{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ECU3JW5AYFUYLZSAJYLJHTNVP5","short_pith_number":"pith:ECU3JW5A","canonical_record":{"source":{"id":"0704.3464","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-04-26T02:03:55Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"355942a8cbfb054d55f9b28417561c70daf0af72af4a7a6fe15e99fe79ab420a","abstract_canon_sha256":"fe809ecfc8452b2005d18eaef7cd7747dfe7f6536a1579c04011a63fa663a723"},"schema_version":"1.0"},"canonical_sha256":"20a9b4dba0c16985e6404e1693cdb57f607f5396827b344995890d5fa754353c","source":{"kind":"arxiv","id":"0704.3464","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3464","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3464v1","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3464","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"ECU3JW5AYFUY","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ECU3JW5AYFUYLZSA","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ECU3JW5A","created_at":"2026-07-04T15:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ECU3JW5AYFUYLZSAJYLJHTNVP5","target":"record","payload":{"canonical_record":{"source":{"id":"0704.3464","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-04-26T02:03:55Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"355942a8cbfb054d55f9b28417561c70daf0af72af4a7a6fe15e99fe79ab420a","abstract_canon_sha256":"fe809ecfc8452b2005d18eaef7cd7747dfe7f6536a1579c04011a63fa663a723"},"schema_version":"1.0"},"canonical_sha256":"20a9b4dba0c16985e6404e1693cdb57f607f5396827b344995890d5fa754353c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:31:12.943456Z","signature_b64":"obl+lSAY7NvzzsriqG6upgtUgweKirnbaE+whvhxNCwm0dThJN0AxvBE32aowQApb1EavDq+ICX8MabqwZvjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20a9b4dba0c16985e6404e1693cdb57f607f5396827b344995890d5fa754353c","last_reissued_at":"2026-07-04T15:31:12.943014Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:31:12.943014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.3464","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":"2026-07-04T15:31:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OxcF1O0uK6GWQbZOYL9wf3ywvC/svyljhhz4X/e4wowzKmLSrf3VvRDqPHbx20jabwSRGMdc6TUYfzDgS5WeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T02:00:55.845272Z"},"content_sha256":"de40c45f62afc7e6fe8f83a5690df87fb0dd52ad0d1228cb5a004c06ca786bdc","schema_version":"1.0","event_id":"sha256:de40c45f62afc7e6fe8f83a5690df87fb0dd52ad0d1228cb5a004c06ca786bdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ECU3JW5AYFUYLZSAJYLJHTNVP5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constraints on $N_c$ in Extensions of the Standard Model","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Robert Shrock","submitted_at":"2007-04-26T02:03:55Z","abstract_excerpt":"We consider a class of theories involving an extension of the Standard Model gauge group to an {\\it a priori} arbitrary number of colors, $N_c$, and derive constraints on $N_c$. One motivation for this is the string theory landscape. For two natural classes of embeddings of this $N_c$-extended Standard Model in a supersymmetric grand unified theory, we show that requiring unbroken electromagnetic gauge invariance, asymptotic freedom of color, and three generations of quarks and leptons forces one to choose $N_c=3$. Similarly, we show that for a theory combining the $N_c$-extended Standard Mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3464","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0704.3464/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":"2026-07-04T15:31:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6a7W0CMA6ZoeEy0qqsHlEWtvCdjiNgGB0TUuqjk/FdA1205+w5MXPeb85vdEk+H3JfysV3edyLhOSS01j/ZICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T02:00:55.845664Z"},"content_sha256":"adbe1b40ace9dc84efa569665201a1e2bd015efda6c86e3849617f1d4558fd1d","schema_version":"1.0","event_id":"sha256:adbe1b40ace9dc84efa569665201a1e2bd015efda6c86e3849617f1d4558fd1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECU3JW5AYFUYLZSAJYLJHTNVP5/bundle.json","state_url":"https://pith.science/pith/ECU3JW5AYFUYLZSAJYLJHTNVP5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECU3JW5AYFUYLZSAJYLJHTNVP5/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":"2026-07-05T02:00:55Z","links":{"resolver":"https://pith.science/pith/ECU3JW5AYFUYLZSAJYLJHTNVP5","bundle":"https://pith.science/pith/ECU3JW5AYFUYLZSAJYLJHTNVP5/bundle.json","state":"https://pith.science/pith/ECU3JW5AYFUYLZSAJYLJHTNVP5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECU3JW5AYFUYLZSAJYLJHTNVP5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ECU3JW5AYFUYLZSAJYLJHTNVP5","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":"fe809ecfc8452b2005d18eaef7cd7747dfe7f6536a1579c04011a63fa663a723","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2007-04-26T02:03:55Z","title_canon_sha256":"355942a8cbfb054d55f9b28417561c70daf0af72af4a7a6fe15e99fe79ab420a"},"schema_version":"1.0","source":{"id":"0704.3464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3464","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3464v1","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3464","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"ECU3JW5AYFUY","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ECU3JW5AYFUYLZSA","created_at":"2026-07-04T15:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ECU3JW5A","created_at":"2026-07-04T15:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:adbe1b40ace9dc84efa569665201a1e2bd015efda6c86e3849617f1d4558fd1d","target":"graph","created_at":"2026-07-04T15:31:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0704.3464/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a class of theories involving an extension of the Standard Model gauge group to an {\\it a priori} arbitrary number of colors, $N_c$, and derive constraints on $N_c$. One motivation for this is the string theory landscape. For two natural classes of embeddings of this $N_c$-extended Standard Model in a supersymmetric grand unified theory, we show that requiring unbroken electromagnetic gauge invariance, asymptotic freedom of color, and three generations of quarks and leptons forces one to choose $N_c=3$. Similarly, we show that for a theory combining the $N_c$-extended Standard Mode","authors_text":"Robert Shrock","cross_cats":["hep-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2007-04-26T02:03:55Z","title":"Constraints on $N_c$ in Extensions of the Standard Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3464","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:de40c45f62afc7e6fe8f83a5690df87fb0dd52ad0d1228cb5a004c06ca786bdc","target":"record","created_at":"2026-07-04T15:31:12Z","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":"fe809ecfc8452b2005d18eaef7cd7747dfe7f6536a1579c04011a63fa663a723","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2007-04-26T02:03:55Z","title_canon_sha256":"355942a8cbfb054d55f9b28417561c70daf0af72af4a7a6fe15e99fe79ab420a"},"schema_version":"1.0","source":{"id":"0704.3464","kind":"arxiv","version":1}},"canonical_sha256":"20a9b4dba0c16985e6404e1693cdb57f607f5396827b344995890d5fa754353c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20a9b4dba0c16985e6404e1693cdb57f607f5396827b344995890d5fa754353c","first_computed_at":"2026-07-04T15:31:12.943014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:31:12.943014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"obl+lSAY7NvzzsriqG6upgtUgweKirnbaE+whvhxNCwm0dThJN0AxvBE32aowQApb1EavDq+ICX8MabqwZvjCA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:31:12.943456Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de40c45f62afc7e6fe8f83a5690df87fb0dd52ad0d1228cb5a004c06ca786bdc","sha256:adbe1b40ace9dc84efa569665201a1e2bd015efda6c86e3849617f1d4558fd1d"],"state_sha256":"dac40759735cea0632671e94ec4d3b0683eed0ddb1e7c2b97524360dac9be3a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tN/ruWb4V0NirLgKFIv7nyLx0S08ETNN2yu48VWKaBnBHN6RbdIsqoVfDqM9qkqYGPnGMlGKd+XReMEHyCNECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T02:00:55.847574Z","bundle_sha256":"1aad83a37959919130b091c51609379b69497bba9c8a50f1ea1b0f556218fef4"}}