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We show that a direct sum of fuzzy spheres $S_F^{2 \\, Int} := S_F^2(\\ell) \\oplus S_F^2 (\\ell) \\oplus S_F^2 \\left ( \\ell + \\frac{1}{2} \\right ) \\oplus S_F^2 \\left ( \\ell - \\frac{1}{2} \\right )$ emerges as the vacuum solution after the spontaneous breaking of the gauge symmetry and lay the way for us to interpret the spontaneously b"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.02524","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-10T00:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"c1a39a93b603a42532ede0977138b10ef36524ad8406dcad669fabaf48e928c7","abstract_canon_sha256":"e2349487ef9477f1661098fe6a7b60989bbe5a66514b78c87788f827fcc5b09d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:47.891789Z","signature_b64":"IkFt9bgpbKl2UutmZUvvmI/wn1sRv6XKRiPh+CsCkz40DIE61xSVzNdF7KY9qri9ZeTdAwwpt9HnXkOdQL4RDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63bed8820d1b335484a4274ad0bb611e3584f92965a9d11da8b98b8c39bfaba8","last_reissued_at":"2026-05-18T01:36:47.891117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:47.891117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Fuzzy Extra Dimensions from $SU({\\cal N})$ Gauge Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Seckin Kurkcuoglu","submitted_at":"2015-04-10T00:52:28Z","abstract_excerpt":"We start with an $SU(\\cal {N})$ Yang-Mills theory on a manifold ${\\cal M}$, suitably coupled to two distinct set of scalar fields in the adjoint representation of $SU({\\cal N})$, which are forming a doublet and a triplet, respectively under a global $SU(2)$ symmetry. We show that a direct sum of fuzzy spheres $S_F^{2 \\, Int} := S_F^2(\\ell) \\oplus S_F^2 (\\ell) \\oplus S_F^2 \\left ( \\ell + \\frac{1}{2} \\right ) \\oplus S_F^2 \\left ( \\ell - \\frac{1}{2} \\right )$ emerges as the vacuum solution after the spontaneous breaking of the gauge symmetry and lay the way for us to interpret the spontaneously b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02524","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.02524","created_at":"2026-05-18T01:36:47.891208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02524v2","created_at":"2026-05-18T01:36:47.891208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02524","created_at":"2026-05-18T01:36:47.891208+00:00"},{"alias_kind":"pith_short_12","alias_value":"MO7NRAQNDMZV","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MO7NRAQNDMZVJBFE","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MO7NRAQN","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY","json":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY.json","graph_json":"https://pith.science/api/pith-number/MO7NRAQNDMZVJBFEE5FNBO3BDY/graph.json","events_json":"https://pith.science/api/pith-number/MO7NRAQNDMZVJBFEE5FNBO3BDY/events.json","paper":"https://pith.science/paper/MO7NRAQN"},"agent_actions":{"view_html":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY","download_json":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY.json","view_paper":"https://pith.science/paper/MO7NRAQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02524&json=true","fetch_graph":"https://pith.science/api/pith-number/MO7NRAQNDMZVJBFEE5FNBO3BDY/graph.json","fetch_events":"https://pith.science/api/pith-number/MO7NRAQNDMZVJBFEE5FNBO3BDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY/action/storage_attestation","attest_author":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY/action/author_attestation","sign_citation":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY/action/citation_signature","submit_replication":"https://pith.science/pith/MO7NRAQNDMZVJBFEE5FNBO3BDY/action/replication_record"}},"created_at":"2026-05-18T01:36:47.891208+00:00","updated_at":"2026-05-18T01:36:47.891208+00:00"}