{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FXZ4K5GR7IUQFOCCPSUUMEGRC2","short_pith_number":"pith:FXZ4K5GR","canonical_record":{"source":{"id":"1210.3647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-12T21:36:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f278ee8e9beff5e3262cca1e7932018beebd415e0f9c9bcbcec7b3912089394b","abstract_canon_sha256":"05e69d5881508e4a506604e1e5e305a0ca4080fd182879ce9903d45c64da1921"},"schema_version":"1.0"},"canonical_sha256":"2df3c574d1fa2902b8427ca94610d11680d89372089df750a35b09be84273b54","source":{"kind":"arxiv","id":"1210.3647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3647","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3647v1","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3647","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"FXZ4K5GR7IUQ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FXZ4K5GR7IUQFOCC","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FXZ4K5GR","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FXZ4K5GR7IUQFOCCPSUUMEGRC2","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-12T21:36:56Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f278ee8e9beff5e3262cca1e7932018beebd415e0f9c9bcbcec7b3912089394b","abstract_canon_sha256":"05e69d5881508e4a506604e1e5e305a0ca4080fd182879ce9903d45c64da1921"},"schema_version":"1.0"},"canonical_sha256":"2df3c574d1fa2902b8427ca94610d11680d89372089df750a35b09be84273b54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:55.884487Z","signature_b64":"s0Hnh7KJGmpr9h7+uh6uyMQhF/EoGbWq2Lx/0Bv57s0wnEcqTQLN76rhlgNZDCRtYrY13Zf3zn+LnW9P+oSBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2df3c574d1fa2902b8427ca94610d11680d89372089df750a35b09be84273b54","last_reissued_at":"2026-05-18T01:53:55.883772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:55.883772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3647","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":"2026-05-18T01:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2tT6BfJ/mGl8MDgKVnYBKnZv7tO2Q5igFscmTlITVLix651tLzVeitriSMdFVNXhaK6tW86QWr1VIgwBYdoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:41:12.215626Z"},"content_sha256":"296a1f6e47766995d1cc207e645f753597ddf8eefa75d62b4ed85ae47de4ad54","schema_version":"1.0","event_id":"sha256:296a1f6e47766995d1cc207e645f753597ddf8eefa75d62b4ed85ae47de4ad54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FXZ4K5GR7IUQFOCCPSUUMEGRC2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of \\lambda-symmetry reduction for systems of ODEs: \\sigma-symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher","submitted_at":"2012-10-12T21:36:56Z","abstract_excerpt":"We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the \"invariants by differentiation\" property, and can hence be used to reduce ODEs satisfying suitable invariance conditions in a fully algorithmic way, similarly to what happens for standard prolongations and symmetries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3647","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":"2026-05-18T01:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaYh0m7EcSW2xs6X1EZnfk0b4GyCj1oiADgThED6haH0I2KNRTGtbjoYnGD7ecRauGrwYWgdoeu//fKwiiYXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:41:12.215974Z"},"content_sha256":"bb694ec91d30fc4a25f48b87a70f4c039353849a04a76f59f94cda95f1d3c920","schema_version":"1.0","event_id":"sha256:bb694ec91d30fc4a25f48b87a70f4c039353849a04a76f59f94cda95f1d3c920"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXZ4K5GR7IUQFOCCPSUUMEGRC2/bundle.json","state_url":"https://pith.science/pith/FXZ4K5GR7IUQFOCCPSUUMEGRC2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXZ4K5GR7IUQFOCCPSUUMEGRC2/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":"2026-06-23T15:41:12Z","links":{"resolver":"https://pith.science/pith/FXZ4K5GR7IUQFOCCPSUUMEGRC2","bundle":"https://pith.science/pith/FXZ4K5GR7IUQFOCCPSUUMEGRC2/bundle.json","state":"https://pith.science/pith/FXZ4K5GR7IUQFOCCPSUUMEGRC2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXZ4K5GR7IUQFOCCPSUUMEGRC2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FXZ4K5GR7IUQFOCCPSUUMEGRC2","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":"05e69d5881508e4a506604e1e5e305a0ca4080fd182879ce9903d45c64da1921","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-12T21:36:56Z","title_canon_sha256":"f278ee8e9beff5e3262cca1e7932018beebd415e0f9c9bcbcec7b3912089394b"},"schema_version":"1.0","source":{"id":"1210.3647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3647","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3647v1","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3647","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"FXZ4K5GR7IUQ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FXZ4K5GR7IUQFOCC","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FXZ4K5GR","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:bb694ec91d30fc4a25f48b87a70f4c039353849a04a76f59f94cda95f1d3c920","target":"graph","created_at":"2026-05-18T01:53:55Z","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 consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the \"invariants by differentiation\" property, and can hence be used to reduce ODEs satisfying suitable invariance conditions in a fully algorithmic way, similarly to what happens for standard prolongations and symmetries.","authors_text":"Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-12T21:36:56Z","title":"A generalization of \\lambda-symmetry reduction for systems of ODEs: \\sigma-symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3647","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":"sha256:296a1f6e47766995d1cc207e645f753597ddf8eefa75d62b4ed85ae47de4ad54","target":"record","created_at":"2026-05-18T01:53:55Z","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":"05e69d5881508e4a506604e1e5e305a0ca4080fd182879ce9903d45c64da1921","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-12T21:36:56Z","title_canon_sha256":"f278ee8e9beff5e3262cca1e7932018beebd415e0f9c9bcbcec7b3912089394b"},"schema_version":"1.0","source":{"id":"1210.3647","kind":"arxiv","version":1}},"canonical_sha256":"2df3c574d1fa2902b8427ca94610d11680d89372089df750a35b09be84273b54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2df3c574d1fa2902b8427ca94610d11680d89372089df750a35b09be84273b54","first_computed_at":"2026-05-18T01:53:55.883772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:55.883772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s0Hnh7KJGmpr9h7+uh6uyMQhF/EoGbWq2Lx/0Bv57s0wnEcqTQLN76rhlgNZDCRtYrY13Zf3zn+LnW9P+oSBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:55.884487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:296a1f6e47766995d1cc207e645f753597ddf8eefa75d62b4ed85ae47de4ad54","sha256:bb694ec91d30fc4a25f48b87a70f4c039353849a04a76f59f94cda95f1d3c920"],"state_sha256":"fbd4396f4e02bf1ab4e75a9960ca726f2dd97a96cd56b054888848af5e825c4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/mavYO80ui4GtjoASDhoIXSYM52/8cNLNNa7f0KK84fGNCP+38eLCN3Hn+NDVXoMDVs/K+ZOdODYqwqFiROCBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:41:12.217933Z","bundle_sha256":"a3b79f3d108aac3ee2cc4765976af43104b8a31b4197cdc630aba0afeca2cbb2"}}