{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:K6X6BQYT5T4PM4PMNPE7IFMRKR","short_pith_number":"pith:K6X6BQYT","canonical_record":{"source":{"id":"1512.07489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-23T14:25:42Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"03b9b9235c919ebfaf83cfa4f77529ed89bc2f8ca20d2f3831f30d6763875488","abstract_canon_sha256":"3b8d38029a93e8ea2c4e6406eaf2c4e328b7ca68dd7ad27f723a7d860218658f"},"schema_version":"1.0"},"canonical_sha256":"57afe0c313ecf8f671ec6bc9f415915468d38113afcb9c9811750c868cf8a6d3","source":{"kind":"arxiv","id":"1512.07489","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07489","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07489v2","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07489","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"K6X6BQYT5T4P","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K6X6BQYT5T4PM4PM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K6X6BQYT","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:K6X6BQYT5T4PM4PMNPE7IFMRKR","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-23T14:25:42Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"03b9b9235c919ebfaf83cfa4f77529ed89bc2f8ca20d2f3831f30d6763875488","abstract_canon_sha256":"3b8d38029a93e8ea2c4e6406eaf2c4e328b7ca68dd7ad27f723a7d860218658f"},"schema_version":"1.0"},"canonical_sha256":"57afe0c313ecf8f671ec6bc9f415915468d38113afcb9c9811750c868cf8a6d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:08.309034Z","signature_b64":"TMUBKpmINcT9sQ1Jh+piaz1otUAfp+Ghm9Mz413chhL3iqoF8XUQZ+pKGl2vL8W3ms2r4b9TbwrYp9heUfgsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57afe0c313ecf8f671ec6bc9f415915468d38113afcb9c9811750c868cf8a6d3","last_reissued_at":"2026-05-18T00:41:08.308448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:08.308448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07489","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":"2026-05-18T00:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZ0CVozJApoChq3aJnK5sFI3g553xjLgDjyorjE7+/US08k3I9TRBQk5anisHDZSGirktxSpMveyhqffneQkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:21:41.836680Z"},"content_sha256":"c19484cb5d29a389c4a1ae308083beb1c2e5dc1f2fc2f462b8ea6f7bcf47d1c1","schema_version":"1.0","event_id":"sha256:c19484cb5d29a389c4a1ae308083beb1c2e5dc1f2fc2f462b8ea6f7bcf47d1c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:K6X6BQYT5T4PM4PMNPE7IFMRKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lobachevsky geometry in TTW and PW systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Armen Nersessian, Hovhannes Shmavonyan, Tigran Hakobyan","submitted_at":"2015-12-23T14:25:42Z","abstract_excerpt":"We review the classical properties of Tremblay-Turbiner-Winternitz and Post-Wintenitz systems and their relation with N-dimensional rational Calogero model with oscillator and Coulomb potentials, paying special attention to their hidden symmetries. Then we show that combining the radial coordinate and momentum in a single complex coordinate in proper way, we get an elegant description for the hidden and dynamical symmetries in these systems related with action-angle variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07489","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":"2026-05-18T00:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1llYSqmhyHw1trqEN0HFpOjHKHS/zP0YHQCD52M3Qmnox7yxHEbsnbOgymjpGgSn8MXyaIBgWjwh8Q7x5uXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:21:41.837024Z"},"content_sha256":"16e1188c1a3cf53fa08d2c5ba29aa1129d7b47f18429275d67ad4338d7495771","schema_version":"1.0","event_id":"sha256:16e1188c1a3cf53fa08d2c5ba29aa1129d7b47f18429275d67ad4338d7495771"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6X6BQYT5T4PM4PMNPE7IFMRKR/bundle.json","state_url":"https://pith.science/pith/K6X6BQYT5T4PM4PMNPE7IFMRKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6X6BQYT5T4PM4PMNPE7IFMRKR/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":"2026-06-03T12:21:41Z","links":{"resolver":"https://pith.science/pith/K6X6BQYT5T4PM4PMNPE7IFMRKR","bundle":"https://pith.science/pith/K6X6BQYT5T4PM4PMNPE7IFMRKR/bundle.json","state":"https://pith.science/pith/K6X6BQYT5T4PM4PMNPE7IFMRKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6X6BQYT5T4PM4PMNPE7IFMRKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K6X6BQYT5T4PM4PMNPE7IFMRKR","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":"3b8d38029a93e8ea2c4e6406eaf2c4e328b7ca68dd7ad27f723a7d860218658f","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-23T14:25:42Z","title_canon_sha256":"03b9b9235c919ebfaf83cfa4f77529ed89bc2f8ca20d2f3831f30d6763875488"},"schema_version":"1.0","source":{"id":"1512.07489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07489","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07489v2","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07489","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"K6X6BQYT5T4P","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K6X6BQYT5T4PM4PM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K6X6BQYT","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:16e1188c1a3cf53fa08d2c5ba29aa1129d7b47f18429275d67ad4338d7495771","target":"graph","created_at":"2026-05-18T00:41:08Z","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 review the classical properties of Tremblay-Turbiner-Winternitz and Post-Wintenitz systems and their relation with N-dimensional rational Calogero model with oscillator and Coulomb potentials, paying special attention to their hidden symmetries. Then we show that combining the radial coordinate and momentum in a single complex coordinate in proper way, we get an elegant description for the hidden and dynamical symmetries in these systems related with action-angle variables.","authors_text":"Armen Nersessian, Hovhannes Shmavonyan, Tigran Hakobyan","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-23T14:25:42Z","title":"Lobachevsky geometry in TTW and PW systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07489","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:c19484cb5d29a389c4a1ae308083beb1c2e5dc1f2fc2f462b8ea6f7bcf47d1c1","target":"record","created_at":"2026-05-18T00:41:08Z","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":"3b8d38029a93e8ea2c4e6406eaf2c4e328b7ca68dd7ad27f723a7d860218658f","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-23T14:25:42Z","title_canon_sha256":"03b9b9235c919ebfaf83cfa4f77529ed89bc2f8ca20d2f3831f30d6763875488"},"schema_version":"1.0","source":{"id":"1512.07489","kind":"arxiv","version":2}},"canonical_sha256":"57afe0c313ecf8f671ec6bc9f415915468d38113afcb9c9811750c868cf8a6d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57afe0c313ecf8f671ec6bc9f415915468d38113afcb9c9811750c868cf8a6d3","first_computed_at":"2026-05-18T00:41:08.308448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:08.308448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMUBKpmINcT9sQ1Jh+piaz1otUAfp+Ghm9Mz413chhL3iqoF8XUQZ+pKGl2vL8W3ms2r4b9TbwrYp9heUfgsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:08.309034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c19484cb5d29a389c4a1ae308083beb1c2e5dc1f2fc2f462b8ea6f7bcf47d1c1","sha256:16e1188c1a3cf53fa08d2c5ba29aa1129d7b47f18429275d67ad4338d7495771"],"state_sha256":"8fa73ff82efc07a0a63c70772fe70ca4a681a0e59ab3c0f204f37d13d8b64556"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENTAjqPaATUZxVDTaSYE3BYEBUb+Sgf3mzQ9gL2RBpjU840Jj4nI0QSMoLYVGYdGbSp0dt/TPjKgH5ErmOj7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:21:41.839010Z","bundle_sha256":"beff36b666c9b9711b4f04b27692bb3441d47607c4590f4c4ed2847cb29b8198"}}