{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GNKZUMDZQ73ORE7DATXSQ5D3TY","short_pith_number":"pith:GNKZUMDZ","canonical_record":{"source":{"id":"1110.3409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-15T12:59:16Z","cross_cats_sorted":["math.GR","math.MP","nlin.SI"],"title_canon_sha256":"585cdcccab4e1cd2cc2122c9e98f502888e4c18d341c13746d0180005edb90f4","abstract_canon_sha256":"882bb516e3a2fe7f1781ee7e24641ebcc7b095d49b66496e1fc86f491589781f"},"schema_version":"1.0"},"canonical_sha256":"33559a307987f6e893e304ef28747b9e2d8539ca24dcd81d23dc75dde526b80c","source":{"kind":"arxiv","id":"1110.3409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3409","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3409v1","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3409","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"GNKZUMDZQ73O","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GNKZUMDZQ73ORE7D","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GNKZUMDZ","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GNKZUMDZQ73ORE7DATXSQ5D3TY","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-15T12:59:16Z","cross_cats_sorted":["math.GR","math.MP","nlin.SI"],"title_canon_sha256":"585cdcccab4e1cd2cc2122c9e98f502888e4c18d341c13746d0180005edb90f4","abstract_canon_sha256":"882bb516e3a2fe7f1781ee7e24641ebcc7b095d49b66496e1fc86f491589781f"},"schema_version":"1.0"},"canonical_sha256":"33559a307987f6e893e304ef28747b9e2d8539ca24dcd81d23dc75dde526b80c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:12.024245Z","signature_b64":"SbXWTuXm89Xrm9hVDEU1nswD4RXYY5/vWeMy6bRIFQ+iYDTAn9zBBlmmsb7oj7nQGKq5U4COMziagZGhzhAnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33559a307987f6e893e304ef28747b9e2d8539ca24dcd81d23dc75dde526b80c","last_reissued_at":"2026-05-18T02:00:12.023766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:12.023766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3409","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":"2026-05-18T02:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lrEwJEPi0jaOwM9paWZDGODu7GoJx1bO6AWFmasTK9HaO5OC52fmGl5eTnTD5kp4IsvqAiKT8blCGrDBLFVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T00:34:17.519410Z"},"content_sha256":"62f088c6ef2de4ba0b343b8f0502144a6fab00400ec4a0237f2953adf58aa014","schema_version":"1.0","event_id":"sha256:62f088c6ef2de4ba0b343b8f0502144a6fab00400ec4a0237f2953adf58aa014"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GNKZUMDZQ73ORE7DATXSQ5D3TY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contact transformations for difference schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Decio Levi, Pavel Winternitz, Zora Thomova","submitted_at":"2011-10-15T12:59:16Z","abstract_excerpt":"We define a class of transformations of the dependent and independent variables in an ordinary difference scheme. The transformations leave the solution set of the system invariant and reduces to a group of contact transformations in the continuous limit. We use a simple example to show that the class is not empty and that such \"contact transformations for discrete systems\" genuinely exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3409","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":"2026-05-18T02:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9RG7yFhlE4Bn3fQwx/3j/D1RIQkhLcNfC/QwGhXaAXdfjt9zZGYAo1sSAcl+2MISJzgEKxGjUiL8vwKfpC73Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T00:34:17.519755Z"},"content_sha256":"5021499036f3a8d2951477a04fe45c7403918d00c6823c2c80c55447f3d9f4d9","schema_version":"1.0","event_id":"sha256:5021499036f3a8d2951477a04fe45c7403918d00c6823c2c80c55447f3d9f4d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNKZUMDZQ73ORE7DATXSQ5D3TY/bundle.json","state_url":"https://pith.science/pith/GNKZUMDZQ73ORE7DATXSQ5D3TY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNKZUMDZQ73ORE7DATXSQ5D3TY/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":"2026-06-24T00:34:17Z","links":{"resolver":"https://pith.science/pith/GNKZUMDZQ73ORE7DATXSQ5D3TY","bundle":"https://pith.science/pith/GNKZUMDZQ73ORE7DATXSQ5D3TY/bundle.json","state":"https://pith.science/pith/GNKZUMDZQ73ORE7DATXSQ5D3TY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNKZUMDZQ73ORE7DATXSQ5D3TY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GNKZUMDZQ73ORE7DATXSQ5D3TY","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":"882bb516e3a2fe7f1781ee7e24641ebcc7b095d49b66496e1fc86f491589781f","cross_cats_sorted":["math.GR","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-15T12:59:16Z","title_canon_sha256":"585cdcccab4e1cd2cc2122c9e98f502888e4c18d341c13746d0180005edb90f4"},"schema_version":"1.0","source":{"id":"1110.3409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3409","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3409v1","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3409","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"GNKZUMDZQ73O","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GNKZUMDZQ73ORE7D","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GNKZUMDZ","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:5021499036f3a8d2951477a04fe45c7403918d00c6823c2c80c55447f3d9f4d9","target":"graph","created_at":"2026-05-18T02:00:12Z","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 define a class of transformations of the dependent and independent variables in an ordinary difference scheme. The transformations leave the solution set of the system invariant and reduces to a group of contact transformations in the continuous limit. We use a simple example to show that the class is not empty and that such \"contact transformations for discrete systems\" genuinely exist.","authors_text":"Decio Levi, Pavel Winternitz, Zora Thomova","cross_cats":["math.GR","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-15T12:59:16Z","title":"Contact transformations for difference schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3409","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":"sha256:62f088c6ef2de4ba0b343b8f0502144a6fab00400ec4a0237f2953adf58aa014","target":"record","created_at":"2026-05-18T02:00:12Z","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":"882bb516e3a2fe7f1781ee7e24641ebcc7b095d49b66496e1fc86f491589781f","cross_cats_sorted":["math.GR","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-15T12:59:16Z","title_canon_sha256":"585cdcccab4e1cd2cc2122c9e98f502888e4c18d341c13746d0180005edb90f4"},"schema_version":"1.0","source":{"id":"1110.3409","kind":"arxiv","version":1}},"canonical_sha256":"33559a307987f6e893e304ef28747b9e2d8539ca24dcd81d23dc75dde526b80c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33559a307987f6e893e304ef28747b9e2d8539ca24dcd81d23dc75dde526b80c","first_computed_at":"2026-05-18T02:00:12.023766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:12.023766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SbXWTuXm89Xrm9hVDEU1nswD4RXYY5/vWeMy6bRIFQ+iYDTAn9zBBlmmsb7oj7nQGKq5U4COMziagZGhzhAnCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:12.024245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62f088c6ef2de4ba0b343b8f0502144a6fab00400ec4a0237f2953adf58aa014","sha256:5021499036f3a8d2951477a04fe45c7403918d00c6823c2c80c55447f3d9f4d9"],"state_sha256":"e338341be7318fc3653fceb4f49de5ad37fced28ccb72cc291cc6657ed89b2ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dT5heRUKHGMFdK/ZG4HYOxoexT0ZycNXtDtGdPktjXMphtszJzm2n4bR0lFXn7Vcd6K8KTXc+cUJfWNuPstEBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T00:34:17.521629Z","bundle_sha256":"a47b741493f1b82328a5ec340c38a7c2b1d3b9dba06180b20f7405e3a208ec74"}}