{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UFM24BLLEFNQOIVX5Z6XVTQA5T","short_pith_number":"pith:UFM24BLL","schema_version":"1.0","canonical_sha256":"a159ae056b215b0722b7ee7d7ace00ecc0c30af7b61665e32ba0de63712b47d1","source":{"kind":"arxiv","id":"1908.04543","version":1},"attestation_state":"computed","paper":{"title":"Solution of the self-dual $\\Phi^4$ QFT-model on four-dimensional Moyal space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Hock, Harald Grosse, Raimar Wulkenhaar","submitted_at":"2019-08-13T08:54:38Z","abstract_excerpt":"Previously the exact solution of the planar sector of the self-dual $\\Phi^4$-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant $\\lambda>-\\frac{1}{\\pi}$, the Fredholm equation in terms of a hypergeometric function and thus completes the construction of the planar sector of the model. We prove that the interacting model has spectral dimension $4-2\\frac{\\arcsin(\\lambda\\pi)}{\\pi}$ for $|\\lambda|<\\frac{1}{\\pi}$. It is this dimension drop which for $\\lambda>0$ avoids the triviality problem of the matric"},"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":"1908.04543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-13T08:54:38Z","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"title_canon_sha256":"eebf1aca237a9298bf9a52722b448d0a69a1415f6e387b6e47e1149cf5878fa6","abstract_canon_sha256":"fc106ec0ac8628c0aee1c3179609e06498e0c6524b87e9364965713d41e5fb80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:03:19.941632Z","signature_b64":"Ik4ylcfJYSDpmhMlQxOqC0JIvquhPFQEFOKbAkdSbOVsjojlzIXRA6xoEn9Hc1DWeChbpcQB8flUVNR5E4kGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a159ae056b215b0722b7ee7d7ace00ecc0c30af7b61665e32ba0de63712b47d1","last_reissued_at":"2026-07-05T01:03:19.941142Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:03:19.941142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solution of the self-dual $\\Phi^4$ QFT-model on four-dimensional Moyal space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Hock, Harald Grosse, Raimar Wulkenhaar","submitted_at":"2019-08-13T08:54:38Z","abstract_excerpt":"Previously the exact solution of the planar sector of the self-dual $\\Phi^4$-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant $\\lambda>-\\frac{1}{\\pi}$, the Fredholm equation in terms of a hypergeometric function and thus completes the construction of the planar sector of the model. We prove that the interacting model has spectral dimension $4-2\\frac{\\arcsin(\\lambda\\pi)}{\\pi}$ for $|\\lambda|<\\frac{1}{\\pi}$. It is this dimension drop which for $\\lambda>0$ avoids the triviality problem of the matric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04543","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/1908.04543/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":"1908.04543","created_at":"2026-07-05T01:03:19.941208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.04543v1","created_at":"2026-07-05T01:03:19.941208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04543","created_at":"2026-07-05T01:03:19.941208+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFM24BLLEFNQ","created_at":"2026-07-05T01:03:19.941208+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFM24BLLEFNQOIVX","created_at":"2026-07-05T01:03:19.941208+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFM24BLL","created_at":"2026-07-05T01:03:19.941208+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/UFM24BLLEFNQOIVX5Z6XVTQA5T","json":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T.json","graph_json":"https://pith.science/api/pith-number/UFM24BLLEFNQOIVX5Z6XVTQA5T/graph.json","events_json":"https://pith.science/api/pith-number/UFM24BLLEFNQOIVX5Z6XVTQA5T/events.json","paper":"https://pith.science/paper/UFM24BLL"},"agent_actions":{"view_html":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T","download_json":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T.json","view_paper":"https://pith.science/paper/UFM24BLL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.04543&json=true","fetch_graph":"https://pith.science/api/pith-number/UFM24BLLEFNQOIVX5Z6XVTQA5T/graph.json","fetch_events":"https://pith.science/api/pith-number/UFM24BLLEFNQOIVX5Z6XVTQA5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T/action/storage_attestation","attest_author":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T/action/author_attestation","sign_citation":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T/action/citation_signature","submit_replication":"https://pith.science/pith/UFM24BLLEFNQOIVX5Z6XVTQA5T/action/replication_record"}},"created_at":"2026-07-05T01:03:19.941208+00:00","updated_at":"2026-07-05T01:03:19.941208+00:00"}