{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PB33KMZSGDZ3Q63MASCSIDP7YG","short_pith_number":"pith:PB33KMZS","canonical_record":{"source":{"id":"1309.7226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-09-27T12:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"2f34f10ba431a055866675e8c8c55454ba5c575e58d41a8e7da2768224afdd25","abstract_canon_sha256":"445f3c0c87d24d29a7b63c31c02fe4c6f72970e5cd76446818f95a8fc8fed492"},"schema_version":"1.0"},"canonical_sha256":"7877b5333230f3b87b6c0485240dffc197d67ee6c5c02af6a07a29f9806a39db","source":{"kind":"arxiv","id":"1309.7226","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7226","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7226v1","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7226","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"PB33KMZSGDZ3","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PB33KMZSGDZ3Q63M","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PB33KMZS","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PB33KMZSGDZ3Q63MASCSIDP7YG","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-09-27T12:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"2f34f10ba431a055866675e8c8c55454ba5c575e58d41a8e7da2768224afdd25","abstract_canon_sha256":"445f3c0c87d24d29a7b63c31c02fe4c6f72970e5cd76446818f95a8fc8fed492"},"schema_version":"1.0"},"canonical_sha256":"7877b5333230f3b87b6c0485240dffc197d67ee6c5c02af6a07a29f9806a39db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:56.902245Z","signature_b64":"90slMq3rtBM8Q6f3DlLgo1fsnWUmgC7GQTB0Vgo8cxgeUQD63ceBGTTsF/YCgr72iUe/T/gFFZHG4mjuN0chBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7877b5333230f3b87b6c0485240dffc197d67ee6c5c02af6a07a29f9806a39db","last_reissued_at":"2026-05-18T03:11:56.901561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:56.901561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7226","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":"2026-05-18T03:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OejFhXHdPOGffWWqfctUE48Lo3CKpxu6mxG2rt6fNJQhqFZFTLfprpnkAX5jezk8z58bLPFwwSECSM+K93GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:05:30.970334Z"},"content_sha256":"a6220941d3b9908db99bfb318d24072ce29c99fee27dfdde37219d952244ea42","schema_version":"1.0","event_id":"sha256:a6220941d3b9908db99bfb318d24072ce29c99fee27dfdde37219d952244ea42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PB33KMZSGDZ3Q63MASCSIDP7YG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Computation of Invariant Tori in Volume-Preserving Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Adam M. Fox, James D. Meiss","submitted_at":"2013-09-27T12:51:56Z","abstract_excerpt":"In this paper we implement a numerical algorithm to compute codimension-one tori in three-dimensional, volume-preserving maps. A torus is defined by its conjugacy to rigid rotation, which is in turn given by its Fourier series. The algorithm employs a quasi-Newton scheme to find the Fourier coefficients of a truncation of the series. This technique is based upon the theory developed in the accompanying article by Blass and de la Llave. It is guaranteed to converge assuming the torus exists, the initial estimate is suitably close, and the map satisfies certain nondegeneracy conditions. We demon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7226","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":"2026-05-18T03:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9RX0J/988maOotgJq7VJYLsj/svmI8Dmf8QJoDvxQlzRPPpF14Q5586WR+CmgmiZpCeh6B9abp91/trh1XNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:05:30.970989Z"},"content_sha256":"3df0868fae159482622ff09857ec96d3860ec69c9db5daf313fd546997d8e729","schema_version":"1.0","event_id":"sha256:3df0868fae159482622ff09857ec96d3860ec69c9db5daf313fd546997d8e729"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PB33KMZSGDZ3Q63MASCSIDP7YG/bundle.json","state_url":"https://pith.science/pith/PB33KMZSGDZ3Q63MASCSIDP7YG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PB33KMZSGDZ3Q63MASCSIDP7YG/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":"2026-06-07T08:05:30Z","links":{"resolver":"https://pith.science/pith/PB33KMZSGDZ3Q63MASCSIDP7YG","bundle":"https://pith.science/pith/PB33KMZSGDZ3Q63MASCSIDP7YG/bundle.json","state":"https://pith.science/pith/PB33KMZSGDZ3Q63MASCSIDP7YG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PB33KMZSGDZ3Q63MASCSIDP7YG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PB33KMZSGDZ3Q63MASCSIDP7YG","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":"445f3c0c87d24d29a7b63c31c02fe4c6f72970e5cd76446818f95a8fc8fed492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-09-27T12:51:56Z","title_canon_sha256":"2f34f10ba431a055866675e8c8c55454ba5c575e58d41a8e7da2768224afdd25"},"schema_version":"1.0","source":{"id":"1309.7226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7226","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7226v1","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7226","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"PB33KMZSGDZ3","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PB33KMZSGDZ3Q63M","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PB33KMZS","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:3df0868fae159482622ff09857ec96d3860ec69c9db5daf313fd546997d8e729","target":"graph","created_at":"2026-05-18T03:11:56Z","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 paper we implement a numerical algorithm to compute codimension-one tori in three-dimensional, volume-preserving maps. A torus is defined by its conjugacy to rigid rotation, which is in turn given by its Fourier series. The algorithm employs a quasi-Newton scheme to find the Fourier coefficients of a truncation of the series. This technique is based upon the theory developed in the accompanying article by Blass and de la Llave. It is guaranteed to converge assuming the torus exists, the initial estimate is suitably close, and the map satisfies certain nondegeneracy conditions. We demon","authors_text":"Adam M. Fox, James D. Meiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-09-27T12:51:56Z","title":"Efficient Computation of Invariant Tori in Volume-Preserving Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7226","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:a6220941d3b9908db99bfb318d24072ce29c99fee27dfdde37219d952244ea42","target":"record","created_at":"2026-05-18T03:11:56Z","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":"445f3c0c87d24d29a7b63c31c02fe4c6f72970e5cd76446818f95a8fc8fed492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-09-27T12:51:56Z","title_canon_sha256":"2f34f10ba431a055866675e8c8c55454ba5c575e58d41a8e7da2768224afdd25"},"schema_version":"1.0","source":{"id":"1309.7226","kind":"arxiv","version":1}},"canonical_sha256":"7877b5333230f3b87b6c0485240dffc197d67ee6c5c02af6a07a29f9806a39db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7877b5333230f3b87b6c0485240dffc197d67ee6c5c02af6a07a29f9806a39db","first_computed_at":"2026-05-18T03:11:56.901561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:56.901561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90slMq3rtBM8Q6f3DlLgo1fsnWUmgC7GQTB0Vgo8cxgeUQD63ceBGTTsF/YCgr72iUe/T/gFFZHG4mjuN0chBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:56.902245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6220941d3b9908db99bfb318d24072ce29c99fee27dfdde37219d952244ea42","sha256:3df0868fae159482622ff09857ec96d3860ec69c9db5daf313fd546997d8e729"],"state_sha256":"9bd34e6c7d77aac736a89572c3b3a12159e93e787de3f3a4e1d432ad6dc92bc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYL+Godt3bxExugNZ0rxpmrRsyR5gLY8mn6IsMURG7tev4h6vZc07wk6BMv4h9Lfp5G+6n4XHNOHNknDX+F7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:05:30.974673Z","bundle_sha256":"3973fb1b9600e52d0fb867af7228f357f068f51acd2ab8a2dba014ed1d915052"}}