{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:4YSIINJ67GXYLSS4PAAPQ2OFTL","short_pith_number":"pith:4YSIINJ6","canonical_record":{"source":{"id":"math-ph/0205039","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-05-25T11:49:43Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8932f7c91a2537884004f7fbf948a830eb13348274b22cbc0f361f6dd9645a74","abstract_canon_sha256":"39edfc1622347f39a788fcbd82db04458d736c7f006fa1dd4ed28a87147784b2"},"schema_version":"1.0"},"canonical_sha256":"e62484353ef9af85ca5c7800f869c59ae66e1373260df77c3ce228ab284ca783","source":{"kind":"arxiv","id":"math-ph/0205039","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0205039","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0205039v2","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0205039","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"4YSIINJ67GXY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"4YSIINJ67GXYLSS4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"4YSIINJ6","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:4YSIINJ67GXYLSS4PAAPQ2OFTL","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0205039","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-05-25T11:49:43Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8932f7c91a2537884004f7fbf948a830eb13348274b22cbc0f361f6dd9645a74","abstract_canon_sha256":"39edfc1622347f39a788fcbd82db04458d736c7f006fa1dd4ed28a87147784b2"},"schema_version":"1.0"},"canonical_sha256":"e62484353ef9af85ca5c7800f869c59ae66e1373260df77c3ce228ab284ca783","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:34.183296Z","signature_b64":"5MTARYjpqdCXKrXsXsXGDPI7HZBtb6J6IJiU6fIX+B/AFLURjKArCUJ3D7FrExGOLmHCovbu258DBq7xp8EKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e62484353ef9af85ca5c7800f869c59ae66e1373260df77c3ce228ab284ca783","last_reissued_at":"2026-05-18T01:38:34.182670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:34.182670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0205039","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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w1iS9WsNW3a+KMWfHcV6q0Z6Rr5Ho2OXEbUu/BCAkOyZnjsONaeHKtdoqmdiivH5C+0MrYcnHP6Tq3/edheLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T10:30:14.365700Z"},"content_sha256":"3aa1a18b7cf37c240d6e027d2d50d80a32a9cbdedd577116b1f0114061a803e4","schema_version":"1.0","event_id":"sha256:3aa1a18b7cf37c240d6e027d2d50d80a32a9cbdedd577116b1f0114061a803e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:4YSIINJ67GXYLSS4PAAPQ2OFTL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On frequencies of small oscillations of some dynamical systems associated with root systems","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.M. Perelomov","submitted_at":"2002-05-25T11:49:43Z","abstract_excerpt":"In the paper by F. Calogero and author [Commun. Math. Phys. 59 (1978) 109-116] the formula for frequencies of small oscillations of the Sutherland system ($A_l$ case) was found. In present note the generalization of this formula for the case of arbitrary root system is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0205039","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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tT7cKtW1S+KjXmoG2M881P6fHj7UguEw+mqlanXy0v/3ZBHNz0AkzIhVtighno8J12IZYw4sPXobMmVR1nvZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T10:30:14.366038Z"},"content_sha256":"7e20e90a1ac1343a3cfff4ba2d9aedd23efba52466b1c80e77ee384d5ba47723","schema_version":"1.0","event_id":"sha256:7e20e90a1ac1343a3cfff4ba2d9aedd23efba52466b1c80e77ee384d5ba47723"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YSIINJ67GXYLSS4PAAPQ2OFTL/bundle.json","state_url":"https://pith.science/pith/4YSIINJ67GXYLSS4PAAPQ2OFTL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YSIINJ67GXYLSS4PAAPQ2OFTL/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":"2026-06-30T10:30:14Z","links":{"resolver":"https://pith.science/pith/4YSIINJ67GXYLSS4PAAPQ2OFTL","bundle":"https://pith.science/pith/4YSIINJ67GXYLSS4PAAPQ2OFTL/bundle.json","state":"https://pith.science/pith/4YSIINJ67GXYLSS4PAAPQ2OFTL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YSIINJ67GXYLSS4PAAPQ2OFTL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:4YSIINJ67GXYLSS4PAAPQ2OFTL","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":"39edfc1622347f39a788fcbd82db04458d736c7f006fa1dd4ed28a87147784b2","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-05-25T11:49:43Z","title_canon_sha256":"8932f7c91a2537884004f7fbf948a830eb13348274b22cbc0f361f6dd9645a74"},"schema_version":"1.0","source":{"id":"math-ph/0205039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0205039","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0205039v2","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0205039","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"4YSIINJ67GXY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"4YSIINJ67GXYLSS4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"4YSIINJ6","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:7e20e90a1ac1343a3cfff4ba2d9aedd23efba52466b1c80e77ee384d5ba47723","target":"graph","created_at":"2026-05-18T01:38:34Z","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 the paper by F. Calogero and author [Commun. Math. Phys. 59 (1978) 109-116] the formula for frequencies of small oscillations of the Sutherland system ($A_l$ case) was found. In present note the generalization of this formula for the case of arbitrary root system is given.","authors_text":"A.M. Perelomov","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-05-25T11:49:43Z","title":"On frequencies of small oscillations of some dynamical systems associated with root systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0205039","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":"sha256:3aa1a18b7cf37c240d6e027d2d50d80a32a9cbdedd577116b1f0114061a803e4","target":"record","created_at":"2026-05-18T01:38:34Z","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":"39edfc1622347f39a788fcbd82db04458d736c7f006fa1dd4ed28a87147784b2","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-05-25T11:49:43Z","title_canon_sha256":"8932f7c91a2537884004f7fbf948a830eb13348274b22cbc0f361f6dd9645a74"},"schema_version":"1.0","source":{"id":"math-ph/0205039","kind":"arxiv","version":2}},"canonical_sha256":"e62484353ef9af85ca5c7800f869c59ae66e1373260df77c3ce228ab284ca783","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e62484353ef9af85ca5c7800f869c59ae66e1373260df77c3ce228ab284ca783","first_computed_at":"2026-05-18T01:38:34.182670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:34.182670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5MTARYjpqdCXKrXsXsXGDPI7HZBtb6J6IJiU6fIX+B/AFLURjKArCUJ3D7FrExGOLmHCovbu258DBq7xp8EKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:34.183296Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0205039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3aa1a18b7cf37c240d6e027d2d50d80a32a9cbdedd577116b1f0114061a803e4","sha256:7e20e90a1ac1343a3cfff4ba2d9aedd23efba52466b1c80e77ee384d5ba47723"],"state_sha256":"5c80f2e8e11815cd8b8c8912f6302ebff99a05a94bcc3d3c7a220ca7ed20bc9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eohye4SpVnRphwuKuitee02XZVilgbZDwS6EHd5RpIMmvoROSGDucux5rfzlssJVdO8fpm9ieTdauZv6xIKNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T10:30:14.367929Z","bundle_sha256":"24d471722607edb7d3a2aa783a3b4788e3be70a7429a8211efd872803efd18f6"}}