{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SQ2SB52UX7NRGJIFRULGLSE6GC","short_pith_number":"pith:SQ2SB52U","canonical_record":{"source":{"id":"1712.05434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-14T20:01:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e1732d6b89d68c961f724e9524154d6451fdaa0203b9d23aeb49dbb4f8ea48d6","abstract_canon_sha256":"d6b9cfeec23de891c64671b64e86eb3a455a2f282983483bfc1519f6e321a96b"},"schema_version":"1.0"},"canonical_sha256":"943520f754bfdb1325058d1665c89e30a3cd6054c19c77e5bf909821d3347a76","source":{"kind":"arxiv","id":"1712.05434","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05434","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05434v2","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05434","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"SQ2SB52UX7NR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SQ2SB52UX7NRGJIF","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SQ2SB52U","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SQ2SB52UX7NRGJIFRULGLSE6GC","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-14T20:01:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e1732d6b89d68c961f724e9524154d6451fdaa0203b9d23aeb49dbb4f8ea48d6","abstract_canon_sha256":"d6b9cfeec23de891c64671b64e86eb3a455a2f282983483bfc1519f6e321a96b"},"schema_version":"1.0"},"canonical_sha256":"943520f754bfdb1325058d1665c89e30a3cd6054c19c77e5bf909821d3347a76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:29.344000Z","signature_b64":"wUFUXE2o3sJaiY567Gn5H9J5MjtwHjq6BqgaD+H2mEdQul9R7jljtZajaaQ17ZxwyLo5L4ZQuG7bQXL7p6ZdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"943520f754bfdb1325058d1665c89e30a3cd6054c19c77e5bf909821d3347a76","last_reissued_at":"2026-05-17T23:52:29.343354Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:29.343354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05434","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l5+1gOQPiZOGdRES8cw8LK5kv0BVHzk8zIT36Xs73VvrOAnrWNQWtrf4Z5rneej+/qIMVXetPvRYbdBH0Ne7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:47:49.146615Z"},"content_sha256":"fafe5581ca173e3edd3545ff6153e7975d88fb88521471ccd2962efe9d7924b5","schema_version":"1.0","event_id":"sha256:fafe5581ca173e3edd3545ff6153e7975d88fb88521471ccd2962efe9d7924b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SQ2SB52UX7NRGJIFRULGLSE6GC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Christopher M. Drupieski, Jonathan R. Kujawa","submitted_at":"2017-12-14T20:01:53Z","abstract_excerpt":"We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\\mathcal{N}_r(G)$ of supergroup homomorphisms $\\rho: \\mathbb{M}_r \\rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05434","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Trcql3WIaUlhYjBW4QyEoJbyggGrEBWVpBSDheId3CYqqcuG5kL81318USQc6BmGn7WB5hUM+UoIfaoWViJSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:47:49.146954Z"},"content_sha256":"9072aa7945c6a6c86654507e77a55551f67e2255075c0d129de6c10a95f8b7be","schema_version":"1.0","event_id":"sha256:9072aa7945c6a6c86654507e77a55551f67e2255075c0d129de6c10a95f8b7be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQ2SB52UX7NRGJIFRULGLSE6GC/bundle.json","state_url":"https://pith.science/pith/SQ2SB52UX7NRGJIFRULGLSE6GC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQ2SB52UX7NRGJIFRULGLSE6GC/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":"2026-05-28T10:47:49Z","links":{"resolver":"https://pith.science/pith/SQ2SB52UX7NRGJIFRULGLSE6GC","bundle":"https://pith.science/pith/SQ2SB52UX7NRGJIFRULGLSE6GC/bundle.json","state":"https://pith.science/pith/SQ2SB52UX7NRGJIFRULGLSE6GC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQ2SB52UX7NRGJIFRULGLSE6GC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SQ2SB52UX7NRGJIFRULGLSE6GC","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":"d6b9cfeec23de891c64671b64e86eb3a455a2f282983483bfc1519f6e321a96b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-14T20:01:53Z","title_canon_sha256":"e1732d6b89d68c961f724e9524154d6451fdaa0203b9d23aeb49dbb4f8ea48d6"},"schema_version":"1.0","source":{"id":"1712.05434","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05434","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05434v2","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05434","created_at":"2026-05-17T23:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"SQ2SB52UX7NR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SQ2SB52UX7NRGJIF","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SQ2SB52U","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:9072aa7945c6a6c86654507e77a55551f67e2255075c0d129de6c10a95f8b7be","target":"graph","created_at":"2026-05-17T23:52:29Z","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 show that if $G$ is an infinitesimal elementary supergroup scheme of height $\\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\\mathcal{N}_r(G)$ of supergroup homomorphisms $\\rho: \\mathbb{M}_r \\rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and","authors_text":"Christopher M. Drupieski, Jonathan R. Kujawa","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-14T20:01:53Z","title":"On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05434","kind":"arxiv","version":2},"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:fafe5581ca173e3edd3545ff6153e7975d88fb88521471ccd2962efe9d7924b5","target":"record","created_at":"2026-05-17T23:52:29Z","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":"d6b9cfeec23de891c64671b64e86eb3a455a2f282983483bfc1519f6e321a96b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-14T20:01:53Z","title_canon_sha256":"e1732d6b89d68c961f724e9524154d6451fdaa0203b9d23aeb49dbb4f8ea48d6"},"schema_version":"1.0","source":{"id":"1712.05434","kind":"arxiv","version":2}},"canonical_sha256":"943520f754bfdb1325058d1665c89e30a3cd6054c19c77e5bf909821d3347a76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"943520f754bfdb1325058d1665c89e30a3cd6054c19c77e5bf909821d3347a76","first_computed_at":"2026-05-17T23:52:29.343354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:29.343354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wUFUXE2o3sJaiY567Gn5H9J5MjtwHjq6BqgaD+H2mEdQul9R7jljtZajaaQ17ZxwyLo5L4ZQuG7bQXL7p6ZdAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:29.344000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05434","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fafe5581ca173e3edd3545ff6153e7975d88fb88521471ccd2962efe9d7924b5","sha256:9072aa7945c6a6c86654507e77a55551f67e2255075c0d129de6c10a95f8b7be"],"state_sha256":"04bcfc826877640324492a76ef5deba1bd0e397c85d809b885c1b39698640692"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v0StsitK5g102p+J+vu8jZ9gY4GGJKzoBUUx44nEk5PhtDOkxIZYjwKKHfQFhA+4VuNO+jMSd0XlZ4p5G9/rBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:47:49.148839Z","bundle_sha256":"ea3c28a7240cada5d6eefcb5eb6b642f14fd5d7c71ab25b3354ed29f67b5a6b9"}}