{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:D3KBO77KLY24TSB5YDAPQIRCSG","short_pith_number":"pith:D3KBO77K","canonical_record":{"source":{"id":"1301.3209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-15T02:51:26Z","cross_cats_sorted":[],"title_canon_sha256":"7d3adf0b609f65d8f25990bc85b4972054f273440c0970ec40a2409a8c3d220b","abstract_canon_sha256":"48ceda8baca846489c3c46b93f625233caaba330e905a907a1478ed6b2c07a1c"},"schema_version":"1.0"},"canonical_sha256":"1ed4177fea5e35c9c83dc0c0f8222291a957df351daa48ac6810b69447ec2ee0","source":{"kind":"arxiv","id":"1301.3209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3209","created_at":"2026-05-18T03:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3209v1","created_at":"2026-05-18T03:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3209","created_at":"2026-05-18T03:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"D3KBO77KLY24","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D3KBO77KLY24TSB5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D3KBO77K","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:D3KBO77KLY24TSB5YDAPQIRCSG","target":"record","payload":{"canonical_record":{"source":{"id":"1301.3209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-15T02:51:26Z","cross_cats_sorted":[],"title_canon_sha256":"7d3adf0b609f65d8f25990bc85b4972054f273440c0970ec40a2409a8c3d220b","abstract_canon_sha256":"48ceda8baca846489c3c46b93f625233caaba330e905a907a1478ed6b2c07a1c"},"schema_version":"1.0"},"canonical_sha256":"1ed4177fea5e35c9c83dc0c0f8222291a957df351daa48ac6810b69447ec2ee0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:12.126410Z","signature_b64":"mSMG7xdSt1dEJAI0YmOB7GELN/XIXOr11QuO/LXLQCy4qAxxoFCLYAKk0HfL3c0LMnWcWB/OoyI6BSPJwPHWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ed4177fea5e35c9c83dc0c0f8222291a957df351daa48ac6810b69447ec2ee0","last_reissued_at":"2026-05-18T03:26:12.125651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:12.125651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.3209","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vyNog7CYdMilTRd7WhuCRSe5/23u1DPeJLmLyQuLZTkxNJU20wXyxUhy9DioEcVhI2robXy4EI9obdnujRajDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:47:40.744000Z"},"content_sha256":"b98c3f08e3ada5d6de9640d3b59c48614177a4ec0264b696c3e0e5268cf8271e","schema_version":"1.0","event_id":"sha256:b98c3f08e3ada5d6de9640d3b59c48614177a4ec0264b696c3e0e5268cf8271e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:D3KBO77KLY24TSB5YDAPQIRCSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-Loop Structural Properties of the $\\beta$ Function in Asymptotically Free Vectorial Gauge Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Robert Shrock","submitted_at":"2013-01-15T02:51:26Z","abstract_excerpt":"We investigate some higher-loop structural properties of the $\\beta$ function in asymptotically free vectorial gauge theories. Our main focus is on theories with fermion contents that lead to an infrared (IR) zero in $\\beta$. We present analytic and numerical calculations of the value of the gauge coupling where $\\beta$ reaches a minimum, the value of $\\beta$ at this minimum, and the slope of $\\beta$ at the IR zero, at two-, three-, and four-loop order. The slope of $\\beta$ at the IR zero is relevant for estimates of a dilaton mass in quasiconformal gauge theories. Some inequalities are derive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3209","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6VGjuWaKXheboYSUiYr5FXIqAB0gh//bW2o6lp8c1WTEyLcVVhQWLEqt1anJ7aoMuss02H+5ikEgDXJF1G0nAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:47:40.744356Z"},"content_sha256":"cdadfbeb4e1936150846faadb2df40ab1072485ba820ccf9b6197ef02b4fe8b2","schema_version":"1.0","event_id":"sha256:cdadfbeb4e1936150846faadb2df40ab1072485ba820ccf9b6197ef02b4fe8b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3KBO77KLY24TSB5YDAPQIRCSG/bundle.json","state_url":"https://pith.science/pith/D3KBO77KLY24TSB5YDAPQIRCSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3KBO77KLY24TSB5YDAPQIRCSG/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":"2026-07-04T22:47:40Z","links":{"resolver":"https://pith.science/pith/D3KBO77KLY24TSB5YDAPQIRCSG","bundle":"https://pith.science/pith/D3KBO77KLY24TSB5YDAPQIRCSG/bundle.json","state":"https://pith.science/pith/D3KBO77KLY24TSB5YDAPQIRCSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3KBO77KLY24TSB5YDAPQIRCSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D3KBO77KLY24TSB5YDAPQIRCSG","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":"48ceda8baca846489c3c46b93f625233caaba330e905a907a1478ed6b2c07a1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-15T02:51:26Z","title_canon_sha256":"7d3adf0b609f65d8f25990bc85b4972054f273440c0970ec40a2409a8c3d220b"},"schema_version":"1.0","source":{"id":"1301.3209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3209","created_at":"2026-05-18T03:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3209v1","created_at":"2026-05-18T03:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3209","created_at":"2026-05-18T03:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"D3KBO77KLY24","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D3KBO77KLY24TSB5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D3KBO77K","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:cdadfbeb4e1936150846faadb2df40ab1072485ba820ccf9b6197ef02b4fe8b2","target":"graph","created_at":"2026-05-18T03:26:12Z","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":"We investigate some higher-loop structural properties of the $\\beta$ function in asymptotically free vectorial gauge theories. Our main focus is on theories with fermion contents that lead to an infrared (IR) zero in $\\beta$. We present analytic and numerical calculations of the value of the gauge coupling where $\\beta$ reaches a minimum, the value of $\\beta$ at this minimum, and the slope of $\\beta$ at the IR zero, at two-, three-, and four-loop order. The slope of $\\beta$ at the IR zero is relevant for estimates of a dilaton mass in quasiconformal gauge theories. Some inequalities are derive","authors_text":"Robert Shrock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-15T02:51:26Z","title":"Higher-Loop Structural Properties of the $\\beta$ Function in Asymptotically Free Vectorial Gauge Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3209","kind":"arxiv","version":1},"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:b98c3f08e3ada5d6de9640d3b59c48614177a4ec0264b696c3e0e5268cf8271e","target":"record","created_at":"2026-05-18T03:26:12Z","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":"48ceda8baca846489c3c46b93f625233caaba330e905a907a1478ed6b2c07a1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-15T02:51:26Z","title_canon_sha256":"7d3adf0b609f65d8f25990bc85b4972054f273440c0970ec40a2409a8c3d220b"},"schema_version":"1.0","source":{"id":"1301.3209","kind":"arxiv","version":1}},"canonical_sha256":"1ed4177fea5e35c9c83dc0c0f8222291a957df351daa48ac6810b69447ec2ee0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ed4177fea5e35c9c83dc0c0f8222291a957df351daa48ac6810b69447ec2ee0","first_computed_at":"2026-05-18T03:26:12.125651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:12.125651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mSMG7xdSt1dEJAI0YmOB7GELN/XIXOr11QuO/LXLQCy4qAxxoFCLYAKk0HfL3c0LMnWcWB/OoyI6BSPJwPHWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:12.126410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b98c3f08e3ada5d6de9640d3b59c48614177a4ec0264b696c3e0e5268cf8271e","sha256:cdadfbeb4e1936150846faadb2df40ab1072485ba820ccf9b6197ef02b4fe8b2"],"state_sha256":"56a893a21bb038d7380665e41b191bc86ca56d529a905f33b2517942989b142f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZTRo3ed2DMgn9RRrvUL9qRq1tWYFWz7FN53lzC3yHSB/dtxe6JPXWi3yPwrJlxKmHUdJjQRPt0bmnxODo5zGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T22:47:40.746183Z","bundle_sha256":"ec1a2010156eb9126bf4a62fd60b9f65403acffe0421093e5cb1a2eaf1766bbc"}}