{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:F6LKRPPAM6NXDLLWLVROCAUXJV","short_pith_number":"pith:F6LKRPPA","schema_version":"1.0","canonical_sha256":"2f96a8bde0679b71ad765d62e102974d63431b5da82bff8c399896dffadec4be","source":{"kind":"arxiv","id":"1602.03312","version":2},"attestation_state":"computed","paper":{"title":"The category of $\\mathbb{Z}_2^n$-supermanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Janusz Grabowski, Norbert Poncin, Tiffany Covolo","submitted_at":"2016-02-10T09:59:00Z","abstract_excerpt":"In Physics and in Mathematics $\\mathbb{Z}_2^n$-gradings, $n>1$, appear in various fields. The corresponding sign rule is determined by the `scalar product' of the involved $\\mathbb{Z}_2^n$-degrees. The $\\mathbb{Z}_2^n$-Supergeometry exhibits challenging differences with the classical one: nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise. In this article we develop the foundations of the theory: we define $\\mathbb{Z}_2^n$-supermanifolds and provide examples in the ringed space and coordinate settings. W"},"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":"1602.03312","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-10T09:59:00Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c39393f7f5f4e97a9f84654c4a7a98eb1b35d7bd21f4ee7b6ce2725e346fb131","abstract_canon_sha256":"9eceb7b16ab506b28c2a095ffd287883de1ca712e4b32b59ab96b98b0043f47b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:21.441363Z","signature_b64":"5DOOqHD6CRETtmps/zbA4NFnXZI+C8mE+dQyIX5HCVs0cdBmeVv/NTxWhLsEOUP6t+rjz4Mfmi2raWuI4yFBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f96a8bde0679b71ad765d62e102974d63431b5da82bff8c399896dffadec4be","last_reissued_at":"2026-05-18T01:04:21.440895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:21.440895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The category of $\\mathbb{Z}_2^n$-supermanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Janusz Grabowski, Norbert Poncin, Tiffany Covolo","submitted_at":"2016-02-10T09:59:00Z","abstract_excerpt":"In Physics and in Mathematics $\\mathbb{Z}_2^n$-gradings, $n>1$, appear in various fields. The corresponding sign rule is determined by the `scalar product' of the involved $\\mathbb{Z}_2^n$-degrees. The $\\mathbb{Z}_2^n$-Supergeometry exhibits challenging differences with the classical one: nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise. In this article we develop the foundations of the theory: we define $\\mathbb{Z}_2^n$-supermanifolds and provide examples in the ringed space and coordinate settings. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03312","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":"1602.03312","created_at":"2026-05-18T01:04:21.440972+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.03312v2","created_at":"2026-05-18T01:04:21.440972+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03312","created_at":"2026-05-18T01:04:21.440972+00:00"},{"alias_kind":"pith_short_12","alias_value":"F6LKRPPAM6NX","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"F6LKRPPAM6NXDLLW","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"F6LKRPPA","created_at":"2026-05-18T12:30:15.759754+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/F6LKRPPAM6NXDLLWLVROCAUXJV","json":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV.json","graph_json":"https://pith.science/api/pith-number/F6LKRPPAM6NXDLLWLVROCAUXJV/graph.json","events_json":"https://pith.science/api/pith-number/F6LKRPPAM6NXDLLWLVROCAUXJV/events.json","paper":"https://pith.science/paper/F6LKRPPA"},"agent_actions":{"view_html":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV","download_json":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV.json","view_paper":"https://pith.science/paper/F6LKRPPA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.03312&json=true","fetch_graph":"https://pith.science/api/pith-number/F6LKRPPAM6NXDLLWLVROCAUXJV/graph.json","fetch_events":"https://pith.science/api/pith-number/F6LKRPPAM6NXDLLWLVROCAUXJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV/action/storage_attestation","attest_author":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV/action/author_attestation","sign_citation":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV/action/citation_signature","submit_replication":"https://pith.science/pith/F6LKRPPAM6NXDLLWLVROCAUXJV/action/replication_record"}},"created_at":"2026-05-18T01:04:21.440972+00:00","updated_at":"2026-05-18T01:04:21.440972+00:00"}