{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SJSVUUHDHTZAH4OQ2OW6HW5UMG","short_pith_number":"pith:SJSVUUHD","canonical_record":{"source":{"id":"1405.4340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-17T02:18:42Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"3f3ded0d3e7115d41f064681d08bdea74f3794586c903f7be34661661160cc02","abstract_canon_sha256":"5a5f2da21e3ceb2c638be1057e23f1ad094f38268aa6d9a5fcc7f228caf7af13"},"schema_version":"1.0"},"canonical_sha256":"92655a50e33cf203f1d0d3ade3dbb461a59141627a7a64b673bd290843626309","source":{"kind":"arxiv","id":"1405.4340","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4340","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4340v1","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4340","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"SJSVUUHDHTZA","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SJSVUUHDHTZAH4OQ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SJSVUUHD","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SJSVUUHDHTZAH4OQ2OW6HW5UMG","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-17T02:18:42Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"3f3ded0d3e7115d41f064681d08bdea74f3794586c903f7be34661661160cc02","abstract_canon_sha256":"5a5f2da21e3ceb2c638be1057e23f1ad094f38268aa6d9a5fcc7f228caf7af13"},"schema_version":"1.0"},"canonical_sha256":"92655a50e33cf203f1d0d3ade3dbb461a59141627a7a64b673bd290843626309","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:41.118399Z","signature_b64":"UHxiKSyZMxxyaZ5yfN+e0xU0A5nIT9jmB8MNYx+ncOJAGi56Pv5N24pK7mbF2F76dYSlgI80AhhtvQ/gaSmcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92655a50e33cf203f1d0d3ade3dbb461a59141627a7a64b673bd290843626309","last_reissued_at":"2026-05-18T02:51:41.117996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:41.117996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4340","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":"2026-05-18T02:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zr8H3LYDDS85dtg36v/cigb4PrCiiF58/IJpcWxYC8KzOgGib99CK5KHC+X1i5zqlC7RM/Rbi0x3gVSQeYikBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:38:23.983606Z"},"content_sha256":"5fa20d98b9e82fc68c0a25452de2db9999c3565cb98bc1f5ae556ece9408b666","schema_version":"1.0","event_id":"sha256:5fa20d98b9e82fc68c0a25452de2db9999c3565cb98bc1f5ae556ece9408b666"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SJSVUUHDHTZAH4OQ2OW6HW5UMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double Lie algebras, semidirect product, and integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"H. Montani, S. Capriotti","submitted_at":"2014-05-17T02:18:42Z","abstract_excerpt":"We study integrable systems on double Lie algebras in absence of Ad-invariant bilinear form by passing to the semidirect product with the $\\tau $-representation. We show that in this stage a natural Ad-invariant bilinear form does exist, allowing for a straightforward application of the AKS theory, and giving rise to Manin triple structure, thus bringing the problem to the realm of Lie bialgebras and Poisson-Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4340","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":"2026-05-18T02:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6yFQlSeE468UwUe3KHiU2u6QASai1u4nACX2oP0gAIHFOxhCxSmw3KtmkKx2WZgb+8GMUt65mQyUdRE/ugKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:38:23.983956Z"},"content_sha256":"dab79fe34ac6d5c76853c8b60a12cf89a15fdc91f4a3b7ee7cbcd77fbeaea0c2","schema_version":"1.0","event_id":"sha256:dab79fe34ac6d5c76853c8b60a12cf89a15fdc91f4a3b7ee7cbcd77fbeaea0c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJSVUUHDHTZAH4OQ2OW6HW5UMG/bundle.json","state_url":"https://pith.science/pith/SJSVUUHDHTZAH4OQ2OW6HW5UMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJSVUUHDHTZAH4OQ2OW6HW5UMG/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":"2026-06-22T22:38:23Z","links":{"resolver":"https://pith.science/pith/SJSVUUHDHTZAH4OQ2OW6HW5UMG","bundle":"https://pith.science/pith/SJSVUUHDHTZAH4OQ2OW6HW5UMG/bundle.json","state":"https://pith.science/pith/SJSVUUHDHTZAH4OQ2OW6HW5UMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJSVUUHDHTZAH4OQ2OW6HW5UMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SJSVUUHDHTZAH4OQ2OW6HW5UMG","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":"5a5f2da21e3ceb2c638be1057e23f1ad094f38268aa6d9a5fcc7f228caf7af13","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-17T02:18:42Z","title_canon_sha256":"3f3ded0d3e7115d41f064681d08bdea74f3794586c903f7be34661661160cc02"},"schema_version":"1.0","source":{"id":"1405.4340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4340","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4340v1","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4340","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"SJSVUUHDHTZA","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SJSVUUHDHTZAH4OQ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SJSVUUHD","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:dab79fe34ac6d5c76853c8b60a12cf89a15fdc91f4a3b7ee7cbcd77fbeaea0c2","target":"graph","created_at":"2026-05-18T02:51:41Z","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 integrable systems on double Lie algebras in absence of Ad-invariant bilinear form by passing to the semidirect product with the $\\tau $-representation. We show that in this stage a natural Ad-invariant bilinear form does exist, allowing for a straightforward application of the AKS theory, and giving rise to Manin triple structure, thus bringing the problem to the realm of Lie bialgebras and Poisson-Lie groups.","authors_text":"H. Montani, S. Capriotti","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-17T02:18:42Z","title":"Double Lie algebras, semidirect product, and integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4340","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":"sha256:5fa20d98b9e82fc68c0a25452de2db9999c3565cb98bc1f5ae556ece9408b666","target":"record","created_at":"2026-05-18T02:51:41Z","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":"5a5f2da21e3ceb2c638be1057e23f1ad094f38268aa6d9a5fcc7f228caf7af13","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-17T02:18:42Z","title_canon_sha256":"3f3ded0d3e7115d41f064681d08bdea74f3794586c903f7be34661661160cc02"},"schema_version":"1.0","source":{"id":"1405.4340","kind":"arxiv","version":1}},"canonical_sha256":"92655a50e33cf203f1d0d3ade3dbb461a59141627a7a64b673bd290843626309","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92655a50e33cf203f1d0d3ade3dbb461a59141627a7a64b673bd290843626309","first_computed_at":"2026-05-18T02:51:41.117996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:41.117996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UHxiKSyZMxxyaZ5yfN+e0xU0A5nIT9jmB8MNYx+ncOJAGi56Pv5N24pK7mbF2F76dYSlgI80AhhtvQ/gaSmcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:41.118399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fa20d98b9e82fc68c0a25452de2db9999c3565cb98bc1f5ae556ece9408b666","sha256:dab79fe34ac6d5c76853c8b60a12cf89a15fdc91f4a3b7ee7cbcd77fbeaea0c2"],"state_sha256":"7ce5b3c69d0b4db0cdb5f32f23b2c53652605212d9a089437b8b9d6b20a73832"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"If+zStqsNHtoM6UpFqHei++pcM+f8e7CGC+FjEvdKE12FSBKwCd+Dnmn4UDw0D0mIqIJxFknLSP8FbTyRvRICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:38:23.985949Z","bundle_sha256":"f0d341a49728c50b1c6754e492cc4a06b0bc8df87abe28b6dd4b3cba72117d08"}}