{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZKAF2SNAJPZFWYIJGE35KLB2BG","short_pith_number":"pith:ZKAF2SNA","canonical_record":{"source":{"id":"1111.6175","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-11-26T16:58:16Z","cross_cats_sorted":[],"title_canon_sha256":"968b9abc0031401e21a4f2a4b74f81184d05b9f28a08a3f0ee3dde24c196d7ef","abstract_canon_sha256":"d9b7bcebfbf92325225dd3f36b12f57c77ae0a784a4e88ae107ad5ef33453a7c"},"schema_version":"1.0"},"canonical_sha256":"ca805d49a04bf25b61093137d52c3a098fff27669893203270cf09a2d77eb9a6","source":{"kind":"arxiv","id":"1111.6175","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6175","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6175v5","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6175","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZKAF2SNAJPZF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZKAF2SNAJPZFWYIJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZKAF2SNA","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZKAF2SNAJPZFWYIJGE35KLB2BG","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6175","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-11-26T16:58:16Z","cross_cats_sorted":[],"title_canon_sha256":"968b9abc0031401e21a4f2a4b74f81184d05b9f28a08a3f0ee3dde24c196d7ef","abstract_canon_sha256":"d9b7bcebfbf92325225dd3f36b12f57c77ae0a784a4e88ae107ad5ef33453a7c"},"schema_version":"1.0"},"canonical_sha256":"ca805d49a04bf25b61093137d52c3a098fff27669893203270cf09a2d77eb9a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:30.358897Z","signature_b64":"IJnT7rghRdqUT/E6AriatNkqJSHjEDk46DTLoQ+c8GZwVtdDPA6fcLDV49t8v0pXDvRmg4nf3N9BxbqEEQtEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca805d49a04bf25b61093137d52c3a098fff27669893203270cf09a2d77eb9a6","last_reissued_at":"2026-05-18T02:22:30.358294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:30.358294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6175","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":"2026-05-18T02:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"myaLn8g8AC47tKyn/rHgE8omfLp30Z2wca+GiGfWB7nEasbgybY4RNAYoNvFlMygXiQIbK3wlVx1RS0RX7RZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:42:08.121107Z"},"content_sha256":"91a00f75bdb5aff4638377d374e8743a6c0884e0c6fb7740c2d0a28b9f13cea2","schema_version":"1.0","event_id":"sha256:91a00f75bdb5aff4638377d374e8743a6c0884e0c6fb7740c2d0a28b9f13cea2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZKAF2SNAJPZFWYIJGE35KLB2BG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Stanley J. Brodsky, Xing-Gang Wu","submitted_at":"2011-11-26T16:58:16Z","abstract_excerpt":"A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC) / Brodsky-Lepage"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6175","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":""},"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":"2026-05-18T02:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NsoGhHOJvYfAKDwIMOIZP5Idz+eXbYq50EX/YvcbkYUPo7kbTBDXNT8Pu9BGOOweBk3N6rdV38y5sW6n0n/xDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:42:08.121770Z"},"content_sha256":"0904307a3a1fed7d12500518cd5be8a5a1d29305c96bdb80584fb93682ad6cc1","schema_version":"1.0","event_id":"sha256:0904307a3a1fed7d12500518cd5be8a5a1d29305c96bdb80584fb93682ad6cc1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKAF2SNAJPZFWYIJGE35KLB2BG/bundle.json","state_url":"https://pith.science/pith/ZKAF2SNAJPZFWYIJGE35KLB2BG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKAF2SNAJPZFWYIJGE35KLB2BG/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":"2026-05-28T22:42:08Z","links":{"resolver":"https://pith.science/pith/ZKAF2SNAJPZFWYIJGE35KLB2BG","bundle":"https://pith.science/pith/ZKAF2SNAJPZFWYIJGE35KLB2BG/bundle.json","state":"https://pith.science/pith/ZKAF2SNAJPZFWYIJGE35KLB2BG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKAF2SNAJPZFWYIJGE35KLB2BG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZKAF2SNAJPZFWYIJGE35KLB2BG","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":"d9b7bcebfbf92325225dd3f36b12f57c77ae0a784a4e88ae107ad5ef33453a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-11-26T16:58:16Z","title_canon_sha256":"968b9abc0031401e21a4f2a4b74f81184d05b9f28a08a3f0ee3dde24c196d7ef"},"schema_version":"1.0","source":{"id":"1111.6175","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6175","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6175v5","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6175","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZKAF2SNAJPZF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZKAF2SNAJPZFWYIJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZKAF2SNA","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:0904307a3a1fed7d12500518cd5be8a5a1d29305c96bdb80584fb93682ad6cc1","target":"graph","created_at":"2026-05-18T02:22:30Z","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"},"paper":{"abstract_excerpt":"A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC) / Brodsky-Lepage","authors_text":"Stanley J. Brodsky, Xing-Gang Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-11-26T16:58:16Z","title":"Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6175","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":"sha256:91a00f75bdb5aff4638377d374e8743a6c0884e0c6fb7740c2d0a28b9f13cea2","target":"record","created_at":"2026-05-18T02:22:30Z","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":"d9b7bcebfbf92325225dd3f36b12f57c77ae0a784a4e88ae107ad5ef33453a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-11-26T16:58:16Z","title_canon_sha256":"968b9abc0031401e21a4f2a4b74f81184d05b9f28a08a3f0ee3dde24c196d7ef"},"schema_version":"1.0","source":{"id":"1111.6175","kind":"arxiv","version":5}},"canonical_sha256":"ca805d49a04bf25b61093137d52c3a098fff27669893203270cf09a2d77eb9a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca805d49a04bf25b61093137d52c3a098fff27669893203270cf09a2d77eb9a6","first_computed_at":"2026-05-18T02:22:30.358294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:30.358294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJnT7rghRdqUT/E6AriatNkqJSHjEDk46DTLoQ+c8GZwVtdDPA6fcLDV49t8v0pXDvRmg4nf3N9BxbqEEQtEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:30.358897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6175","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91a00f75bdb5aff4638377d374e8743a6c0884e0c6fb7740c2d0a28b9f13cea2","sha256:0904307a3a1fed7d12500518cd5be8a5a1d29305c96bdb80584fb93682ad6cc1"],"state_sha256":"1baf48772cd194a5498b18f2b2cc56025905cf4baf731488dd5297e271eb4708"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TjObKqaMU3gnI4JP7scsnjeTVDSwQ8Kre+D4L47+b7erIqvuVOeVmQPEWOaosspCyCvWkngAQSJbcpeyIb6MAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:42:08.124972Z","bundle_sha256":"bbf2ba4343d3d2cf36da365d2d571e7bc79dba8141ad7d823e131133a4f54097"}}