{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SYCK6L3SXOAFCT6WMZ2SNCBDKA","short_pith_number":"pith:SYCK6L3S","canonical_record":{"source":{"id":"1007.5248","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-29T15:29:36Z","cross_cats_sorted":["math.OA","math.SP"],"title_canon_sha256":"c5470d6efcdcf2dcf84d7f9fb0a9e480b7a3c476bc523f54c4a25a61ac97035a","abstract_canon_sha256":"a7fa3c4647869c0b4ecee77342d67d35cf8c8d515290f74ae111a8bc3723c7a6"},"schema_version":"1.0"},"canonical_sha256":"9604af2f72bb80514fd6667526882350174007ec2c554af150628964438a56e1","source":{"kind":"arxiv","id":"1007.5248","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5248","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5248v1","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5248","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"SYCK6L3SXOAF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SYCK6L3SXOAFCT6W","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SYCK6L3S","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SYCK6L3SXOAFCT6WMZ2SNCBDKA","target":"record","payload":{"canonical_record":{"source":{"id":"1007.5248","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-29T15:29:36Z","cross_cats_sorted":["math.OA","math.SP"],"title_canon_sha256":"c5470d6efcdcf2dcf84d7f9fb0a9e480b7a3c476bc523f54c4a25a61ac97035a","abstract_canon_sha256":"a7fa3c4647869c0b4ecee77342d67d35cf8c8d515290f74ae111a8bc3723c7a6"},"schema_version":"1.0"},"canonical_sha256":"9604af2f72bb80514fd6667526882350174007ec2c554af150628964438a56e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:43.298295Z","signature_b64":"qlCXZcZgWu9VvfgOxjC2a4+0EL+KrhaFN5r2c6PJGD/xb3P76/+++ZzLjnP8teuUOlR7KqPHRzfrXIoiRVqeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9604af2f72bb80514fd6667526882350174007ec2c554af150628964438a56e1","last_reissued_at":"2026-05-18T03:31:43.297240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:43.297240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.5248","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":"2026-05-18T03:31:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E38eUI51F2loTYe8pEdtpEBXC/5ZD+3+vsO2Wdez+UINi6Iq11NQvtB+PtBHxs9zIQf/3HFU+uGaIogZ/C8WAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:25:08.221440Z"},"content_sha256":"ab1cf08f9ec3f618ad9aa32e4b4369c26e20c7491f68fd6a5ad91d39b88746a1","schema_version":"1.0","event_id":"sha256:ab1cf08f9ec3f618ad9aa32e4b4369c26e20c7491f68fd6a5ad91d39b88746a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SYCK6L3SXOAFCT6WMZ2SNCBDKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral theory for commutative algebras of differential operators on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.SP"],"primary_cat":"math.FA","authors_text":"Alessio Martini","submitted_at":"2010-07-29T15:29:36Z","abstract_excerpt":"The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a \"weighted subcoercive operator\" of ter Elst and Robinson (J. Funct. Anal. 157 (1998) 88-163). The joint spectrum of L_1,...,L_n in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L_1,...,L_n. Connections with the theory of Gelfand pairs are est"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5248","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":"2026-05-18T03:31:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J5dHt7KuLqeYIy+LgHV2Qr0Tiy9PBIavbglJRIaft+kMtAe5bwSOjB8gVAIsAOhzj4B/zlLoCNuN07GGlT+wCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:25:08.222160Z"},"content_sha256":"1c9d85b44e5eb40044148e0513fb193f3021757be51b84d6cc7d519cac815f49","schema_version":"1.0","event_id":"sha256:1c9d85b44e5eb40044148e0513fb193f3021757be51b84d6cc7d519cac815f49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYCK6L3SXOAFCT6WMZ2SNCBDKA/bundle.json","state_url":"https://pith.science/pith/SYCK6L3SXOAFCT6WMZ2SNCBDKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYCK6L3SXOAFCT6WMZ2SNCBDKA/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":"2026-06-05T20:25:08Z","links":{"resolver":"https://pith.science/pith/SYCK6L3SXOAFCT6WMZ2SNCBDKA","bundle":"https://pith.science/pith/SYCK6L3SXOAFCT6WMZ2SNCBDKA/bundle.json","state":"https://pith.science/pith/SYCK6L3SXOAFCT6WMZ2SNCBDKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYCK6L3SXOAFCT6WMZ2SNCBDKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SYCK6L3SXOAFCT6WMZ2SNCBDKA","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":"a7fa3c4647869c0b4ecee77342d67d35cf8c8d515290f74ae111a8bc3723c7a6","cross_cats_sorted":["math.OA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-29T15:29:36Z","title_canon_sha256":"c5470d6efcdcf2dcf84d7f9fb0a9e480b7a3c476bc523f54c4a25a61ac97035a"},"schema_version":"1.0","source":{"id":"1007.5248","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5248","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5248v1","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5248","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"SYCK6L3SXOAF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SYCK6L3SXOAFCT6W","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SYCK6L3S","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:1c9d85b44e5eb40044148e0513fb193f3021757be51b84d6cc7d519cac815f49","target":"graph","created_at":"2026-05-18T03:31:43Z","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":"The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a \"weighted subcoercive operator\" of ter Elst and Robinson (J. Funct. Anal. 157 (1998) 88-163). The joint spectrum of L_1,...,L_n in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L_1,...,L_n. Connections with the theory of Gelfand pairs are est","authors_text":"Alessio Martini","cross_cats":["math.OA","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-29T15:29:36Z","title":"Spectral theory for commutative algebras of differential operators on Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5248","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:ab1cf08f9ec3f618ad9aa32e4b4369c26e20c7491f68fd6a5ad91d39b88746a1","target":"record","created_at":"2026-05-18T03:31:43Z","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":"a7fa3c4647869c0b4ecee77342d67d35cf8c8d515290f74ae111a8bc3723c7a6","cross_cats_sorted":["math.OA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-29T15:29:36Z","title_canon_sha256":"c5470d6efcdcf2dcf84d7f9fb0a9e480b7a3c476bc523f54c4a25a61ac97035a"},"schema_version":"1.0","source":{"id":"1007.5248","kind":"arxiv","version":1}},"canonical_sha256":"9604af2f72bb80514fd6667526882350174007ec2c554af150628964438a56e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9604af2f72bb80514fd6667526882350174007ec2c554af150628964438a56e1","first_computed_at":"2026-05-18T03:31:43.297240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:43.297240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qlCXZcZgWu9VvfgOxjC2a4+0EL+KrhaFN5r2c6PJGD/xb3P76/+++ZzLjnP8teuUOlR7KqPHRzfrXIoiRVqeBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:43.298295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5248","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab1cf08f9ec3f618ad9aa32e4b4369c26e20c7491f68fd6a5ad91d39b88746a1","sha256:1c9d85b44e5eb40044148e0513fb193f3021757be51b84d6cc7d519cac815f49"],"state_sha256":"facd3649853eeb3deb536cde0816fe52ed351f57cb27e6567cdcf8ee23b8c6fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLIRf72vwD8pnhyTxFcOtJVjzRi2tB1zK1erMfJSqK6P4xjoAm9DUnUXqHPrjAKJI0rZTwzFTbvN+XOH/WvgBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:25:08.226568Z","bundle_sha256":"699708b188c3b2231a8eb4daf11ec3392a105fe209733cbaaf3d340e1f1599b4"}}