{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OERNHA5XKNVX4XNOR7MBFN4VQX","short_pith_number":"pith:OERNHA5X","schema_version":"1.0","canonical_sha256":"7122d383b7536b7e5dae8fd812b79585dcc0314c0a67faa8b0810e2325bd34b4","source":{"kind":"arxiv","id":"1012.3081","version":1},"attestation_state":"computed","paper":{"title":"The Universal RG Machine","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Dario Benedetti, Frank Saueressig, Kai Groh, Pedro F. Machado","submitted_at":"2010-12-14T16:23:49Z","abstract_excerpt":"Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational $\\beta$-functions of the Einstein-Hil"},"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":"1012.3081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-14T16:23:49Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"cdc17def1da2454b6f1ba0b278e6ecd0036b29e1d43583f61ab11de6caac4c3c","abstract_canon_sha256":"55973db084398973a2a9834031335edb8116e4e9ee81d91b0779cb8de223be5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:33.391889Z","signature_b64":"ptevRVDPADRZXP1BHmPcSi8sw0iI2QGIXHcVfU0tNPDVilsk62+/9HniPZYvWtiZOe62nM1KzaiHGbyu9EafCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7122d383b7536b7e5dae8fd812b79585dcc0314c0a67faa8b0810e2325bd34b4","last_reissued_at":"2026-05-18T04:19:33.391521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:33.391521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Universal RG Machine","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Dario Benedetti, Frank Saueressig, Kai Groh, Pedro F. Machado","submitted_at":"2010-12-14T16:23:49Z","abstract_excerpt":"Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational $\\beta$-functions of the Einstein-Hil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3081","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":""},"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":"1012.3081","created_at":"2026-05-18T04:19:33.391573+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.3081v1","created_at":"2026-05-18T04:19:33.391573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3081","created_at":"2026-05-18T04:19:33.391573+00:00"},{"alias_kind":"pith_short_12","alias_value":"OERNHA5XKNVX","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OERNHA5XKNVX4XNO","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OERNHA5X","created_at":"2026-05-18T12:26:12.377268+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/OERNHA5XKNVX4XNOR7MBFN4VQX","json":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX.json","graph_json":"https://pith.science/api/pith-number/OERNHA5XKNVX4XNOR7MBFN4VQX/graph.json","events_json":"https://pith.science/api/pith-number/OERNHA5XKNVX4XNOR7MBFN4VQX/events.json","paper":"https://pith.science/paper/OERNHA5X"},"agent_actions":{"view_html":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX","download_json":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX.json","view_paper":"https://pith.science/paper/OERNHA5X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.3081&json=true","fetch_graph":"https://pith.science/api/pith-number/OERNHA5XKNVX4XNOR7MBFN4VQX/graph.json","fetch_events":"https://pith.science/api/pith-number/OERNHA5XKNVX4XNOR7MBFN4VQX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX/action/storage_attestation","attest_author":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX/action/author_attestation","sign_citation":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX/action/citation_signature","submit_replication":"https://pith.science/pith/OERNHA5XKNVX4XNOR7MBFN4VQX/action/replication_record"}},"created_at":"2026-05-18T04:19:33.391573+00:00","updated_at":"2026-05-18T04:19:33.391573+00:00"}