{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:65TUQVU43RYTRMKBUCGOYMRUBJ","short_pith_number":"pith:65TUQVU4","schema_version":"1.0","canonical_sha256":"f76748569cdc7138b141a08cec32340a53dadbbad90aded8a11876767b954149","source":{"kind":"arxiv","id":"1712.07826","version":5},"attestation_state":"computed","paper":{"title":"Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\\ell$- and $\\tilde{\\ell}$-Equivalence Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"hep-th","authors_text":"Jr., Kevin Iga, Kory Stiffler, Lucas Kang, S. James Gates, Vadim Korotkikh","submitted_at":"2017-12-21T08:22:19Z","abstract_excerpt":"Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of $BC_3$, the signed permutation group of three elements, and $BC_4$, the signed permutation group of four elements. It is shown how all 36,864 adinkras can be generated via $BC_4$ boson $\\times$ $BC_3$ color transformations of two quaternion adinkras that satisfy the quaternion algebra. An adinkra inner product has been used for some time, known as the \\emph{gadget}, which is used to distingu"},"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":"1712.07826","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-12-21T08:22:19Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1938a9f0a7193e1a8b4f0df93f4a10d928bf001b28e04f1d90fab063c24ad276","abstract_canon_sha256":"384362f9b1d8c5e84489d3b4357f94739cb0494cbc06335efb1e25f00cfec064"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:44.395104Z","signature_b64":"8duqgzgmQWggPzpbo46rXPVuo7fuXHHOU6Mo4wphn/EoIsAG9jSh0dmqWmIWj0KzfNCu+C6FbigP/owvLHk1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f76748569cdc7138b141a08cec32340a53dadbbad90aded8a11876767b954149","last_reissued_at":"2026-05-17T23:51:44.394498Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:44.394498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\\ell$- and $\\tilde{\\ell}$-Equivalence Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"hep-th","authors_text":"Jr., Kevin Iga, Kory Stiffler, Lucas Kang, S. James Gates, Vadim Korotkikh","submitted_at":"2017-12-21T08:22:19Z","abstract_excerpt":"Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of $BC_3$, the signed permutation group of three elements, and $BC_4$, the signed permutation group of four elements. It is shown how all 36,864 adinkras can be generated via $BC_4$ boson $\\times$ $BC_3$ color transformations of two quaternion adinkras that satisfy the quaternion algebra. An adinkra inner product has been used for some time, known as the \\emph{gadget}, which is used to distingu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07826","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.07826","created_at":"2026-05-17T23:51:44.394588+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.07826v5","created_at":"2026-05-17T23:51:44.394588+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07826","created_at":"2026-05-17T23:51:44.394588+00:00"},{"alias_kind":"pith_short_12","alias_value":"65TUQVU43RYT","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"65TUQVU43RYTRMKB","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"65TUQVU4","created_at":"2026-05-18T12:31:03.183658+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/65TUQVU43RYTRMKBUCGOYMRUBJ","json":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ.json","graph_json":"https://pith.science/api/pith-number/65TUQVU43RYTRMKBUCGOYMRUBJ/graph.json","events_json":"https://pith.science/api/pith-number/65TUQVU43RYTRMKBUCGOYMRUBJ/events.json","paper":"https://pith.science/paper/65TUQVU4"},"agent_actions":{"view_html":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ","download_json":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ.json","view_paper":"https://pith.science/paper/65TUQVU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.07826&json=true","fetch_graph":"https://pith.science/api/pith-number/65TUQVU43RYTRMKBUCGOYMRUBJ/graph.json","fetch_events":"https://pith.science/api/pith-number/65TUQVU43RYTRMKBUCGOYMRUBJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ/action/storage_attestation","attest_author":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ/action/author_attestation","sign_citation":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ/action/citation_signature","submit_replication":"https://pith.science/pith/65TUQVU43RYTRMKBUCGOYMRUBJ/action/replication_record"}},"created_at":"2026-05-17T23:51:44.394588+00:00","updated_at":"2026-05-17T23:51:44.394588+00:00"}