{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:LCNAPIJYRXCSZSBW2QTIKJIFOE","short_pith_number":"pith:LCNAPIJY","schema_version":"1.0","canonical_sha256":"589a07a1388dc52cc836d42685250571398078ce0b2bd21521c75724e8b5553f","source":{"kind":"arxiv","id":"2108.04037","version":2},"attestation_state":"computed","paper":{"title":"Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\\rightarrow\\infty$ limit in $O(N)$-type models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","physics.comp-ph","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adrian Koenigstein, Martin J. Steil","submitted_at":"2021-08-09T13:42:12Z","abstract_excerpt":"Using an $O(N)$-symmetric toy model QFT in zero space-time dimensions we discuss several aspects and limitations of the $\\frac{1}{N}$-expansion. We demonstrate, how slight modifications in a classical UV action can lead the $\\frac{1}{N}$-expansion astray and how the infinite-$N$ limit may alter fundamental properties of a QFT. Thereby we present the problem of calculating correlation functions from two totally different perspectives: First, we explicitly analyze our model within an $\\frac{1}{N}$-saddle-point expansion and show its limitations. Secondly, we picture the same problem within the f"},"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":"2108.04037","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-08-09T13:42:12Z","cross_cats_sorted":["hep-th","physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"c5df72be3a56afee9ea27dafdcd5f0d790658f24ce3f5d44654f3c98f79418ac","abstract_canon_sha256":"aa933f23d0213c00579f4b4b377afed81dce5ae659390cbce7ff80c86e84f6ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:57:42.733676Z","signature_b64":"mmnhHFcFy3C/t85TERDbWH1dt+kNjURKf0cX8nf/rxWQO3LRwlMmi+96gLM19Cho6LCwrm4oygvIN5uLuLtACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"589a07a1388dc52cc836d42685250571398078ce0b2bd21521c75724e8b5553f","last_reissued_at":"2026-07-05T04:57:42.733240Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:57:42.733240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\\rightarrow\\infty$ limit in $O(N)$-type models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","physics.comp-ph","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adrian Koenigstein, Martin J. Steil","submitted_at":"2021-08-09T13:42:12Z","abstract_excerpt":"Using an $O(N)$-symmetric toy model QFT in zero space-time dimensions we discuss several aspects and limitations of the $\\frac{1}{N}$-expansion. We demonstrate, how slight modifications in a classical UV action can lead the $\\frac{1}{N}$-expansion astray and how the infinite-$N$ limit may alter fundamental properties of a QFT. Thereby we present the problem of calculating correlation functions from two totally different perspectives: First, we explicitly analyze our model within an $\\frac{1}{N}$-saddle-point expansion and show its limitations. Secondly, we picture the same problem within the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.04037","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.04037/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":"2108.04037","created_at":"2026-07-05T04:57:42.733293+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.04037v2","created_at":"2026-07-05T04:57:42.733293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.04037","created_at":"2026-07-05T04:57:42.733293+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCNAPIJYRXCS","created_at":"2026-07-05T04:57:42.733293+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCNAPIJYRXCSZSBW","created_at":"2026-07-05T04:57:42.733293+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCNAPIJY","created_at":"2026-07-05T04:57:42.733293+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2507.13011","citing_title":"Physics-informed operator flows and observables","ref_index":68,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE","json":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE.json","graph_json":"https://pith.science/api/pith-number/LCNAPIJYRXCSZSBW2QTIKJIFOE/graph.json","events_json":"https://pith.science/api/pith-number/LCNAPIJYRXCSZSBW2QTIKJIFOE/events.json","paper":"https://pith.science/paper/LCNAPIJY"},"agent_actions":{"view_html":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE","download_json":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE.json","view_paper":"https://pith.science/paper/LCNAPIJY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.04037&json=true","fetch_graph":"https://pith.science/api/pith-number/LCNAPIJYRXCSZSBW2QTIKJIFOE/graph.json","fetch_events":"https://pith.science/api/pith-number/LCNAPIJYRXCSZSBW2QTIKJIFOE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE/action/storage_attestation","attest_author":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE/action/author_attestation","sign_citation":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE/action/citation_signature","submit_replication":"https://pith.science/pith/LCNAPIJYRXCSZSBW2QTIKJIFOE/action/replication_record"}},"created_at":"2026-07-05T04:57:42.733293+00:00","updated_at":"2026-07-05T04:57:42.733293+00:00"}