{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CRIXRU2XNB6V53HBHO3ZX3B6R6","short_pith_number":"pith:CRIXRU2X","canonical_record":{"source":{"id":"1407.4043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-15T16:29:06Z","cross_cats_sorted":["math.MP","math.NA","nlin.SI"],"title_canon_sha256":"bbbaf375f8228427a0639e18b1ac40982e3c9660bf4aac728fc699718b98a366","abstract_canon_sha256":"cdf92d6611547415d9701d0bd135a6a0c2cc151163d38da5dee9b1360ae22e0d"},"schema_version":"1.0"},"canonical_sha256":"145178d357687d5eece13bb79bec3e8fa3e33afdf0d4d2f00683acc66164dece","source":{"kind":"arxiv","id":"1407.4043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4043","created_at":"2026-05-18T01:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4043v1","created_at":"2026-05-18T01:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4043","created_at":"2026-05-18T01:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"CRIXRU2XNB6V","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CRIXRU2XNB6V53HB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CRIXRU2X","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CRIXRU2XNB6V53HBHO3ZX3B6R6","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-15T16:29:06Z","cross_cats_sorted":["math.MP","math.NA","nlin.SI"],"title_canon_sha256":"bbbaf375f8228427a0639e18b1ac40982e3c9660bf4aac728fc699718b98a366","abstract_canon_sha256":"cdf92d6611547415d9701d0bd135a6a0c2cc151163d38da5dee9b1360ae22e0d"},"schema_version":"1.0"},"canonical_sha256":"145178d357687d5eece13bb79bec3e8fa3e33afdf0d4d2f00683acc66164dece","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:36.575166Z","signature_b64":"megmDDlBjerW/1G0CtcudQ0hBgfTL3G0Khv0bdTdF6XNIVgCyhHKkKOipSshEHPK1cqwAmx5j4o1zWlQeF4WBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"145178d357687d5eece13bb79bec3e8fa3e33afdf0d4d2f00683acc66164dece","last_reissued_at":"2026-05-18T01:42:36.574723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:36.574723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4043","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":"2026-05-18T01:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxP6GIck9gum6X50VKGEJtijCtoy5C5FnLWj/vtQNcGOf2UPrMY/fkS8eR0SSj4sghb6H4CWe3LKZihXki2zBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:16:23.879270Z"},"content_sha256":"c7727b994ee323a88d5af69790e3a0c1e2850934224f60d82bbac488a447ce53","schema_version":"1.0","event_id":"sha256:c7727b994ee323a88d5af69790e3a0c1e2850934224f60d82bbac488a447ce53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CRIXRU2XNB6V53HBHO3ZX3B6R6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie-point symmetries of the discrete Liouville equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Decio Levi, Luigi Martina, Pavel Winternitz","submitted_at":"2014-07-15T16:29:06Z","abstract_excerpt":"The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point symmetries. We do however construct a difference system approximating the Liouville equation that is invariant under the maximal finite subalgebra $ SL_x \\lf 2 , \\mathbb{R} \\rg \\otimes SL_y \\lf 2 , \\mathbb{R} \\rg $. The invariant scheme is an explicit one and provides a much better approximation of ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4043","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":"2026-05-18T01:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bvHg8wiLl+g0fPhvsm+KS3A5oFNlLHNqlzL6t0McAC2Yc7dhm50qVKRe8YorClKGTaLPMWQozg+qDy5mXKDFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:16:23.879643Z"},"content_sha256":"d49d378bea4b27041227b68eaa94e6fe8dc3370880f31ec9799f7460d3d0f866","schema_version":"1.0","event_id":"sha256:d49d378bea4b27041227b68eaa94e6fe8dc3370880f31ec9799f7460d3d0f866"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRIXRU2XNB6V53HBHO3ZX3B6R6/bundle.json","state_url":"https://pith.science/pith/CRIXRU2XNB6V53HBHO3ZX3B6R6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRIXRU2XNB6V53HBHO3ZX3B6R6/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":"2026-06-23T23:16:23Z","links":{"resolver":"https://pith.science/pith/CRIXRU2XNB6V53HBHO3ZX3B6R6","bundle":"https://pith.science/pith/CRIXRU2XNB6V53HBHO3ZX3B6R6/bundle.json","state":"https://pith.science/pith/CRIXRU2XNB6V53HBHO3ZX3B6R6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRIXRU2XNB6V53HBHO3ZX3B6R6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CRIXRU2XNB6V53HBHO3ZX3B6R6","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":"cdf92d6611547415d9701d0bd135a6a0c2cc151163d38da5dee9b1360ae22e0d","cross_cats_sorted":["math.MP","math.NA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-15T16:29:06Z","title_canon_sha256":"bbbaf375f8228427a0639e18b1ac40982e3c9660bf4aac728fc699718b98a366"},"schema_version":"1.0","source":{"id":"1407.4043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4043","created_at":"2026-05-18T01:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4043v1","created_at":"2026-05-18T01:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4043","created_at":"2026-05-18T01:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"CRIXRU2XNB6V","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CRIXRU2XNB6V53HB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CRIXRU2X","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:d49d378bea4b27041227b68eaa94e6fe8dc3370880f31ec9799f7460d3d0f866","target":"graph","created_at":"2026-05-18T01:42:36Z","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":"The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point symmetries. We do however construct a difference system approximating the Liouville equation that is invariant under the maximal finite subalgebra $ SL_x \\lf 2 , \\mathbb{R} \\rg \\otimes SL_y \\lf 2 , \\mathbb{R} \\rg $. The invariant scheme is an explicit one and provides a much better approximation of ex","authors_text":"Decio Levi, Luigi Martina, Pavel Winternitz","cross_cats":["math.MP","math.NA","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-15T16:29:06Z","title":"Lie-point symmetries of the discrete Liouville equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4043","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:c7727b994ee323a88d5af69790e3a0c1e2850934224f60d82bbac488a447ce53","target":"record","created_at":"2026-05-18T01:42:36Z","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":"cdf92d6611547415d9701d0bd135a6a0c2cc151163d38da5dee9b1360ae22e0d","cross_cats_sorted":["math.MP","math.NA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-15T16:29:06Z","title_canon_sha256":"bbbaf375f8228427a0639e18b1ac40982e3c9660bf4aac728fc699718b98a366"},"schema_version":"1.0","source":{"id":"1407.4043","kind":"arxiv","version":1}},"canonical_sha256":"145178d357687d5eece13bb79bec3e8fa3e33afdf0d4d2f00683acc66164dece","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"145178d357687d5eece13bb79bec3e8fa3e33afdf0d4d2f00683acc66164dece","first_computed_at":"2026-05-18T01:42:36.574723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:36.574723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"megmDDlBjerW/1G0CtcudQ0hBgfTL3G0Khv0bdTdF6XNIVgCyhHKkKOipSshEHPK1cqwAmx5j4o1zWlQeF4WBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:36.575166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7727b994ee323a88d5af69790e3a0c1e2850934224f60d82bbac488a447ce53","sha256:d49d378bea4b27041227b68eaa94e6fe8dc3370880f31ec9799f7460d3d0f866"],"state_sha256":"9cf99cc6fa01d43f9aa3cb4ba95445191c2c95fd672d485587b52595ff981e95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9EuBUQQu2N2prI7wb2RDHLT3nAdD6M7gjV/eO7TuQQg7NznAJwj4T8nstxy3FSxy1N4C3vIRw4RGd+Pgb3WuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T23:16:23.881664Z","bundle_sha256":"f8e2ad83b20cd18740509295f19bf0c54aad65dce87cb8331a05202f71ba4f54"}}