{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XAVXCCVM6LW6H2BGAQAULJWOWN","short_pith_number":"pith:XAVXCCVM","canonical_record":{"source":{"id":"1808.04942","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-08-15T01:48:41Z","cross_cats_sorted":[],"title_canon_sha256":"0556cc94fba2aa634780c5cfad642f32398dd71d480bcb1c234aaeb89e754757","abstract_canon_sha256":"d84a1a1b9cf1f70dab5be7fba10c983143a7b59b12c683effe5da2a17866657d"},"schema_version":"1.0"},"canonical_sha256":"b82b710aacf2ede3e826040145a6ceb360d32e4ae5395d70805acbd544415c00","source":{"kind":"arxiv","id":"1808.04942","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04942","created_at":"2026-05-17T23:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04942v2","created_at":"2026-05-17T23:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04942","created_at":"2026-05-17T23:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"XAVXCCVM6LW6","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XAVXCCVM6LW6H2BG","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XAVXCCVM","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XAVXCCVM6LW6H2BGAQAULJWOWN","target":"record","payload":{"canonical_record":{"source":{"id":"1808.04942","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-08-15T01:48:41Z","cross_cats_sorted":[],"title_canon_sha256":"0556cc94fba2aa634780c5cfad642f32398dd71d480bcb1c234aaeb89e754757","abstract_canon_sha256":"d84a1a1b9cf1f70dab5be7fba10c983143a7b59b12c683effe5da2a17866657d"},"schema_version":"1.0"},"canonical_sha256":"b82b710aacf2ede3e826040145a6ceb360d32e4ae5395d70805acbd544415c00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:43.102891Z","signature_b64":"FH/6FLxJ8ERNn+dU35Lqg+E4dW058iWw0WKW+XC8LmN3lz5nTjrrJ1akAUffhaOtxCu7TTT3jRR2shaWQ18HCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b82b710aacf2ede3e826040145a6ceb360d32e4ae5395d70805acbd544415c00","last_reissued_at":"2026-05-17T23:44:43.102262Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:43.102262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.04942","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uqe0Qtc0zMhtCEwXn91r90kU1+50Aq9GzYhLGSADeBIz44Pzr3ejOeY8wBYbFfSKrw9PMwPBdRGrSB3PeoKLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:26:11.513171Z"},"content_sha256":"56017bdb0ce593855fee1125a3d85f9791435e2b9b73870b34012f9cdba08978","schema_version":"1.0","event_id":"sha256:56017bdb0ce593855fee1125a3d85f9791435e2b9b73870b34012f9cdba08978"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XAVXCCVM6LW6H2BGAQAULJWOWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity and integrability in 4D bi-rational maps with two invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"C-M. Viallet, D. T. Tran, G. Gubbiotti, N. Joshi","submitted_at":"2018-08-15T01:48:41Z","abstract_excerpt":"In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04942","kind":"arxiv","version":2},"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":"2026-05-17T23:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvn84n4YW70qu3xPXLilyvrKigHwbaE6osN6yMMTXKM9xT+swJaiwi6+z39KzknxGRoynpwiM8LwzME/nIZaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:26:11.513610Z"},"content_sha256":"508e81975ee110c736a96700c7da880da8d1ba0248b9154d698316ea50482363","schema_version":"1.0","event_id":"sha256:508e81975ee110c736a96700c7da880da8d1ba0248b9154d698316ea50482363"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAVXCCVM6LW6H2BGAQAULJWOWN/bundle.json","state_url":"https://pith.science/pith/XAVXCCVM6LW6H2BGAQAULJWOWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAVXCCVM6LW6H2BGAQAULJWOWN/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":"2026-05-28T21:26:11Z","links":{"resolver":"https://pith.science/pith/XAVXCCVM6LW6H2BGAQAULJWOWN","bundle":"https://pith.science/pith/XAVXCCVM6LW6H2BGAQAULJWOWN/bundle.json","state":"https://pith.science/pith/XAVXCCVM6LW6H2BGAQAULJWOWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAVXCCVM6LW6H2BGAQAULJWOWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XAVXCCVM6LW6H2BGAQAULJWOWN","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":"d84a1a1b9cf1f70dab5be7fba10c983143a7b59b12c683effe5da2a17866657d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-08-15T01:48:41Z","title_canon_sha256":"0556cc94fba2aa634780c5cfad642f32398dd71d480bcb1c234aaeb89e754757"},"schema_version":"1.0","source":{"id":"1808.04942","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04942","created_at":"2026-05-17T23:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04942v2","created_at":"2026-05-17T23:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04942","created_at":"2026-05-17T23:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"XAVXCCVM6LW6","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XAVXCCVM6LW6H2BG","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XAVXCCVM","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:508e81975ee110c736a96700c7da880da8d1ba0248b9154d698316ea50482363","target":"graph","created_at":"2026-05-17T23:44:43Z","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":"In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem.","authors_text":"C-M. Viallet, D. T. Tran, G. Gubbiotti, N. Joshi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-08-15T01:48:41Z","title":"Complexity and integrability in 4D bi-rational maps with two invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04942","kind":"arxiv","version":2},"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":"sha256:56017bdb0ce593855fee1125a3d85f9791435e2b9b73870b34012f9cdba08978","target":"record","created_at":"2026-05-17T23:44:43Z","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":"d84a1a1b9cf1f70dab5be7fba10c983143a7b59b12c683effe5da2a17866657d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-08-15T01:48:41Z","title_canon_sha256":"0556cc94fba2aa634780c5cfad642f32398dd71d480bcb1c234aaeb89e754757"},"schema_version":"1.0","source":{"id":"1808.04942","kind":"arxiv","version":2}},"canonical_sha256":"b82b710aacf2ede3e826040145a6ceb360d32e4ae5395d70805acbd544415c00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b82b710aacf2ede3e826040145a6ceb360d32e4ae5395d70805acbd544415c00","first_computed_at":"2026-05-17T23:44:43.102262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:43.102262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FH/6FLxJ8ERNn+dU35Lqg+E4dW058iWw0WKW+XC8LmN3lz5nTjrrJ1akAUffhaOtxCu7TTT3jRR2shaWQ18HCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:43.102891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04942","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56017bdb0ce593855fee1125a3d85f9791435e2b9b73870b34012f9cdba08978","sha256:508e81975ee110c736a96700c7da880da8d1ba0248b9154d698316ea50482363"],"state_sha256":"1bbe7743ae3bb93c46daeb9337ca033c6ec1a7012b0dde22cf9dace3dc56c4ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tZzahse7RySTNB5DGL2iDgYre9xJ3jUcuK83uEEeHrdjg9g9+Qd7xvdthIdIy5NhVULQh9gPABA/I+z4fgxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:26:11.517488Z","bundle_sha256":"3f2d6f2ca10c91a89ac2ca166618b7677c43e58f7ff50cb6de7c832f0fc29979"}}