{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YYIBXZKLMWTYLNBGJMETCRFCCG","short_pith_number":"pith:YYIBXZKL","canonical_record":{"source":{"id":"1307.1986","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-08T08:59:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8cbeec8f439e9b9ff2fb110849272c41b913464f7c59cf921b844ee67f11729a","abstract_canon_sha256":"67cab86d47caa201871fa18a9d14cfaaafe6c9947866b4e0923712a6f921e048"},"schema_version":"1.0"},"canonical_sha256":"c6101be54b65a785b4264b093144a211ac9e22016b8c447ca636a14f541afdf4","source":{"kind":"arxiv","id":"1307.1986","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1986","created_at":"2026-05-18T01:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1986v1","created_at":"2026-05-18T01:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1986","created_at":"2026-05-18T01:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"YYIBXZKLMWTY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YYIBXZKLMWTYLNBG","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YYIBXZKL","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YYIBXZKLMWTYLNBGJMETCRFCCG","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1986","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-08T08:59:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8cbeec8f439e9b9ff2fb110849272c41b913464f7c59cf921b844ee67f11729a","abstract_canon_sha256":"67cab86d47caa201871fa18a9d14cfaaafe6c9947866b4e0923712a6f921e048"},"schema_version":"1.0"},"canonical_sha256":"c6101be54b65a785b4264b093144a211ac9e22016b8c447ca636a14f541afdf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:58.824148Z","signature_b64":"rVEQkmjmj+HrEcdBJ+9B4NzfadgqcNH/WMlTzs5aj4mVPRKiUNAbUb01IJr2GUsPIiV4LF9GrUPQILw2YkkFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6101be54b65a785b4264b093144a211ac9e22016b8c447ca636a14f541afdf4","last_reissued_at":"2026-05-18T01:48:58.823564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:58.823564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1986","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":"2026-05-18T01:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yrsw8YyqSLvBOB3v3cb1eKtj4TBJnz8q0ymdbWT7ySMCCkn9MX2ysh90i4It9QMH8yYmQKxgJHWUMALJ6HPXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:10:47.304574Z"},"content_sha256":"fd6589418d1b03027705e110a019ab746a40616df7ba970b9d0fb8cc936101ec","schema_version":"1.0","event_id":"sha256:fd6589418d1b03027705e110a019ab746a40616df7ba970b9d0fb8cc936101ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YYIBXZKLMWTYLNBGJMETCRFCCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized notions of symmetry of ODE's and reduction procedures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Giampaolo Cicogna","submitted_at":"2013-07-08T08:59:09Z","abstract_excerpt":"This paper describes the notion of \\sigma -symmetry, which extends the one of \\lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider orbital symmetries, which give rise to a different form of reduction of dynamical systems. Finally, we discuss how dynamical systems can be transformed into higher-order ordinary differential equations, and how these symmetry properties of the dynamical systems can be transferred into reduction properties of the corresponding ordinary differential equations. Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1986","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":"2026-05-18T01:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZ9gh2lghZDwsdFo9hFlO5IFKqXAXYMK/MGUPLgOZZYXhTPflm3Pt2NYUra7iOJM7AesR6/X913JVHMqLlOfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:10:47.304921Z"},"content_sha256":"2e0483a9aa2c5ce1f1541e150c7f37bc7318f25e7440bcb51064eb1c1c40fb5d","schema_version":"1.0","event_id":"sha256:2e0483a9aa2c5ce1f1541e150c7f37bc7318f25e7440bcb51064eb1c1c40fb5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYIBXZKLMWTYLNBGJMETCRFCCG/bundle.json","state_url":"https://pith.science/pith/YYIBXZKLMWTYLNBGJMETCRFCCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYIBXZKLMWTYLNBGJMETCRFCCG/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":"2026-06-23T18:10:47Z","links":{"resolver":"https://pith.science/pith/YYIBXZKLMWTYLNBGJMETCRFCCG","bundle":"https://pith.science/pith/YYIBXZKLMWTYLNBGJMETCRFCCG/bundle.json","state":"https://pith.science/pith/YYIBXZKLMWTYLNBGJMETCRFCCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYIBXZKLMWTYLNBGJMETCRFCCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YYIBXZKLMWTYLNBGJMETCRFCCG","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":"67cab86d47caa201871fa18a9d14cfaaafe6c9947866b4e0923712a6f921e048","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-08T08:59:09Z","title_canon_sha256":"8cbeec8f439e9b9ff2fb110849272c41b913464f7c59cf921b844ee67f11729a"},"schema_version":"1.0","source":{"id":"1307.1986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1986","created_at":"2026-05-18T01:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1986v1","created_at":"2026-05-18T01:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1986","created_at":"2026-05-18T01:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"YYIBXZKLMWTY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YYIBXZKLMWTYLNBG","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YYIBXZKL","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:2e0483a9aa2c5ce1f1541e150c7f37bc7318f25e7440bcb51064eb1c1c40fb5d","target":"graph","created_at":"2026-05-18T01:48:58Z","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":"This paper describes the notion of \\sigma -symmetry, which extends the one of \\lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider orbital symmetries, which give rise to a different form of reduction of dynamical systems. Finally, we discuss how dynamical systems can be transformed into higher-order ordinary differential equations, and how these symmetry properties of the dynamical systems can be transferred into reduction properties of the corresponding ordinary differential equations. Ma","authors_text":"Giampaolo Cicogna","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-08T08:59:09Z","title":"Generalized notions of symmetry of ODE's and reduction procedures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1986","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:fd6589418d1b03027705e110a019ab746a40616df7ba970b9d0fb8cc936101ec","target":"record","created_at":"2026-05-18T01:48:58Z","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":"67cab86d47caa201871fa18a9d14cfaaafe6c9947866b4e0923712a6f921e048","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-08T08:59:09Z","title_canon_sha256":"8cbeec8f439e9b9ff2fb110849272c41b913464f7c59cf921b844ee67f11729a"},"schema_version":"1.0","source":{"id":"1307.1986","kind":"arxiv","version":1}},"canonical_sha256":"c6101be54b65a785b4264b093144a211ac9e22016b8c447ca636a14f541afdf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6101be54b65a785b4264b093144a211ac9e22016b8c447ca636a14f541afdf4","first_computed_at":"2026-05-18T01:48:58.823564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:58.823564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVEQkmjmj+HrEcdBJ+9B4NzfadgqcNH/WMlTzs5aj4mVPRKiUNAbUb01IJr2GUsPIiV4LF9GrUPQILw2YkkFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:58.824148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd6589418d1b03027705e110a019ab746a40616df7ba970b9d0fb8cc936101ec","sha256:2e0483a9aa2c5ce1f1541e150c7f37bc7318f25e7440bcb51064eb1c1c40fb5d"],"state_sha256":"23a76512ba03b9ac4ef8d301d7dafab3e6580d119ef5133f4f04ab54f1b2cf5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dyy4YHehliOPA5xpRnpPnTWX0T3lfPYo2CAkuKLQ0wN+8co3ZeHwChJGF61zQukeaV1OWtvzuhr8P8z8OFFrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:10:47.307357Z","bundle_sha256":"2b15229552aba8f59153e2b5174241ff4f1b97b933324d39d3648ba211af6a6c"}}