{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3S4CDS6JJCW7TITOG4KPWSK3GV","short_pith_number":"pith:3S4CDS6J","schema_version":"1.0","canonical_sha256":"dcb821cbc948adf9a26e3714fb495b356c157d0b19e92d11fb982f7a4b836a85","source":{"kind":"arxiv","id":"1711.08530","version":1},"attestation_state":"computed","paper":{"title":"Alternative Angle-Based Approach to the KS-Map. An Interpretation Through Symmetry and Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Francisco Crespo, Sebastian Ferrer","submitted_at":"2017-11-22T22:47:56Z","abstract_excerpt":"The $\\mathcal{KS}$ map is revisited in terms of an $S^1$-action in $T^*\\mathbb{H}_0$ with the bilinear function as the associated momentum map. Indeed, the $\\mathcal{KS}$ transformation maps the $S^1$-fibers related to the mentioned action to single points. By means of this perspective a second twin-bilinear function is obtained with an analogous $S^1$-action. We also show that the connection between the 4-D isotropic harmonic oscillator and the spatial Kepler systems can be done in a straightforward way after regularization and through the extension to 4 degrees of freedom of the Euler angles"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.08530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-11-22T22:47:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"002441503b7b21555866785c7716ded4c9b0a3ada09d486a41761c353c6c4657","abstract_canon_sha256":"b984a81e6fa1ddf2e434d12298454292a2acc8028a93b39d23866fdd31af1159"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:44.763575Z","signature_b64":"jw6RjZMEh8lp9oLZBwkiXSakihp5zfM/oyi448OuFRvIgh4iVBpoXJESxzeDKOAfGXsJ4TuUxXj7bFsfIdR+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcb821cbc948adf9a26e3714fb495b356c157d0b19e92d11fb982f7a4b836a85","last_reissued_at":"2026-05-18T00:29:44.762949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:44.762949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alternative Angle-Based Approach to the KS-Map. An Interpretation Through Symmetry and Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Francisco Crespo, Sebastian Ferrer","submitted_at":"2017-11-22T22:47:56Z","abstract_excerpt":"The $\\mathcal{KS}$ map is revisited in terms of an $S^1$-action in $T^*\\mathbb{H}_0$ with the bilinear function as the associated momentum map. Indeed, the $\\mathcal{KS}$ transformation maps the $S^1$-fibers related to the mentioned action to single points. By means of this perspective a second twin-bilinear function is obtained with an analogous $S^1$-action. We also show that the connection between the 4-D isotropic harmonic oscillator and the spatial Kepler systems can be done in a straightforward way after regularization and through the extension to 4 degrees of freedom of the Euler angles"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08530","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.08530","created_at":"2026-05-18T00:29:44.763024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.08530v1","created_at":"2026-05-18T00:29:44.763024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08530","created_at":"2026-05-18T00:29:44.763024+00:00"},{"alias_kind":"pith_short_12","alias_value":"3S4CDS6JJCW7","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3S4CDS6JJCW7TITO","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3S4CDS6J","created_at":"2026-05-18T12:30:58.224056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV","json":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV.json","graph_json":"https://pith.science/api/pith-number/3S4CDS6JJCW7TITOG4KPWSK3GV/graph.json","events_json":"https://pith.science/api/pith-number/3S4CDS6JJCW7TITOG4KPWSK3GV/events.json","paper":"https://pith.science/paper/3S4CDS6J"},"agent_actions":{"view_html":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV","download_json":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV.json","view_paper":"https://pith.science/paper/3S4CDS6J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.08530&json=true","fetch_graph":"https://pith.science/api/pith-number/3S4CDS6JJCW7TITOG4KPWSK3GV/graph.json","fetch_events":"https://pith.science/api/pith-number/3S4CDS6JJCW7TITOG4KPWSK3GV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV/action/storage_attestation","attest_author":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV/action/author_attestation","sign_citation":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV/action/citation_signature","submit_replication":"https://pith.science/pith/3S4CDS6JJCW7TITOG4KPWSK3GV/action/replication_record"}},"created_at":"2026-05-18T00:29:44.763024+00:00","updated_at":"2026-05-18T00:29:44.763024+00:00"}