{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RZ52POOZIDULSQGF2JSYG3TA7F","short_pith_number":"pith:RZ52POOZ","schema_version":"1.0","canonical_sha256":"8e7ba7b9d940e8b940c5d265836e60f951ded9b06d9c2332ff0c09ee66adf04e","source":{"kind":"arxiv","id":"2509.06190","version":1},"attestation_state":"computed","paper":{"title":"To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-lat","hep-th"],"primary_cat":"hep-ph","authors_text":"Ling-Xiao Xu","submitted_at":"2025-09-07T19:59:44Z","abstract_excerpt":"This is a pedagogical review of some recent progress in rigorously proving chiral symmetry breaking in a class of QCD-like theories that closely resemble the real-world QCD, namely the $SU(N_c)$ Yang-Mills theory coupled to $N_f$ flavors of massless quarks in the fundamental representation. Based on 't Hooft anomaly matching and persistent mass conditions, a general no-go theorem is formulated: assuming that the theory flows in the infrared to a fully color-screened, infrared-free phase described by color-singlet hadrons, symmetry and anomaly constraints necessarily imply spontaneous chiral sy"},"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":"2509.06190","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-09-07T19:59:44Z","cross_cats_sorted":["hep-lat","hep-th"],"title_canon_sha256":"66d8d6fa07d57c7fcde6eb85a3d80c8103c4a7ace2b7afc390d651cb2501667d","abstract_canon_sha256":"80bb79e57e3368ca9c4f4bec40d9f9f76abb5f60e6f69dae13215ba37f3f46bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:31.350714Z","signature_b64":"0ABzE+Wz93Goa4ZVb+9GcDk6PfsMnzPvZyY+nTk0JODDtVh7sFaX5JJm2OOhrxzqd/HTtwQcc+JLb8DREeNbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e7ba7b9d940e8b940c5d265836e60f951ded9b06d9c2332ff0c09ee66adf04e","last_reissued_at":"2026-07-05T12:06:31.350270Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:31.350270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-lat","hep-th"],"primary_cat":"hep-ph","authors_text":"Ling-Xiao Xu","submitted_at":"2025-09-07T19:59:44Z","abstract_excerpt":"This is a pedagogical review of some recent progress in rigorously proving chiral symmetry breaking in a class of QCD-like theories that closely resemble the real-world QCD, namely the $SU(N_c)$ Yang-Mills theory coupled to $N_f$ flavors of massless quarks in the fundamental representation. Based on 't Hooft anomaly matching and persistent mass conditions, a general no-go theorem is formulated: assuming that the theory flows in the infrared to a fully color-screened, infrared-free phase described by color-singlet hadrons, symmetry and anomaly constraints necessarily imply spontaneous chiral sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06190","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/2509.06190/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":"2509.06190","created_at":"2026-07-05T12:06:31.350323+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.06190v1","created_at":"2026-07-05T12:06:31.350323+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.06190","created_at":"2026-07-05T12:06:31.350323+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZ52POOZIDUL","created_at":"2026-07-05T12:06:31.350323+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZ52POOZIDULSQGF","created_at":"2026-07-05T12:06:31.350323+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZ52POOZ","created_at":"2026-07-05T12:06:31.350323+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/RZ52POOZIDULSQGF2JSYG3TA7F","json":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F.json","graph_json":"https://pith.science/api/pith-number/RZ52POOZIDULSQGF2JSYG3TA7F/graph.json","events_json":"https://pith.science/api/pith-number/RZ52POOZIDULSQGF2JSYG3TA7F/events.json","paper":"https://pith.science/paper/RZ52POOZ"},"agent_actions":{"view_html":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F","download_json":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F.json","view_paper":"https://pith.science/paper/RZ52POOZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.06190&json=true","fetch_graph":"https://pith.science/api/pith-number/RZ52POOZIDULSQGF2JSYG3TA7F/graph.json","fetch_events":"https://pith.science/api/pith-number/RZ52POOZIDULSQGF2JSYG3TA7F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F/action/storage_attestation","attest_author":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F/action/author_attestation","sign_citation":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F/action/citation_signature","submit_replication":"https://pith.science/pith/RZ52POOZIDULSQGF2JSYG3TA7F/action/replication_record"}},"created_at":"2026-07-05T12:06:31.350323+00:00","updated_at":"2026-07-05T12:06:31.350323+00:00"}