{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4DFA77DVT5M6EQS7JRYU3JAH4X","short_pith_number":"pith:4DFA77DV","canonical_record":{"source":{"id":"1012.0550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-02T19:46:15Z","cross_cats_sorted":[],"title_canon_sha256":"7a7f116a2009b4113bd18cae85ed7c3d523a2db4420935f9b73b9eaf7f9a6ec6","abstract_canon_sha256":"4659dfceffdb356f8ce522fc86f0a289095cb32995e5d321b8af602f177791ad"},"schema_version":"1.0"},"canonical_sha256":"e0ca0ffc759f59e2425f4c714da407e5e09d3f9fed6750a178c3d313a1b50a20","source":{"kind":"arxiv","id":"1012.0550","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0550","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0550v1","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0550","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"4DFA77DVT5M6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4DFA77DVT5M6EQS7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4DFA77DV","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4DFA77DVT5M6EQS7JRYU3JAH4X","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-02T19:46:15Z","cross_cats_sorted":[],"title_canon_sha256":"7a7f116a2009b4113bd18cae85ed7c3d523a2db4420935f9b73b9eaf7f9a6ec6","abstract_canon_sha256":"4659dfceffdb356f8ce522fc86f0a289095cb32995e5d321b8af602f177791ad"},"schema_version":"1.0"},"canonical_sha256":"e0ca0ffc759f59e2425f4c714da407e5e09d3f9fed6750a178c3d313a1b50a20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:09.710614Z","signature_b64":"+TDnFNC7Nyjo5stuLffzOcob55IHd2MnBTRnIEtfVcmhnVlC8kZKJtz0buCrtuv6+P4sTq9Fa+nx38oVBcnqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0ca0ffc759f59e2425f4c714da407e5e09d3f9fed6750a178c3d313a1b50a20","last_reissued_at":"2026-05-18T04:34:09.710195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:09.710195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0550","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UT6cVrNCLge2bCAbHcG8DrJsyZPEaU76pTH2xKTdzaT8OLyBltIQDP2gQlhjcYIVT1QD0Th9qhGLhL5g05udDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:36:00.019983Z"},"content_sha256":"e8fd538f0944d561d869b019e816d2514ed9fbea6e2083cd9a4c285cf0e4e0e8","schema_version":"1.0","event_id":"sha256:e8fd538f0944d561d869b019e816d2514ed9fbea6e2083cd9a4c285cf0e4e0e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4DFA77DVT5M6EQS7JRYU3JAH4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension of Symmetric Spaces and Restriction of Weyl Groups and Invariant Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gestur Olafsson, Joseph A. Wolf","submitted_at":"2010-12-02T19:46:15Z","abstract_excerpt":"Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. In another paper we will apply our criterion to problems in Fourier analysis on projective/injective limits, specifically to theorems of Paley--Wiener type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0550","kind":"arxiv","version":1},"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":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n7UB1+w79JlLG1vi7W5OSFF2KsMqtfaYPV6GMoS2IJQFZHAX19f7HicZSP7dZ8e76PIqWFMwprWt2p3OXh9mAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:36:00.020334Z"},"content_sha256":"b72672d41b328df916a517f375c2d35031b6345183ea6362c5fc6309c5f45fbb","schema_version":"1.0","event_id":"sha256:b72672d41b328df916a517f375c2d35031b6345183ea6362c5fc6309c5f45fbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4DFA77DVT5M6EQS7JRYU3JAH4X/bundle.json","state_url":"https://pith.science/pith/4DFA77DVT5M6EQS7JRYU3JAH4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4DFA77DVT5M6EQS7JRYU3JAH4X/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":"2026-06-26T11:36:00Z","links":{"resolver":"https://pith.science/pith/4DFA77DVT5M6EQS7JRYU3JAH4X","bundle":"https://pith.science/pith/4DFA77DVT5M6EQS7JRYU3JAH4X/bundle.json","state":"https://pith.science/pith/4DFA77DVT5M6EQS7JRYU3JAH4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4DFA77DVT5M6EQS7JRYU3JAH4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4DFA77DVT5M6EQS7JRYU3JAH4X","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":"4659dfceffdb356f8ce522fc86f0a289095cb32995e5d321b8af602f177791ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-02T19:46:15Z","title_canon_sha256":"7a7f116a2009b4113bd18cae85ed7c3d523a2db4420935f9b73b9eaf7f9a6ec6"},"schema_version":"1.0","source":{"id":"1012.0550","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0550","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0550v1","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0550","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"4DFA77DVT5M6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4DFA77DVT5M6EQS7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4DFA77DV","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:b72672d41b328df916a517f375c2d35031b6345183ea6362c5fc6309c5f45fbb","target":"graph","created_at":"2026-05-18T04:34:09Z","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":"Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. In another paper we will apply our criterion to problems in Fourier analysis on projective/injective limits, specifically to theorems of Paley--Wiener type.","authors_text":"Gestur Olafsson, Joseph A. Wolf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-02T19:46:15Z","title":"Extension of Symmetric Spaces and Restriction of Weyl Groups and Invariant Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0550","kind":"arxiv","version":1},"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:e8fd538f0944d561d869b019e816d2514ed9fbea6e2083cd9a4c285cf0e4e0e8","target":"record","created_at":"2026-05-18T04:34:09Z","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":"4659dfceffdb356f8ce522fc86f0a289095cb32995e5d321b8af602f177791ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-02T19:46:15Z","title_canon_sha256":"7a7f116a2009b4113bd18cae85ed7c3d523a2db4420935f9b73b9eaf7f9a6ec6"},"schema_version":"1.0","source":{"id":"1012.0550","kind":"arxiv","version":1}},"canonical_sha256":"e0ca0ffc759f59e2425f4c714da407e5e09d3f9fed6750a178c3d313a1b50a20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0ca0ffc759f59e2425f4c714da407e5e09d3f9fed6750a178c3d313a1b50a20","first_computed_at":"2026-05-18T04:34:09.710195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:09.710195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+TDnFNC7Nyjo5stuLffzOcob55IHd2MnBTRnIEtfVcmhnVlC8kZKJtz0buCrtuv6+P4sTq9Fa+nx38oVBcnqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:09.710614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0550","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8fd538f0944d561d869b019e816d2514ed9fbea6e2083cd9a4c285cf0e4e0e8","sha256:b72672d41b328df916a517f375c2d35031b6345183ea6362c5fc6309c5f45fbb"],"state_sha256":"dc5ea0647049f589c0fbd69be4cd2eea91124b1029507a5cd45717313cb9e01f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzs0Q6LgiiqQX6ycijDTfsMHbLPqkm9svDpHZ0FQSkpcpvXdFTm0Vg86XATPKH3VRHVDOBagT+b9fpIUx0MnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:36:00.022293Z","bundle_sha256":"46dde200a339e3b1a51d062c168c25f4434214d22d155e6fe33107a07af0d9e1"}}