{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:6EWNPA2LB7U56O5TGG6P7NDFRH","short_pith_number":"pith:6EWNPA2L","canonical_record":{"source":{"id":"0710.2643","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2007-10-14T09:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"fb06a00fba7a558b01924d0a17cddc66f1a6e211cec8ec9066fdcb3167d59857","abstract_canon_sha256":"cc5a30105f2b1e45483b77b84fed247f9ab8dab71d301a0ba2c7bb4c298d6196"},"schema_version":"1.0"},"canonical_sha256":"f12cd7834b0fe9df3bb331bcffb46589ebfbd500ca6ec87e6bc02d365942b698","source":{"kind":"arxiv","id":"0710.2643","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.2643","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"arxiv_version","alias_value":"0710.2643v1","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.2643","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"pith_short_12","alias_value":"6EWNPA2LB7U5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6EWNPA2LB7U56O5T","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6EWNPA2L","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:6EWNPA2LB7U56O5TGG6P7NDFRH","target":"record","payload":{"canonical_record":{"source":{"id":"0710.2643","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2007-10-14T09:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"fb06a00fba7a558b01924d0a17cddc66f1a6e211cec8ec9066fdcb3167d59857","abstract_canon_sha256":"cc5a30105f2b1e45483b77b84fed247f9ab8dab71d301a0ba2c7bb4c298d6196"},"schema_version":"1.0"},"canonical_sha256":"f12cd7834b0fe9df3bb331bcffb46589ebfbd500ca6ec87e6bc02d365942b698","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:10.501285Z","signature_b64":"342tQS0BcJFZB6tmnb9MpJcuIWWn10xxJZpd6S/hCbv6+Oj13ppxPWhKV4lNjqO6UyGJsXK3FjVlFjnMEkMBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f12cd7834b0fe9df3bb331bcffb46589ebfbd500ca6ec87e6bc02d365942b698","last_reissued_at":"2026-05-18T02:16:10.500583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:10.500583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.2643","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":"2026-05-18T02:16:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npQNKYqOjL+RwyGDEbAcE89jtBBfwYt159WjRAQhDGO1/x7CLI/oltuS2O+xr/tayNfPBDn1dp/C50Ybb4dnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:15:32.446417Z"},"content_sha256":"a9e64fbd352934a2ecc58728d95cdea4027b7fd59c5684406b09059b94ab10c9","schema_version":"1.0","event_id":"sha256:a9e64fbd352934a2ecc58728d95cdea4027b7fd59c5684406b09059b94ab10c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:6EWNPA2LB7U56O5TGG6P7NDFRH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Frank Nijhoff, James Atkinson","submitted_at":"2007-10-14T09:58:33Z","abstract_excerpt":"The BT of Adler's lattice equation is inherent in the equation itself by virtue of its multidimensional consistency. We refer to a solution of the equation that is related to itself by the composition of two BTs (with different Backlund parameters) as a 2-cycle of the BT. In this article we will show that such solutions are associated with a commuting one-parameter family of rank-2 (i.e., 2-variable), 2-valued mappings. We will construct the explicit solution of the mappings within this family and hence give the solutions of Adler's equation that are 2-cycles of the BT."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2643","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":"2026-05-18T02:16:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HSka+4ocOaP0pVgYT+4ZWH7IWLUbULcyYHcIFm6Y2GEiGIkgXA66FJRHOBqkxMMTr550wqkSDyUY40vSbxQYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:15:32.446764Z"},"content_sha256":"4c059f96de0a97c45bd364932e5d19118532053b10fcd90808b65d84ca6d4d34","schema_version":"1.0","event_id":"sha256:4c059f96de0a97c45bd364932e5d19118532053b10fcd90808b65d84ca6d4d34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EWNPA2LB7U56O5TGG6P7NDFRH/bundle.json","state_url":"https://pith.science/pith/6EWNPA2LB7U56O5TGG6P7NDFRH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EWNPA2LB7U56O5TGG6P7NDFRH/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":"2026-06-03T23:15:32Z","links":{"resolver":"https://pith.science/pith/6EWNPA2LB7U56O5TGG6P7NDFRH","bundle":"https://pith.science/pith/6EWNPA2LB7U56O5TGG6P7NDFRH/bundle.json","state":"https://pith.science/pith/6EWNPA2LB7U56O5TGG6P7NDFRH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EWNPA2LB7U56O5TGG6P7NDFRH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:6EWNPA2LB7U56O5TGG6P7NDFRH","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":"cc5a30105f2b1e45483b77b84fed247f9ab8dab71d301a0ba2c7bb4c298d6196","cross_cats_sorted":[],"license":"","primary_cat":"nlin.SI","submitted_at":"2007-10-14T09:58:33Z","title_canon_sha256":"fb06a00fba7a558b01924d0a17cddc66f1a6e211cec8ec9066fdcb3167d59857"},"schema_version":"1.0","source":{"id":"0710.2643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.2643","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"arxiv_version","alias_value":"0710.2643v1","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.2643","created_at":"2026-05-18T02:16:10Z"},{"alias_kind":"pith_short_12","alias_value":"6EWNPA2LB7U5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6EWNPA2LB7U56O5T","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6EWNPA2L","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:4c059f96de0a97c45bd364932e5d19118532053b10fcd90808b65d84ca6d4d34","target":"graph","created_at":"2026-05-18T02:16:10Z","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 BT of Adler's lattice equation is inherent in the equation itself by virtue of its multidimensional consistency. We refer to a solution of the equation that is related to itself by the composition of two BTs (with different Backlund parameters) as a 2-cycle of the BT. In this article we will show that such solutions are associated with a commuting one-parameter family of rank-2 (i.e., 2-variable), 2-valued mappings. We will construct the explicit solution of the mappings within this family and hence give the solutions of Adler's equation that are 2-cycles of the BT.","authors_text":"Frank Nijhoff, James Atkinson","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.SI","submitted_at":"2007-10-14T09:58:33Z","title":"Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2643","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:a9e64fbd352934a2ecc58728d95cdea4027b7fd59c5684406b09059b94ab10c9","target":"record","created_at":"2026-05-18T02:16:10Z","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":"cc5a30105f2b1e45483b77b84fed247f9ab8dab71d301a0ba2c7bb4c298d6196","cross_cats_sorted":[],"license":"","primary_cat":"nlin.SI","submitted_at":"2007-10-14T09:58:33Z","title_canon_sha256":"fb06a00fba7a558b01924d0a17cddc66f1a6e211cec8ec9066fdcb3167d59857"},"schema_version":"1.0","source":{"id":"0710.2643","kind":"arxiv","version":1}},"canonical_sha256":"f12cd7834b0fe9df3bb331bcffb46589ebfbd500ca6ec87e6bc02d365942b698","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f12cd7834b0fe9df3bb331bcffb46589ebfbd500ca6ec87e6bc02d365942b698","first_computed_at":"2026-05-18T02:16:10.500583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:10.500583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"342tQS0BcJFZB6tmnb9MpJcuIWWn10xxJZpd6S/hCbv6+Oj13ppxPWhKV4lNjqO6UyGJsXK3FjVlFjnMEkMBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:10.501285Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.2643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9e64fbd352934a2ecc58728d95cdea4027b7fd59c5684406b09059b94ab10c9","sha256:4c059f96de0a97c45bd364932e5d19118532053b10fcd90808b65d84ca6d4d34"],"state_sha256":"1a326a8aa2790748255f14b63af25e9e1ab6fc75f2dab6cc0ccb51966974cb72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XAecnkgp4taj+ovgOTuUQLcp2aDgVbDdvXp3F1IwFjrG9uosJk9eIZBHE1mWjUw/IF8PGeZSFuXDv7GpyNh/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T23:15:32.448723Z","bundle_sha256":"412ebeb641141d09c8179b11f9f3795a1cd172c020f423734c85fe07ce76ac22"}}