{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ESERZSX52VCLOMDR4HD5U7T6JV","short_pith_number":"pith:ESERZSX5","schema_version":"1.0","canonical_sha256":"24891ccafdd544b73071e1c7da7e7e4d568727f0337c6ca6f1bd0ca8a8853c9a","source":{"kind":"arxiv","id":"1607.06360","version":3},"attestation_state":"computed","paper":{"title":"$\\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"hep-lat","authors_text":"Claudio Bonati, Ettore Vicari, Massimo D'Elia, Paolo Rossi","submitted_at":"2016-07-21T15:18:40Z","abstract_excerpt":"We study the large-$N$ scaling behavior of the $\\theta$ dependence of the ground-state energy density $E(\\theta)$ of four-dimensional (4D) $SU(N)$ gauge theories and two-dimensional (2D) $CP^{N-1}$ models, where $\\theta$ is the parameter associated with the Lagrangian topological term. We consider its $\\theta$ expansion around $\\theta=0$, $E(\\theta)-E(0) = {1\\over 2}\\chi \\,\\theta^2 ( 1 + b_2 \\theta^2 + b_4\\theta^4 +\\cdots)$ where $\\chi$ is the topological susceptibility and $b_{2n}$ are dimensionless coefficients. We focus on the first few coefficients $b_{2n}$, which parametrize the deviation"},"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":"1607.06360","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-07-21T15:18:40Z","cross_cats_sorted":["hep-ph","hep-th"],"title_canon_sha256":"26a1451bc68a6eb5d87bbf6b4178154918af6f4a7d2130cba3870f777d83d379","abstract_canon_sha256":"5fe6cb6286c3fe229726ec513df9e9eace362a57b11bf215c6a294fb2114043d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:30.941949Z","signature_b64":"rcNmHQHF2G31w9NmJeXzvDX+CrWBEuQggzWQ0suwMkKJ1x0aO1WKbC6Kp4f+suR9E1C/KUxUh2OGDJpMo43TBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24891ccafdd544b73071e1c7da7e7e4d568727f0337c6ca6f1bd0ca8a8853c9a","last_reissued_at":"2026-05-18T01:01:30.941438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:30.941438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"hep-lat","authors_text":"Claudio Bonati, Ettore Vicari, Massimo D'Elia, Paolo Rossi","submitted_at":"2016-07-21T15:18:40Z","abstract_excerpt":"We study the large-$N$ scaling behavior of the $\\theta$ dependence of the ground-state energy density $E(\\theta)$ of four-dimensional (4D) $SU(N)$ gauge theories and two-dimensional (2D) $CP^{N-1}$ models, where $\\theta$ is the parameter associated with the Lagrangian topological term. We consider its $\\theta$ expansion around $\\theta=0$, $E(\\theta)-E(0) = {1\\over 2}\\chi \\,\\theta^2 ( 1 + b_2 \\theta^2 + b_4\\theta^4 +\\cdots)$ where $\\chi$ is the topological susceptibility and $b_{2n}$ are dimensionless coefficients. We focus on the first few coefficients $b_{2n}$, which parametrize the deviation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06360","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":"1607.06360","created_at":"2026-05-18T01:01:30.941513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06360v3","created_at":"2026-05-18T01:01:30.941513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06360","created_at":"2026-05-18T01:01:30.941513+00:00"},{"alias_kind":"pith_short_12","alias_value":"ESERZSX52VCL","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"ESERZSX52VCLOMDR","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"ESERZSX5","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2603.09413","citing_title":"Pure Natural Inflation Passes the ACT","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2509.17059","citing_title":"Axions as Dark Matter, Dark Energy, and Dark Radiation","ref_index":110,"is_internal_anchor":true},{"citing_arxiv_id":"2510.25704","citing_title":"Scaling flow-based approaches for topology sampling in $\\mathrm{SU}(3)$ gauge theory","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2603.24732","citing_title":"Confinement in Holographic Theories at Finite Theta","ref_index":46,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV","json":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV.json","graph_json":"https://pith.science/api/pith-number/ESERZSX52VCLOMDR4HD5U7T6JV/graph.json","events_json":"https://pith.science/api/pith-number/ESERZSX52VCLOMDR4HD5U7T6JV/events.json","paper":"https://pith.science/paper/ESERZSX5"},"agent_actions":{"view_html":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV","download_json":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV.json","view_paper":"https://pith.science/paper/ESERZSX5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06360&json=true","fetch_graph":"https://pith.science/api/pith-number/ESERZSX52VCLOMDR4HD5U7T6JV/graph.json","fetch_events":"https://pith.science/api/pith-number/ESERZSX52VCLOMDR4HD5U7T6JV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV/action/storage_attestation","attest_author":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV/action/author_attestation","sign_citation":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV/action/citation_signature","submit_replication":"https://pith.science/pith/ESERZSX52VCLOMDR4HD5U7T6JV/action/replication_record"}},"created_at":"2026-05-18T01:01:30.941513+00:00","updated_at":"2026-05-18T01:01:30.941513+00:00"}