{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:J26JDEVLBAHIKSCXIXW3IMNLLI","short_pith_number":"pith:J26JDEVL","schema_version":"1.0","canonical_sha256":"4ebc9192ab080e85485745edb431ab5a29d14fc87c23a35245e3662b9796d736","source":{"kind":"arxiv","id":"1005.4370","version":2},"attestation_state":"computed","paper":{"title":"Non-factorization of four-quark condensates at low energies within Chiral Perturbation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. Gomez Nicola, J.R. Pelaez, J. Ruiz de Elvira, (U. Complutense de Madrid)","submitted_at":"2010-05-24T16:11:08Z","abstract_excerpt":"Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within Chiral Perturbation Theory. Factorization of the four-quark condensate holds to leading and next to leading order. However at next to next to leading order, a term with a nontrivial space-time dependence in the four-quark correlator yields a divergent four-quark condensate, whereas the two-quark condensate and the scalar susceptibility are finite. Such a non-factorization term vanishes only in the chiral limit. We also comment on how factorization still holds in the large $N_c$ limit, provided such "},"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":"1005.4370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-05-24T16:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"86520ec657636e17951ca4195007eee246b849cc5ed870909c42a93d7d9f38f7","abstract_canon_sha256":"53c8facf6186237a04ec77effc922e50eaf004178188443715842d6b443b469e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:48.221997Z","signature_b64":"A5LNDC3zTS7cQqAxn7CKruRJ/po/lbYHFDDc7KyAYAyd2kLgrqWYSTKeT+Nd2KkO/h47fY1G/CbsZ8xTKKuaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ebc9192ab080e85485745edb431ab5a29d14fc87c23a35245e3662b9796d736","last_reissued_at":"2026-05-18T04:38:48.221545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:48.221545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-factorization of four-quark condensates at low energies within Chiral Perturbation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. Gomez Nicola, J.R. Pelaez, J. Ruiz de Elvira, (U. Complutense de Madrid)","submitted_at":"2010-05-24T16:11:08Z","abstract_excerpt":"Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within Chiral Perturbation Theory. Factorization of the four-quark condensate holds to leading and next to leading order. However at next to next to leading order, a term with a nontrivial space-time dependence in the four-quark correlator yields a divergent four-quark condensate, whereas the two-quark condensate and the scalar susceptibility are finite. Such a non-factorization term vanishes only in the chiral limit. We also comment on how factorization still holds in the large $N_c$ limit, provided such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4370","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":"1005.4370","created_at":"2026-05-18T04:38:48.221622+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.4370v2","created_at":"2026-05-18T04:38:48.221622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4370","created_at":"2026-05-18T04:38:48.221622+00:00"},{"alias_kind":"pith_short_12","alias_value":"J26JDEVLBAHI","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"J26JDEVLBAHIKSCX","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"J26JDEVL","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/J26JDEVLBAHIKSCXIXW3IMNLLI","json":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI.json","graph_json":"https://pith.science/api/pith-number/J26JDEVLBAHIKSCXIXW3IMNLLI/graph.json","events_json":"https://pith.science/api/pith-number/J26JDEVLBAHIKSCXIXW3IMNLLI/events.json","paper":"https://pith.science/paper/J26JDEVL"},"agent_actions":{"view_html":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI","download_json":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI.json","view_paper":"https://pith.science/paper/J26JDEVL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.4370&json=true","fetch_graph":"https://pith.science/api/pith-number/J26JDEVLBAHIKSCXIXW3IMNLLI/graph.json","fetch_events":"https://pith.science/api/pith-number/J26JDEVLBAHIKSCXIXW3IMNLLI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI/action/storage_attestation","attest_author":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI/action/author_attestation","sign_citation":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI/action/citation_signature","submit_replication":"https://pith.science/pith/J26JDEVLBAHIKSCXIXW3IMNLLI/action/replication_record"}},"created_at":"2026-05-18T04:38:48.221622+00:00","updated_at":"2026-05-18T04:38:48.221622+00:00"}