{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BAL2GLOPID2GLP3Y6S6GKGFJRR","short_pith_number":"pith:BAL2GLOP","canonical_record":{"source":{"id":"1312.6087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-20T19:36:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"25b7569d14c6ca641b82f0779dcd40829342fbea23e298e7379cf1cb5ec5c9bc","abstract_canon_sha256":"f8b318544e80c64a4331549d4d9faca387ecb3aae3df8b4983a86ae0709b4950"},"schema_version":"1.0"},"canonical_sha256":"0817a32dcf40f465bf78f4bc6518a98c4483e1c43c79bde78bf32afaa9f8723a","source":{"kind":"arxiv","id":"1312.6087","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6087","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6087v1","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6087","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"BAL2GLOPID2G","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BAL2GLOPID2GLP3Y","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BAL2GLOP","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BAL2GLOPID2GLP3Y6S6GKGFJRR","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-20T19:36:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"25b7569d14c6ca641b82f0779dcd40829342fbea23e298e7379cf1cb5ec5c9bc","abstract_canon_sha256":"f8b318544e80c64a4331549d4d9faca387ecb3aae3df8b4983a86ae0709b4950"},"schema_version":"1.0"},"canonical_sha256":"0817a32dcf40f465bf78f4bc6518a98c4483e1c43c79bde78bf32afaa9f8723a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:07.173222Z","signature_b64":"IABwMwNH1G/1v6mHpRYcOpGVmXPSKpAweUYztA9uxitEPEm9qkiN1Vslx+gtza6bbeeJ8NSDpOFjXSz/7wEPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0817a32dcf40f465bf78f4bc6518a98c4483e1c43c79bde78bf32afaa9f8723a","last_reissued_at":"2026-05-18T03:04:07.172640Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:07.172640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6087","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":"2026-05-18T03:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTiLRyON4x47A5n+X5+RUBIrdR/qrqn4I0lKjVHz51JfGiMwo4ycQ7xp6lORqcq5DZlBV60RYvwiVbQWZYpHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:17:24.542512Z"},"content_sha256":"55e353d253030afd83e388f40b3a4e3b6891d2a6855cb714d7bd437753ace7cd","schema_version":"1.0","event_id":"sha256:55e353d253030afd83e388f40b3a4e3b6891d2a6855cb714d7bd437753ace7cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BAL2GLOPID2GLP3Y6S6GKGFJRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher index focus-focus singularities in the Jayne-Cummings-Gaudin model : symplectic invariants and monodromy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Benoit Doucot (LPTHE), Olivier Babelon (LPTHE)","submitted_at":"2013-12-20T19:36:16Z","abstract_excerpt":"We study the symplectic geometry of the Jaynes-Cummings-Gaudin model with $n=2m-1$ spins. We show that there are focus-focus singularities of maximal Williamson type $(0,0,m)$. We construct the linearized normal flows in the vicinity of such a point and show that soliton type solutions extend them globally on the critical torus. This allows us to compute the leading term in the Taylor expansion of the symplectic invariants and the monodromy associated to this singularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6087","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":"2026-05-18T03:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kFDl7ZDqUe99MAA5QdBnIDYZUs38BMvezXZQw0N7FqCs8dXDzEBRl8nMq1/IYoXtnd85kScGVtqzaARt8OIiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:17:24.543152Z"},"content_sha256":"4cb9eff8d6792d31f2f33d5c4d0796131d5472be4c07ec92f1856b4709c5d257","schema_version":"1.0","event_id":"sha256:4cb9eff8d6792d31f2f33d5c4d0796131d5472be4c07ec92f1856b4709c5d257"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAL2GLOPID2GLP3Y6S6GKGFJRR/bundle.json","state_url":"https://pith.science/pith/BAL2GLOPID2GLP3Y6S6GKGFJRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAL2GLOPID2GLP3Y6S6GKGFJRR/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":"2026-05-27T03:17:24Z","links":{"resolver":"https://pith.science/pith/BAL2GLOPID2GLP3Y6S6GKGFJRR","bundle":"https://pith.science/pith/BAL2GLOPID2GLP3Y6S6GKGFJRR/bundle.json","state":"https://pith.science/pith/BAL2GLOPID2GLP3Y6S6GKGFJRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAL2GLOPID2GLP3Y6S6GKGFJRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BAL2GLOPID2GLP3Y6S6GKGFJRR","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":"f8b318544e80c64a4331549d4d9faca387ecb3aae3df8b4983a86ae0709b4950","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-20T19:36:16Z","title_canon_sha256":"25b7569d14c6ca641b82f0779dcd40829342fbea23e298e7379cf1cb5ec5c9bc"},"schema_version":"1.0","source":{"id":"1312.6087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6087","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6087v1","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6087","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"BAL2GLOPID2G","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BAL2GLOPID2GLP3Y","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BAL2GLOP","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:4cb9eff8d6792d31f2f33d5c4d0796131d5472be4c07ec92f1856b4709c5d257","target":"graph","created_at":"2026-05-18T03:04:07Z","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 study the symplectic geometry of the Jaynes-Cummings-Gaudin model with $n=2m-1$ spins. We show that there are focus-focus singularities of maximal Williamson type $(0,0,m)$. We construct the linearized normal flows in the vicinity of such a point and show that soliton type solutions extend them globally on the critical torus. This allows us to compute the leading term in the Taylor expansion of the symplectic invariants and the monodromy associated to this singularity.","authors_text":"Benoit Doucot (LPTHE), Olivier Babelon (LPTHE)","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-20T19:36:16Z","title":"Higher index focus-focus singularities in the Jayne-Cummings-Gaudin model : symplectic invariants and monodromy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6087","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":"sha256:55e353d253030afd83e388f40b3a4e3b6891d2a6855cb714d7bd437753ace7cd","target":"record","created_at":"2026-05-18T03:04:07Z","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":"f8b318544e80c64a4331549d4d9faca387ecb3aae3df8b4983a86ae0709b4950","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-20T19:36:16Z","title_canon_sha256":"25b7569d14c6ca641b82f0779dcd40829342fbea23e298e7379cf1cb5ec5c9bc"},"schema_version":"1.0","source":{"id":"1312.6087","kind":"arxiv","version":1}},"canonical_sha256":"0817a32dcf40f465bf78f4bc6518a98c4483e1c43c79bde78bf32afaa9f8723a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0817a32dcf40f465bf78f4bc6518a98c4483e1c43c79bde78bf32afaa9f8723a","first_computed_at":"2026-05-18T03:04:07.172640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:07.172640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IABwMwNH1G/1v6mHpRYcOpGVmXPSKpAweUYztA9uxitEPEm9qkiN1Vslx+gtza6bbeeJ8NSDpOFjXSz/7wEPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:07.173222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55e353d253030afd83e388f40b3a4e3b6891d2a6855cb714d7bd437753ace7cd","sha256:4cb9eff8d6792d31f2f33d5c4d0796131d5472be4c07ec92f1856b4709c5d257"],"state_sha256":"9a4572f667c2d9724462919e1829e94ba2b58696a08f200b9f9abfb6a7098b4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qGu3dqb9nVr1UMBAWypQ0Wy4KpzStEPYQ6Se7QePy33X9BUiT87kMJoe539HEivxluqVnLt5rwrRWto/R5nRAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:17:24.545829Z","bundle_sha256":"49c39b1df9dc93f9e913fa401c4647112bc0d1374fd854b69c3ef3a2f0d75cb4"}}