{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IS7RRETBSKESNCZYJERRKJJYUV","short_pith_number":"pith:IS7RRETB","schema_version":"1.0","canonical_sha256":"44bf1892619289268b384923152538a5548ec28c581f5bc6a7203d6c9eb9bc94","source":{"kind":"arxiv","id":"1005.2382","version":3},"attestation_state":"computed","paper":{"title":"Undecidability of linear inequalities in graph homomorphism densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Hamed Hatami, Serguei Norine","submitted_at":"2010-05-13T17:51:10Z","abstract_excerpt":"The purpose of this article is to show that even the most elementary problems in asymptotic extremal graph theory can be highly non-trivial. We study linear inequalities between graph homomorphism densities. In the language of quantum graphs the validity of such an inequality is equivalent to the positivity of a corresponding quantum graph. Similar to the setting of polynomials, a quantum graph that can be represented as a sum of squares of labeled quantum graphs is necessarily positive. Lov\\'asz asks whether the opposite is also true. We answer this question and also a related question of Raz"},"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":"1005.2382","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-13T17:51:10Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2d19997cb2439f922d41cdc45a4a4b3d5049c75413b149af1aaf42623245788b","abstract_canon_sha256":"31831e916df4a27cf11ae8b8fe4cca9821d7510c2cea2a5f68310863fa5ebc89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:10.053704Z","signature_b64":"3vmP2XemtYXISog/nBRixeqXhsrBHh62P455xJpH+8uc1nSdjv9dXYSlQcGS4gB/oAH7ftxYBttI/f08GNf1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44bf1892619289268b384923152538a5548ec28c581f5bc6a7203d6c9eb9bc94","last_reissued_at":"2026-05-18T04:39:10.053078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:10.053078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Undecidability of linear inequalities in graph homomorphism densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Hamed Hatami, Serguei Norine","submitted_at":"2010-05-13T17:51:10Z","abstract_excerpt":"The purpose of this article is to show that even the most elementary problems in asymptotic extremal graph theory can be highly non-trivial. We study linear inequalities between graph homomorphism densities. In the language of quantum graphs the validity of such an inequality is equivalent to the positivity of a corresponding quantum graph. Similar to the setting of polynomials, a quantum graph that can be represented as a sum of squares of labeled quantum graphs is necessarily positive. Lov\\'asz asks whether the opposite is also true. We answer this question and also a related question of Raz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2382","kind":"arxiv","version":3},"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":"1005.2382","created_at":"2026-05-18T04:39:10.053168+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.2382v3","created_at":"2026-05-18T04:39:10.053168+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2382","created_at":"2026-05-18T04:39:10.053168+00:00"},{"alias_kind":"pith_short_12","alias_value":"IS7RRETBSKES","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IS7RRETBSKESNCZY","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IS7RRETB","created_at":"2026-05-18T12:26:09.077623+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/IS7RRETBSKESNCZYJERRKJJYUV","json":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV.json","graph_json":"https://pith.science/api/pith-number/IS7RRETBSKESNCZYJERRKJJYUV/graph.json","events_json":"https://pith.science/api/pith-number/IS7RRETBSKESNCZYJERRKJJYUV/events.json","paper":"https://pith.science/paper/IS7RRETB"},"agent_actions":{"view_html":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV","download_json":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV.json","view_paper":"https://pith.science/paper/IS7RRETB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.2382&json=true","fetch_graph":"https://pith.science/api/pith-number/IS7RRETBSKESNCZYJERRKJJYUV/graph.json","fetch_events":"https://pith.science/api/pith-number/IS7RRETBSKESNCZYJERRKJJYUV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV/action/storage_attestation","attest_author":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV/action/author_attestation","sign_citation":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV/action/citation_signature","submit_replication":"https://pith.science/pith/IS7RRETBSKESNCZYJERRKJJYUV/action/replication_record"}},"created_at":"2026-05-18T04:39:10.053168+00:00","updated_at":"2026-05-18T04:39:10.053168+00:00"}