{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EKPNDBSG3H5Q2CBAB2JQIJVLCM","short_pith_number":"pith:EKPNDBSG","canonical_record":{"source":{"id":"1109.4505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-21T11:22:26Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"759be9b8e4ea66ef6937bee8575622944b3f1dddb3322f16a45f90bf4e8c9962","abstract_canon_sha256":"a32b77e1df5038d58dba6ad19f696ca4e480b23984c6229764a944fca419dd83"},"schema_version":"1.0"},"canonical_sha256":"229ed18646d9fb0d08200e930426ab13175de59f5863f2ae322207f35eaaf16d","source":{"kind":"arxiv","id":"1109.4505","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4505","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4505v3","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4505","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"EKPNDBSG3H5Q","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EKPNDBSG3H5Q2CBA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EKPNDBSG","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EKPNDBSG3H5Q2CBAB2JQIJVLCM","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-21T11:22:26Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"759be9b8e4ea66ef6937bee8575622944b3f1dddb3322f16a45f90bf4e8c9962","abstract_canon_sha256":"a32b77e1df5038d58dba6ad19f696ca4e480b23984c6229764a944fca419dd83"},"schema_version":"1.0"},"canonical_sha256":"229ed18646d9fb0d08200e930426ab13175de59f5863f2ae322207f35eaaf16d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:26.290148Z","signature_b64":"Ki94J9opNtDJ0u5iH9STCTQ6UQ85E8UP/ILcpVMZ8kPwgwW3VUrPMdp9Cq2+E3KQw7ys61JEE2rcj1X+sE6UCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"229ed18646d9fb0d08200e930426ab13175de59f5863f2ae322207f35eaaf16d","last_reissued_at":"2026-05-18T03:52:26.288511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:26.288511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4505","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FMvMJd3FzTU8/pkoXIbHtrhuKjTk4S2zd+FXjCjCf3z/prMjjAGJvrXX5BYrNdap9jmexirotzVePO4WK4Z6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:18:05.036415Z"},"content_sha256":"44f6adbdf5fde5ba23b2f6b045b3bce03c41ce8345482e38a7263e579b173003","schema_version":"1.0","event_id":"sha256:44f6adbdf5fde5ba23b2f6b045b3bce03c41ce8345482e38a7263e579b173003"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EKPNDBSG3H5Q2CBAB2JQIJVLCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive representations of finite groups in Riesz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.FA","authors_text":"Marcel de Jeu, Marten Wortel","submitted_at":"2011-09-21T11:22:26Z","abstract_excerpt":"In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite dimensional posi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4505","kind":"arxiv","version":3},"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":"2026-05-18T03:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmAPChR60spFTZbUR7QuEkndqkZbGRzMSLI0O7SXZ+tMdnO/sVbuzoggxnFAjYEnE3L3UGzjhYqtPPNqP3zxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:18:05.037101Z"},"content_sha256":"c7681f34cac3f1bb405e4549994448149e551bef9e4fe69eb06dc4fd86936007","schema_version":"1.0","event_id":"sha256:c7681f34cac3f1bb405e4549994448149e551bef9e4fe69eb06dc4fd86936007"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKPNDBSG3H5Q2CBAB2JQIJVLCM/bundle.json","state_url":"https://pith.science/pith/EKPNDBSG3H5Q2CBAB2JQIJVLCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKPNDBSG3H5Q2CBAB2JQIJVLCM/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":"2026-05-31T18:18:05Z","links":{"resolver":"https://pith.science/pith/EKPNDBSG3H5Q2CBAB2JQIJVLCM","bundle":"https://pith.science/pith/EKPNDBSG3H5Q2CBAB2JQIJVLCM/bundle.json","state":"https://pith.science/pith/EKPNDBSG3H5Q2CBAB2JQIJVLCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKPNDBSG3H5Q2CBAB2JQIJVLCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EKPNDBSG3H5Q2CBAB2JQIJVLCM","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":"a32b77e1df5038d58dba6ad19f696ca4e480b23984c6229764a944fca419dd83","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-21T11:22:26Z","title_canon_sha256":"759be9b8e4ea66ef6937bee8575622944b3f1dddb3322f16a45f90bf4e8c9962"},"schema_version":"1.0","source":{"id":"1109.4505","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4505","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4505v3","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4505","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"EKPNDBSG3H5Q","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EKPNDBSG3H5Q2CBA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EKPNDBSG","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:c7681f34cac3f1bb405e4549994448149e551bef9e4fe69eb06dc4fd86936007","target":"graph","created_at":"2026-05-18T03:52:26Z","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":"In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite dimensional posi","authors_text":"Marcel de Jeu, Marten Wortel","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-21T11:22:26Z","title":"Positive representations of finite groups in Riesz spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4505","kind":"arxiv","version":3},"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":"sha256:44f6adbdf5fde5ba23b2f6b045b3bce03c41ce8345482e38a7263e579b173003","target":"record","created_at":"2026-05-18T03:52:26Z","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":"a32b77e1df5038d58dba6ad19f696ca4e480b23984c6229764a944fca419dd83","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-21T11:22:26Z","title_canon_sha256":"759be9b8e4ea66ef6937bee8575622944b3f1dddb3322f16a45f90bf4e8c9962"},"schema_version":"1.0","source":{"id":"1109.4505","kind":"arxiv","version":3}},"canonical_sha256":"229ed18646d9fb0d08200e930426ab13175de59f5863f2ae322207f35eaaf16d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"229ed18646d9fb0d08200e930426ab13175de59f5863f2ae322207f35eaaf16d","first_computed_at":"2026-05-18T03:52:26.288511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:26.288511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ki94J9opNtDJ0u5iH9STCTQ6UQ85E8UP/ILcpVMZ8kPwgwW3VUrPMdp9Cq2+E3KQw7ys61JEE2rcj1X+sE6UCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:26.290148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4505","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44f6adbdf5fde5ba23b2f6b045b3bce03c41ce8345482e38a7263e579b173003","sha256:c7681f34cac3f1bb405e4549994448149e551bef9e4fe69eb06dc4fd86936007"],"state_sha256":"1177f2fa620a330721b7bbeb948ad4d540ce26904597d904084bd5c46d18ebf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMvuPow1uiiDfc+FfH90b2WHkql3htkgrl9D1MXhMXRB3TK4IQ4wyUyw3uhHKYBA+m7fv57x3KQLXmUgQFE2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:18:05.040958Z","bundle_sha256":"c6399bedff17930343bec0d748ad5f619b1dad7d3e5b6880d23381c142349223"}}