{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DFLC7EMGCSAXCXY4GWX2OGP5LS","short_pith_number":"pith:DFLC7EMG","schema_version":"1.0","canonical_sha256":"19562f91861481715f1c35afa719fd5ca2849295245b5074b517610c92c275ac","source":{"kind":"arxiv","id":"1610.01647","version":2},"attestation_state":"computed","paper":{"title":"Chiral density wave versus pion condensation in the 1+1 dimensional NJL model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Jens O. Andersen, Prabal Adhikari","submitted_at":"2016-09-24T12:33:52Z","abstract_excerpt":"In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $\\mu$ using dimensional regularization. The phase diagram in the $\\mu$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $\\mu>\\mu_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave "},"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":"1610.01647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-24T12:33:52Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"972b1357a2e4a85ee098a7f794417f9796e4750f88b7b236b68217b70ea8f5e5","abstract_canon_sha256":"20228dbe1ea8b52258630a5cb896aeb1ebf8fc17d27db360483a7ab288065196"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:09.163892Z","signature_b64":"oUyKO43QYwti5WcgkR9YiSsIJSk5PiAJz53mAQDMtz4Jo+VffT6yQ2YV4YDPve3BtV3iSOgBX435gpiOUl3JDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19562f91861481715f1c35afa719fd5ca2849295245b5074b517610c92c275ac","last_reissued_at":"2026-05-18T00:43:09.163108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:09.163108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chiral density wave versus pion condensation in the 1+1 dimensional NJL model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Jens O. Andersen, Prabal Adhikari","submitted_at":"2016-09-24T12:33:52Z","abstract_excerpt":"In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $\\mu$ using dimensional regularization. The phase diagram in the $\\mu$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $\\mu>\\mu_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01647","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":"1610.01647","created_at":"2026-05-18T00:43:09.163242+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01647v2","created_at":"2026-05-18T00:43:09.163242+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01647","created_at":"2026-05-18T00:43:09.163242+00:00"},{"alias_kind":"pith_short_12","alias_value":"DFLC7EMGCSAX","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DFLC7EMGCSAXCXY4","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DFLC7EMG","created_at":"2026-05-18T12:30:12.583610+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/DFLC7EMGCSAXCXY4GWX2OGP5LS","json":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS.json","graph_json":"https://pith.science/api/pith-number/DFLC7EMGCSAXCXY4GWX2OGP5LS/graph.json","events_json":"https://pith.science/api/pith-number/DFLC7EMGCSAXCXY4GWX2OGP5LS/events.json","paper":"https://pith.science/paper/DFLC7EMG"},"agent_actions":{"view_html":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS","download_json":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS.json","view_paper":"https://pith.science/paper/DFLC7EMG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01647&json=true","fetch_graph":"https://pith.science/api/pith-number/DFLC7EMGCSAXCXY4GWX2OGP5LS/graph.json","fetch_events":"https://pith.science/api/pith-number/DFLC7EMGCSAXCXY4GWX2OGP5LS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS/action/storage_attestation","attest_author":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS/action/author_attestation","sign_citation":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS/action/citation_signature","submit_replication":"https://pith.science/pith/DFLC7EMGCSAXCXY4GWX2OGP5LS/action/replication_record"}},"created_at":"2026-05-18T00:43:09.163242+00:00","updated_at":"2026-05-18T00:43:09.163242+00:00"}