstract_excerpt":"Since a tropical Nullstellensatz fails even for tropical univariate polynomials we study a conjecture on a tropical {\\it dual} Nullstellensatz for tropical polynomial systems in terms of solvability of a tropical linear system with the Cayley matrix associated to the tropical polynomial system. The conjecture on a tropical effective dual Nullstellensatz is proved for tropical univariate polynomials."},"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":"1108.0519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-08-02T08:56:53Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"2c1db0a20e5d5cfc7673d3b7a5d3310fe7cbb53f96e35f2f190c61e120c4addc","abstract_canon_sha256":"c1f10aeb01adc0e7ca1f0eee6e615cf224cbd0dc43bd78b30b23787d9cc01f69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:30.263515Z","signature_b64":"fq+mN3hioF7mPIIoRQWP4IIOQOA0grfTszXY6wXLzYcicPOdzqLBLert2tCTTr8rwhDWS0vLDaFBsSgRayaDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dd31fd20cf11117356caa881b5618734a2d67035042fad8b20d4c32187cbae5","last_reissued_at":"2026-05-18T04:16:30.262997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:30.262997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a tropical dual Nullstellensatz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Dima Grigoriev","submitted_at":"2011-08-02T08:56:53Z","abstract_excerpt":"Since a tropical Nullstellensatz fails even for tropical univariate polynomials we study a conjecture on a tropical {\\it dual} Nullstellensatz for tropical polynomial systems in terms of solvability of a tropical linear system with the Cayley matrix associated to the tropical polynomial system. The conjecture on a tropical effective dual Nullstellensatz is proved for tropical univariate polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0519","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.0519","created_at":"2026-05-18T04:16:30.263066+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.0519v1","created_at":"2026-05-18T04:16:30.263066+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0519","created_at":"2026-05-18T04:16:30.263066+00:00"},{"alias_kind":"pith_short_12","alias_value":"NXJR7UQM6EIR","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NXJR7UQM6EIRONLM","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NXJR7UQM","created_at":"2026-05-18T12:26:37.096874+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/NXJR7UQM6EIRONLMVKEBWVQYON","json":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON.json","graph_json":"https://pith.science/api/pith-number/NXJR7UQM6EIRONLMVKEBWVQYON/graph.json","events_json":"https://pith.science/api/pith-number/NXJR7UQM6EIRONLMVKEBWVQYON/events.json","paper":"https://pith.science/paper/NXJR7UQM"},"agent_actions":{"view_html":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON","download_json":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON.json","view_paper":"https://pith.science/paper/NXJR7UQM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.0519&json=true","fetch_graph":"https://pith.science/api/pith-number/NXJR7UQM6EIRONLMVKEBWVQYON/graph.json","fetch_events":"https://pith.science/api/pith-number/NXJR7UQM6EIRONLMVKEBWVQYON/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON/action/storage_attestation","attest_author":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON/action/author_attestation","sign_citation":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON/action/citation_signature","submit_replication":"https://pith.science/pith/NXJR7UQM6EIRONLMVKEBWVQYON/action/replication_record"}},"created_at":"2026-05-18T04:16:30.263066+00:00","updated_at":"2026-05-18T04:16:30.263066+00:00"}