{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PPEJAMPCC3EXCLF2F5H6VUFBA7","short_pith_number":"pith:PPEJAMPC","canonical_record":{"source":{"id":"1704.08591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-27T14:18:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"aaca604add41673a390afd280f2326277b18550101e82168cf6bf1d82e8876f1","abstract_canon_sha256":"450e6e0c0751437aee8c1be3eed2639a6a48c31b514547b43dd0b66f7f472755"},"schema_version":"1.0"},"canonical_sha256":"7bc89031e216c9712cba2f4fead0a107ce2733f3a10f120e8275c3370b5e1542","source":{"kind":"arxiv","id":"1704.08591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08591","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08591v2","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08591","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"PPEJAMPCC3EX","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPEJAMPCC3EXCLF2","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPEJAMPC","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PPEJAMPCC3EXCLF2F5H6VUFBA7","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-27T14:18:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"aaca604add41673a390afd280f2326277b18550101e82168cf6bf1d82e8876f1","abstract_canon_sha256":"450e6e0c0751437aee8c1be3eed2639a6a48c31b514547b43dd0b66f7f472755"},"schema_version":"1.0"},"canonical_sha256":"7bc89031e216c9712cba2f4fead0a107ce2733f3a10f120e8275c3370b5e1542","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:49.436493Z","signature_b64":"J8/iRChn7D2DyUefhwZT102nMyg/HqmOn0Yb3Xepgy5RqPOaAvHuHtPPiD5nOshPNcJqymUXmaFV3S4iu7yGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bc89031e216c9712cba2f4fead0a107ce2733f3a10f120e8275c3370b5e1542","last_reissued_at":"2026-05-17T23:50:49.435887Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:49.435887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08591","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":"2026-05-17T23:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h9kE38ZqFpcYZnc9HzxqMKQr5ISWbhaS3aeiA2ZtsBG8B7/AMvSjacnznAo0cat6ppKqBfdl59MG6R5/juKRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:31:30.226344Z"},"content_sha256":"00f5203f959264cfc7f17d01cc25909028094c0688a0d37fffca2dbd412896fb","schema_version":"1.0","event_id":"sha256:00f5203f959264cfc7f17d01cc25909028094c0688a0d37fffca2dbd412896fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PPEJAMPCC3EXCLF2F5H6VUFBA7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric representations of finite groups on real toric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AT","authors_text":"Shizuo Kaji, Soojin Cho, Suyoung Choi","submitted_at":"2017-04-27T14:18:16Z","abstract_excerpt":"We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the $G$-module structure of the homology of $X^{\\mathbb R}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type $A$ and $B$, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08591","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":"2026-05-17T23:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5mH0OzJud27vSyvoKbF84LSjKlYLE5kzup6FcVAaBYN4ILsSPXWxedrK0ttDnXVLcgn7JhUgKG3Unar08ZjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:31:30.226697Z"},"content_sha256":"ae12f0e7dc2f98a8f8795e9cd9c2c51f1dd21b759dadd75d21157e72f5b437db","schema_version":"1.0","event_id":"sha256:ae12f0e7dc2f98a8f8795e9cd9c2c51f1dd21b759dadd75d21157e72f5b437db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPEJAMPCC3EXCLF2F5H6VUFBA7/bundle.json","state_url":"https://pith.science/pith/PPEJAMPCC3EXCLF2F5H6VUFBA7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPEJAMPCC3EXCLF2F5H6VUFBA7/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":"2026-06-01T17:31:30Z","links":{"resolver":"https://pith.science/pith/PPEJAMPCC3EXCLF2F5H6VUFBA7","bundle":"https://pith.science/pith/PPEJAMPCC3EXCLF2F5H6VUFBA7/bundle.json","state":"https://pith.science/pith/PPEJAMPCC3EXCLF2F5H6VUFBA7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPEJAMPCC3EXCLF2F5H6VUFBA7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PPEJAMPCC3EXCLF2F5H6VUFBA7","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":"450e6e0c0751437aee8c1be3eed2639a6a48c31b514547b43dd0b66f7f472755","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-27T14:18:16Z","title_canon_sha256":"aaca604add41673a390afd280f2326277b18550101e82168cf6bf1d82e8876f1"},"schema_version":"1.0","source":{"id":"1704.08591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08591","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08591v2","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08591","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"PPEJAMPCC3EX","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPEJAMPCC3EXCLF2","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPEJAMPC","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:ae12f0e7dc2f98a8f8795e9cd9c2c51f1dd21b759dadd75d21157e72f5b437db","target":"graph","created_at":"2026-05-17T23:50:49Z","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 develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the $G$-module structure of the homology of $X^{\\mathbb R}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type $A$ and $B$, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representatio","authors_text":"Shizuo Kaji, Soojin Cho, Suyoung Choi","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-27T14:18:16Z","title":"Geometric representations of finite groups on real toric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08591","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":"sha256:00f5203f959264cfc7f17d01cc25909028094c0688a0d37fffca2dbd412896fb","target":"record","created_at":"2026-05-17T23:50:49Z","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":"450e6e0c0751437aee8c1be3eed2639a6a48c31b514547b43dd0b66f7f472755","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-27T14:18:16Z","title_canon_sha256":"aaca604add41673a390afd280f2326277b18550101e82168cf6bf1d82e8876f1"},"schema_version":"1.0","source":{"id":"1704.08591","kind":"arxiv","version":2}},"canonical_sha256":"7bc89031e216c9712cba2f4fead0a107ce2733f3a10f120e8275c3370b5e1542","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bc89031e216c9712cba2f4fead0a107ce2733f3a10f120e8275c3370b5e1542","first_computed_at":"2026-05-17T23:50:49.435887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:49.435887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J8/iRChn7D2DyUefhwZT102nMyg/HqmOn0Yb3Xepgy5RqPOaAvHuHtPPiD5nOshPNcJqymUXmaFV3S4iu7yGBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:49.436493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00f5203f959264cfc7f17d01cc25909028094c0688a0d37fffca2dbd412896fb","sha256:ae12f0e7dc2f98a8f8795e9cd9c2c51f1dd21b759dadd75d21157e72f5b437db"],"state_sha256":"9a4f2eede7cfa6a892c4a211be497f9eb454c3c9ebfb0c6b8dfd211017c2a188"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MpQvdm1WCAyS5cH4+qyPUzLWKoRtyBJ3REKHIBJ7zLS93fyBxZiZXH4XVLCY+GgwT874q8SYiQu45NVjV6+GDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:31:30.228683Z","bundle_sha256":"cf514ab5c4782deca0c941804953770febf86316426e33635a186ffc81b26d01"}}