{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:K5AVX357CIEXLGZ6AWCZFMAY2E","short_pith_number":"pith:K5AVX357","canonical_record":{"source":{"id":"1104.2205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-04-12T13:26:53Z","cross_cats_sorted":["math.DS","nlin.SI"],"title_canon_sha256":"af20e7e13907aa23a710f53313729b4634bd4756d10907d6d339146957e3f0bc","abstract_canon_sha256":"ef005512dbc4649793e88a84a5bc2445e39067bcb12fb5ada4ba5d36b126e97a"},"schema_version":"1.0"},"canonical_sha256":"57415befbf1209759b3e058592b018d12348f83c3813408dd6cabea814915b8c","source":{"kind":"arxiv","id":"1104.2205","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2205","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2205v1","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2205","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"K5AVX357CIEX","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5AVX357CIEXLGZ6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5AVX357","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:K5AVX357CIEXLGZ6AWCZFMAY2E","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-04-12T13:26:53Z","cross_cats_sorted":["math.DS","nlin.SI"],"title_canon_sha256":"af20e7e13907aa23a710f53313729b4634bd4756d10907d6d339146957e3f0bc","abstract_canon_sha256":"ef005512dbc4649793e88a84a5bc2445e39067bcb12fb5ada4ba5d36b126e97a"},"schema_version":"1.0"},"canonical_sha256":"57415befbf1209759b3e058592b018d12348f83c3813408dd6cabea814915b8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:09.709348Z","signature_b64":"JbkpruUEYvhx41X/P3GBdUtJL39nZlZ8TK+b7l8VkZEyFShc7kOm9SU2A/o3we8EQWRhHFoL91XnFgG9QG1bBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57415befbf1209759b3e058592b018d12348f83c3813408dd6cabea814915b8c","last_reissued_at":"2026-05-18T02:22:09.708701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:09.708701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2205","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":"2026-05-18T02:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xoOvi6M5qfNFJ+PqYpy57KrEQvXGOthUl3OXI1ocv2/QS3CPzjqvDEiMscWZ2miY2VPRHiFUUL1sDsHCKlSgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:05:18.416598Z"},"content_sha256":"e238c57387e4927bde84597f4bd696be9dac3a997f7f9af5f59b8da58d07aea8","schema_version":"1.0","event_id":"sha256:e238c57387e4927bde84597f4bd696be9dac3a997f7f9af5f59b8da58d07aea8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:K5AVX357CIEXLGZ6AWCZFMAY2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding complex dynamics by means of an associated Riemann surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.SI"],"primary_cat":"nlin.CD","authors_text":"David Gomez-Ullate, Francesco Calogero, Matteo Sommacal, Paolo Santini","submitted_at":"2011-04-12T13:26:53Z","abstract_excerpt":"We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the orbits can be derived, which is shown to depend on the initial data and the continued fraction expansion of a simple ratio of the coupling constants of the problem. For rational values of this ratio and generic values of the initial data, all orbits are periodic and the system is isochronous. For irrational values of the ratio, there exist periodic and quasi-pe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2205","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":"2026-05-18T02:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cv0MLb7hY4/6H7pmjDwiOaAC7NI0yVKxI7TlsfW470va2497Hko+FULHdR7avcft9AHrr5OysBNdz4fxur8SBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:05:18.416993Z"},"content_sha256":"33e541c46346221f178b4852a9e7ded78126953a783904860429d627464f0f5b","schema_version":"1.0","event_id":"sha256:33e541c46346221f178b4852a9e7ded78126953a783904860429d627464f0f5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5AVX357CIEXLGZ6AWCZFMAY2E/bundle.json","state_url":"https://pith.science/pith/K5AVX357CIEXLGZ6AWCZFMAY2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5AVX357CIEXLGZ6AWCZFMAY2E/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":"2026-05-22T19:05:18Z","links":{"resolver":"https://pith.science/pith/K5AVX357CIEXLGZ6AWCZFMAY2E","bundle":"https://pith.science/pith/K5AVX357CIEXLGZ6AWCZFMAY2E/bundle.json","state":"https://pith.science/pith/K5AVX357CIEXLGZ6AWCZFMAY2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5AVX357CIEXLGZ6AWCZFMAY2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K5AVX357CIEXLGZ6AWCZFMAY2E","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":"ef005512dbc4649793e88a84a5bc2445e39067bcb12fb5ada4ba5d36b126e97a","cross_cats_sorted":["math.DS","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-04-12T13:26:53Z","title_canon_sha256":"af20e7e13907aa23a710f53313729b4634bd4756d10907d6d339146957e3f0bc"},"schema_version":"1.0","source":{"id":"1104.2205","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2205","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2205v1","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2205","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"K5AVX357CIEX","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5AVX357CIEXLGZ6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5AVX357","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:33e541c46346221f178b4852a9e7ded78126953a783904860429d627464f0f5b","target":"graph","created_at":"2026-05-18T02:22:09Z","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 provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the orbits can be derived, which is shown to depend on the initial data and the continued fraction expansion of a simple ratio of the coupling constants of the problem. For rational values of this ratio and generic values of the initial data, all orbits are periodic and the system is isochronous. For irrational values of the ratio, there exist periodic and quasi-pe","authors_text":"David Gomez-Ullate, Francesco Calogero, Matteo Sommacal, Paolo Santini","cross_cats":["math.DS","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-04-12T13:26:53Z","title":"Understanding complex dynamics by means of an associated Riemann surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2205","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:e238c57387e4927bde84597f4bd696be9dac3a997f7f9af5f59b8da58d07aea8","target":"record","created_at":"2026-05-18T02:22:09Z","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":"ef005512dbc4649793e88a84a5bc2445e39067bcb12fb5ada4ba5d36b126e97a","cross_cats_sorted":["math.DS","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-04-12T13:26:53Z","title_canon_sha256":"af20e7e13907aa23a710f53313729b4634bd4756d10907d6d339146957e3f0bc"},"schema_version":"1.0","source":{"id":"1104.2205","kind":"arxiv","version":1}},"canonical_sha256":"57415befbf1209759b3e058592b018d12348f83c3813408dd6cabea814915b8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57415befbf1209759b3e058592b018d12348f83c3813408dd6cabea814915b8c","first_computed_at":"2026-05-18T02:22:09.708701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:09.708701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JbkpruUEYvhx41X/P3GBdUtJL39nZlZ8TK+b7l8VkZEyFShc7kOm9SU2A/o3we8EQWRhHFoL91XnFgG9QG1bBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:09.709348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e238c57387e4927bde84597f4bd696be9dac3a997f7f9af5f59b8da58d07aea8","sha256:33e541c46346221f178b4852a9e7ded78126953a783904860429d627464f0f5b"],"state_sha256":"b00da7edd19fb0f0b05be490653c3a366bbac84958170079d46b1542dcd06faf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ji+qxJA0HA1ZVrE8JvJ14U78SSFzsNcXSJYlf6EiNfoCON58PxX7ZnEDJ5M/zNxKbLYS8yOsic9aDH/GxaBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T19:05:18.419897Z","bundle_sha256":"35cb78f0c6cfbd4bc30eefe192c719cf99581baff18e6bbd73fb9c3ce1e256a9"}}