{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:5RQQDYNLF5ZRQ2JC6MLFOUNBDW","short_pith_number":"pith:5RQQDYNL","canonical_record":{"source":{"id":"hep-ph/0203027","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2002-03-04T16:56:51Z","cross_cats_sorted":[],"title_canon_sha256":"97dc3c7934c47ef65f1bf7e327daf308202ee1cc9fa93aae361d0eadb8099375","abstract_canon_sha256":"4b21c3c94a895f550ab48aa882219767715ffc86abe7dc6542091f23b91dcec1"},"schema_version":"1.0"},"canonical_sha256":"ec6101e1ab2f73186922f3165751a11d922009b7c5113ab7e56ab6f13064420f","source":{"kind":"arxiv","id":"hep-ph/0203027","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0203027","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0203027v5","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0203027","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"5RQQDYNLF5ZR","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RQQDYNLF5ZRQ2JC","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RQQDYNL","created_at":"2026-07-04T16:34:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:5RQQDYNLF5ZRQ2JC6MLFOUNBDW","target":"record","payload":{"canonical_record":{"source":{"id":"hep-ph/0203027","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2002-03-04T16:56:51Z","cross_cats_sorted":[],"title_canon_sha256":"97dc3c7934c47ef65f1bf7e327daf308202ee1cc9fa93aae361d0eadb8099375","abstract_canon_sha256":"4b21c3c94a895f550ab48aa882219767715ffc86abe7dc6542091f23b91dcec1"},"schema_version":"1.0"},"canonical_sha256":"ec6101e1ab2f73186922f3165751a11d922009b7c5113ab7e56ab6f13064420f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:34:01.817481Z","signature_b64":"NtgiAGsGQurVaHgNwZ5WrlytmkzWPvKGU0lctoRG0Fuh8wqOE9YBFSG9/rSRbjt6gQB2+EGobSFnYFM0S9BcCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec6101e1ab2f73186922f3165751a11d922009b7c5113ab7e56ab6f13064420f","last_reissued_at":"2026-07-04T16:34:01.817056Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:34:01.817056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-ph/0203027","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"msJo5BeXI6w7ygHpc+CE6XO63hgWefR+VXUa0d8vbyq6zPUoqCDIEY713i6Q3rlXahzUV68oZqKCKk2WHJb/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:43:43.261308Z"},"content_sha256":"1a9817b88a646c5313cbc4ae831600ba76842519c1bba98070dbdaa46c855a25","schema_version":"1.0","event_id":"sha256:1a9817b88a646c5313cbc4ae831600ba76842519c1bba98070dbdaa46c855a25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:5RQQDYNLF5ZRQ2JC6MLFOUNBDW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supergraph Techniques and Two-Loop Beta-Functions for Renormalizable and Non-Renormalizable Operators","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Michael Ratz, Stefan Antusch","submitted_at":"2002-03-04T16:56:51Z","abstract_excerpt":"We present a construction kit for calculating two-loop beta functions in N=1 supersymmetric theories for the operators of the superpotential using supergraph techniques. In particular, it allows to compute the beta functions for every desired, even higher dimensional, operator of the superpotential from the wavefunction renormalization constants of the theory. We apply this method to calculate the two-loop beta functions for the lowest-dimensional effective neutrino mass operator in the Minimal Supersymmetric Standard Model (MSSM) and for the Yukawa couplings in the MSSM extended by singlet su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0203027","kind":"arxiv","version":5},"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/hep-ph/0203027/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kUL4QaBRTNZaRRXfnFU2s1vRrG9cqbM859RbVo4Of+QabCaiGJkv7PQ/QKjN1JcnEs0SSzO95f15MlKx2xZEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:43:43.261815Z"},"content_sha256":"fbd3f9fb502a21047486a9e9f26d5aef9986c51d06213028d924e2fa6dfadda9","schema_version":"1.0","event_id":"sha256:fbd3f9fb502a21047486a9e9f26d5aef9986c51d06213028d924e2fa6dfadda9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RQQDYNLF5ZRQ2JC6MLFOUNBDW/bundle.json","state_url":"https://pith.science/pith/5RQQDYNLF5ZRQ2JC6MLFOUNBDW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RQQDYNLF5ZRQ2JC6MLFOUNBDW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T07:43:43Z","links":{"resolver":"https://pith.science/pith/5RQQDYNLF5ZRQ2JC6MLFOUNBDW","bundle":"https://pith.science/pith/5RQQDYNLF5ZRQ2JC6MLFOUNBDW/bundle.json","state":"https://pith.science/pith/5RQQDYNLF5ZRQ2JC6MLFOUNBDW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RQQDYNLF5ZRQ2JC6MLFOUNBDW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:5RQQDYNLF5ZRQ2JC6MLFOUNBDW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4b21c3c94a895f550ab48aa882219767715ffc86abe7dc6542091f23b91dcec1","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2002-03-04T16:56:51Z","title_canon_sha256":"97dc3c7934c47ef65f1bf7e327daf308202ee1cc9fa93aae361d0eadb8099375"},"schema_version":"1.0","source":{"id":"hep-ph/0203027","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0203027","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0203027v5","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0203027","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"5RQQDYNLF5ZR","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RQQDYNLF5ZRQ2JC","created_at":"2026-07-04T16:34:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RQQDYNL","created_at":"2026-07-04T16:34:01Z"}],"graph_snapshots":[{"event_id":"sha256:fbd3f9fb502a21047486a9e9f26d5aef9986c51d06213028d924e2fa6dfadda9","target":"graph","created_at":"2026-07-04T16:34:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-ph/0203027/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a construction kit for calculating two-loop beta functions in N=1 supersymmetric theories for the operators of the superpotential using supergraph techniques. In particular, it allows to compute the beta functions for every desired, even higher dimensional, operator of the superpotential from the wavefunction renormalization constants of the theory. We apply this method to calculate the two-loop beta functions for the lowest-dimensional effective neutrino mass operator in the Minimal Supersymmetric Standard Model (MSSM) and for the Yukawa couplings in the MSSM extended by singlet su","authors_text":"Michael Ratz, Stefan Antusch","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2002-03-04T16:56:51Z","title":"Supergraph Techniques and Two-Loop Beta-Functions for Renormalizable and Non-Renormalizable Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0203027","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1a9817b88a646c5313cbc4ae831600ba76842519c1bba98070dbdaa46c855a25","target":"record","created_at":"2026-07-04T16:34:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4b21c3c94a895f550ab48aa882219767715ffc86abe7dc6542091f23b91dcec1","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2002-03-04T16:56:51Z","title_canon_sha256":"97dc3c7934c47ef65f1bf7e327daf308202ee1cc9fa93aae361d0eadb8099375"},"schema_version":"1.0","source":{"id":"hep-ph/0203027","kind":"arxiv","version":5}},"canonical_sha256":"ec6101e1ab2f73186922f3165751a11d922009b7c5113ab7e56ab6f13064420f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec6101e1ab2f73186922f3165751a11d922009b7c5113ab7e56ab6f13064420f","first_computed_at":"2026-07-04T16:34:01.817056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:34:01.817056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NtgiAGsGQurVaHgNwZ5WrlytmkzWPvKGU0lctoRG0Fuh8wqOE9YBFSG9/rSRbjt6gQB2+EGobSFnYFM0S9BcCg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:34:01.817481Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0203027","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a9817b88a646c5313cbc4ae831600ba76842519c1bba98070dbdaa46c855a25","sha256:fbd3f9fb502a21047486a9e9f26d5aef9986c51d06213028d924e2fa6dfadda9"],"state_sha256":"e5af3ecc632fbd4a50ee7e026ae6fd709ff0f422752b130d3b70138cc466e89d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"829lOsV/jlwPS+i/4Io3PpEAB6ije2hkq5ze0OpcTPU491HmAmrc451Zr5lfG8BvV7uSZri14qWUkQJOc66XAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:43:43.266775Z","bundle_sha256":"c61f8d64a0eb6d23f5ea7d12013908ba26d5e45d5748726b88ddc6d3372c4cb3"}}