{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:T6GKBCE6LDKSMHWCPIKDJA5UZG","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":"b096bd596ef0d1f62a2f68523473920e17e747c6dc7bd20038c5004119a2bd89","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-08-02T15:20:26Z","title_canon_sha256":"910df60c17c4fb0e5dfdc7a334afbc46569ed1f712a4e7c7fcd0ae031bb94f37"},"schema_version":"1.0","source":{"id":"math-ph/0608008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0608008","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0608008v1","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0608008","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"T6GKBCE6LDKS","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"T6GKBCE6LDKSMHWC","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"T6GKBCE6","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:3492498dadfedc0ee8f4a2281ed956de77a528df1aa98500d277d00442598d05","target":"graph","created_at":"2026-05-18T01:38:32Z","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":"I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard 2-D Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was denoted by ${\\mathbb H}_2 $, gets reduced by the symmetry breaking term, defined by the Hamiltonian \\[ H(\\beta)= \\frac 1 {2m} (p_1^2+p_2^2)- \\frac \\alpha r - \\beta r^{-1/2} \\cos ((\\phi-\\gamma)/2). \\] For this $H (\\beta)$ I define two symmetry loop algebras ${\\mathfrak L}_{i}(\\beta), i=1,2$, by choosing the `basic generators' differently. These ${\\mathfrak L}_{i}","authors_text":"Jamil Daboul","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-08-02T15:20:26Z","title":"Contraction of broken symmetries via Kac-Moody formalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0608008","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:b2b09aaff91f222be3ad666395c6d289e550c92a5b350ed4183ac50723e1ecb7","target":"record","created_at":"2026-05-18T01:38:32Z","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":"b096bd596ef0d1f62a2f68523473920e17e747c6dc7bd20038c5004119a2bd89","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-08-02T15:20:26Z","title_canon_sha256":"910df60c17c4fb0e5dfdc7a334afbc46569ed1f712a4e7c7fcd0ae031bb94f37"},"schema_version":"1.0","source":{"id":"math-ph/0608008","kind":"arxiv","version":1}},"canonical_sha256":"9f8ca0889e58d5261ec27a143483b4c99e79b39cd8e93227c888fe38e3fcad19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f8ca0889e58d5261ec27a143483b4c99e79b39cd8e93227c888fe38e3fcad19","first_computed_at":"2026-05-18T01:38:32.703640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:32.703640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mRmKllvSjMD39lujO506OtaSnxLkc8uqTsW7DrezxSzVQNXriupk915cy3F0Ji1W5aSzmvlTiS1uOG77V38NBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:32.704188Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0608008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2b09aaff91f222be3ad666395c6d289e550c92a5b350ed4183ac50723e1ecb7","sha256:3492498dadfedc0ee8f4a2281ed956de77a528df1aa98500d277d00442598d05"],"state_sha256":"569cab49b33411efcbd83226f73c14fe4d8ad82fca496faa28158c9954cf772d"}