{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CY7NSAX2X3BECLLT6DIU6NUGIA","short_pith_number":"pith:CY7NSAX2","canonical_record":{"source":{"id":"1705.00751","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2017-05-02T00:59:31Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"a3dc046a1cfc377a45715edf4ce6b775f00f4c4f583d76688e0e27a0462b31b6","abstract_canon_sha256":"71efadfc2ca6b8af16f3635fa76bdd4c0a8c604bacd386ec7563ee2f47ae470d"},"schema_version":"1.0"},"canonical_sha256":"163ed902fabec2412d73f0d14f36864022c6a2c4d3fabc0d052051169d25ea37","source":{"kind":"arxiv","id":"1705.00751","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00751","created_at":"2026-05-18T00:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00751v6","created_at":"2026-05-18T00:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00751","created_at":"2026-05-18T00:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"CY7NSAX2X3BE","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CY7NSAX2X3BECLLT","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CY7NSAX2","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CY7NSAX2X3BECLLT6DIU6NUGIA","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00751","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2017-05-02T00:59:31Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"a3dc046a1cfc377a45715edf4ce6b775f00f4c4f583d76688e0e27a0462b31b6","abstract_canon_sha256":"71efadfc2ca6b8af16f3635fa76bdd4c0a8c604bacd386ec7563ee2f47ae470d"},"schema_version":"1.0"},"canonical_sha256":"163ed902fabec2412d73f0d14f36864022c6a2c4d3fabc0d052051169d25ea37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:50.066359Z","signature_b64":"FjDc3DEOkb8V7xtstd5pS3ZuC13DnvHbQTmMW1QVtfWk2W/QBXnWGIick+BZJwcW+M1fpk9zSgsctVaq+tHlBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"163ed902fabec2412d73f0d14f36864022c6a2c4d3fabc0d052051169d25ea37","last_reissued_at":"2026-05-18T00:33:50.065718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:50.065718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00751","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mddAnUNhdC28IBdf31QgsbSI1+tFIlP/vvYoVcYiJX1kRppe9oG9D80bh0L623tOXEV6kYiiHKeDA4RPUx7jDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:47:04.720678Z"},"content_sha256":"d64feb0dd115b6e06538423fa90813043ff481a57e69cdda26ee7d2fdefbe915","schema_version":"1.0","event_id":"sha256:d64feb0dd115b6e06538423fa90813043ff481a57e69cdda26ee7d2fdefbe915"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CY7NSAX2X3BECLLT6DIU6NUGIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic freedom in certain $SO(N)$ and $SU(N)$ models","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"D R Timothy Jones, Martin B Einhorn","submitted_at":"2017-05-02T00:59:31Z","abstract_excerpt":"We calculate the $\\beta$-functions for $SO(N)$ and $SU(N)$ gauge theories coupled to adjoint and fundamental scalar representations, correcting long-standing, previous results. We explore the constraints on $N$ resulting from requiring asymptotic freedom for all couplings. When we take into account the actual allowed behavior of the gauge coupling, the minimum value of $N$ in both cases turns out to be larger than realized in earlier treatments. We also show that in the large $N$ limit, both models have large regions of parameter space corresponding to total asymptotic freedom."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00751","kind":"arxiv","version":6},"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":"2026-05-18T00:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5tNlJs34yxKOwMA1HkUfztYVmhsPR/vFmgiQEyP7Fc3Uytzxv1A25tZq6EwKpSaEgTWa6bDT77vKxBgV/l0RBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:47:04.721442Z"},"content_sha256":"b617d3cc2379470aaea8fde869664db07634e6321f8070c2fed3dce4ac3a3296","schema_version":"1.0","event_id":"sha256:b617d3cc2379470aaea8fde869664db07634e6321f8070c2fed3dce4ac3a3296"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CY7NSAX2X3BECLLT6DIU6NUGIA/bundle.json","state_url":"https://pith.science/pith/CY7NSAX2X3BECLLT6DIU6NUGIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CY7NSAX2X3BECLLT6DIU6NUGIA/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":"2026-05-30T03:47:04Z","links":{"resolver":"https://pith.science/pith/CY7NSAX2X3BECLLT6DIU6NUGIA","bundle":"https://pith.science/pith/CY7NSAX2X3BECLLT6DIU6NUGIA/bundle.json","state":"https://pith.science/pith/CY7NSAX2X3BECLLT6DIU6NUGIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CY7NSAX2X3BECLLT6DIU6NUGIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CY7NSAX2X3BECLLT6DIU6NUGIA","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":"71efadfc2ca6b8af16f3635fa76bdd4c0a8c604bacd386ec7563ee2f47ae470d","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2017-05-02T00:59:31Z","title_canon_sha256":"a3dc046a1cfc377a45715edf4ce6b775f00f4c4f583d76688e0e27a0462b31b6"},"schema_version":"1.0","source":{"id":"1705.00751","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00751","created_at":"2026-05-18T00:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00751v6","created_at":"2026-05-18T00:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00751","created_at":"2026-05-18T00:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"CY7NSAX2X3BE","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CY7NSAX2X3BECLLT","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CY7NSAX2","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:b617d3cc2379470aaea8fde869664db07634e6321f8070c2fed3dce4ac3a3296","target":"graph","created_at":"2026-05-18T00:33:50Z","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 calculate the $\\beta$-functions for $SO(N)$ and $SU(N)$ gauge theories coupled to adjoint and fundamental scalar representations, correcting long-standing, previous results. We explore the constraints on $N$ resulting from requiring asymptotic freedom for all couplings. When we take into account the actual allowed behavior of the gauge coupling, the minimum value of $N$ in both cases turns out to be larger than realized in earlier treatments. We also show that in the large $N$ limit, both models have large regions of parameter space corresponding to total asymptotic freedom.","authors_text":"D R Timothy Jones, Martin B Einhorn","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2017-05-02T00:59:31Z","title":"Asymptotic freedom in certain $SO(N)$ and $SU(N)$ models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00751","kind":"arxiv","version":6},"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:d64feb0dd115b6e06538423fa90813043ff481a57e69cdda26ee7d2fdefbe915","target":"record","created_at":"2026-05-18T00:33:50Z","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":"71efadfc2ca6b8af16f3635fa76bdd4c0a8c604bacd386ec7563ee2f47ae470d","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2017-05-02T00:59:31Z","title_canon_sha256":"a3dc046a1cfc377a45715edf4ce6b775f00f4c4f583d76688e0e27a0462b31b6"},"schema_version":"1.0","source":{"id":"1705.00751","kind":"arxiv","version":6}},"canonical_sha256":"163ed902fabec2412d73f0d14f36864022c6a2c4d3fabc0d052051169d25ea37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"163ed902fabec2412d73f0d14f36864022c6a2c4d3fabc0d052051169d25ea37","first_computed_at":"2026-05-18T00:33:50.065718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:50.065718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FjDc3DEOkb8V7xtstd5pS3ZuC13DnvHbQTmMW1QVtfWk2W/QBXnWGIick+BZJwcW+M1fpk9zSgsctVaq+tHlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:50.066359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00751","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d64feb0dd115b6e06538423fa90813043ff481a57e69cdda26ee7d2fdefbe915","sha256:b617d3cc2379470aaea8fde869664db07634e6321f8070c2fed3dce4ac3a3296"],"state_sha256":"89ecf02cd8fb1efe6f8211daebe43012cbda5cc452b6f0366219967ee2afafe9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQ278ofWs/7zj3XdbntPVF+sDq15+C7/LUAsoEyds5DblfI8Wp6yl+3wzQQEPl04IxqJRT2JnUISOLaHB4I1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:47:04.726119Z","bundle_sha256":"80265a52cf1f3fc602808b2de86f73fadb989c7bc162014e02120e075c0e5b2e"}}