{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3ZDB5QVZ6WVTCXEFR5O465ZXFF","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":"d6ce9cd1e4c221a6435a77f4fb6fe069adc8337b8ec227e83a0f635bba2e52bc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-19T15:50:15Z","title_canon_sha256":"0fd4255c825c0bbd5de8c44069aac66b69cbfdf8be74b2398257ae2b68ab5e0e"},"schema_version":"1.0","source":{"id":"1008.3334","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3334","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3334v3","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3334","created_at":"2026-05-18T04:30:36Z"},{"alias_kind":"pith_short_12","alias_value":"3ZDB5QVZ6WVT","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3ZDB5QVZ6WVTCXEF","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3ZDB5QVZ","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:ae0afd044164620f58c7fdfedfca93fd0e9c81cbb157319bf82afb7e98ce4161","target":"graph","created_at":"2026-05-18T04:30:36Z","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 examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.","authors_text":"Jan Govaerts, Sean Murray","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-19T15:50:15Z","title":"Noncommutative Spherically Symmetric Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3334","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":"sha256:0824c579f3d890b0d92875cda2ba6eb855f55475966b454d494d2e60039baab5","target":"record","created_at":"2026-05-18T04:30:36Z","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":"d6ce9cd1e4c221a6435a77f4fb6fe069adc8337b8ec227e83a0f635bba2e52bc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-19T15:50:15Z","title_canon_sha256":"0fd4255c825c0bbd5de8c44069aac66b69cbfdf8be74b2398257ae2b68ab5e0e"},"schema_version":"1.0","source":{"id":"1008.3334","kind":"arxiv","version":3}},"canonical_sha256":"de461ec2b9f5ab315c858f5dcf7737296ca14ff03815eeda25d6167de8d5542d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de461ec2b9f5ab315c858f5dcf7737296ca14ff03815eeda25d6167de8d5542d","first_computed_at":"2026-05-18T04:30:36.542158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:36.542158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gdbf61cCYuuul3Qt5wBqfYKsdIqbpbtL37sJQ90s+7ANnGnJEXT20TxkzVeFg4YNVeSMMdP76ScEIVeFYfKMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:36.542829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3334","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0824c579f3d890b0d92875cda2ba6eb855f55475966b454d494d2e60039baab5","sha256:ae0afd044164620f58c7fdfedfca93fd0e9c81cbb157319bf82afb7e98ce4161"],"state_sha256":"a0225f635a6150bceea26066718c14fc4bcff402b7d6349a9f0abdc5ea622e6b"}