{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ZJ6AEJOLRBZG76XX5KKWZRLLVD","short_pith_number":"pith:ZJ6AEJOL","canonical_record":{"source":{"id":"0905.3730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-22T17:23:33Z","cross_cats_sorted":[],"title_canon_sha256":"33117870f3dc04424a05bb3e6007da3366271c26f0c6ff89e0430368030ee9e7","abstract_canon_sha256":"90fa8fc45e1a77b77888703b98417fe94631cd56ba54d08e214f9d57bea2b4f5"},"schema_version":"1.0"},"canonical_sha256":"ca7c0225cb88726ffaf7ea956cc56ba8f5eb4093cc3841c90b494d0bbe52611e","source":{"kind":"arxiv","id":"0905.3730","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3730","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3730v1","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3730","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ6AEJOLRBZG","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ6AEJOLRBZG76XX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ6AEJOL","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ZJ6AEJOLRBZG76XX5KKWZRLLVD","target":"record","payload":{"canonical_record":{"source":{"id":"0905.3730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-22T17:23:33Z","cross_cats_sorted":[],"title_canon_sha256":"33117870f3dc04424a05bb3e6007da3366271c26f0c6ff89e0430368030ee9e7","abstract_canon_sha256":"90fa8fc45e1a77b77888703b98417fe94631cd56ba54d08e214f9d57bea2b4f5"},"schema_version":"1.0"},"canonical_sha256":"ca7c0225cb88726ffaf7ea956cc56ba8f5eb4093cc3841c90b494d0bbe52611e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:37.951613Z","signature_b64":"5TCvxYGwjYAMbNwQwAn3t+6T0vb/BOFk/0uJLKRjeTpxUIWOgX8eW6PH/i9TNv0U6YBuYATz23t0ZfB411F/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca7c0225cb88726ffaf7ea956cc56ba8f5eb4093cc3841c90b494d0bbe52611e","last_reissued_at":"2026-05-18T02:13:37.951030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:37.951030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.3730","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":"2026-05-18T02:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ibsWt01IlKo1MT2uSWusTaopqV8YZ9kS6sJ6vfD8N/T073dXTY5qyLOWd6ZW/HKW0tUkfRDBPV9OZfOZbu1OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:40:34.633006Z"},"content_sha256":"25f971bfcab29d09d309f56521dac302a9fc751dbba0465ff6de59d8c8c98cb5","schema_version":"1.0","event_id":"sha256:25f971bfcab29d09d309f56521dac302a9fc751dbba0465ff6de59d8c8c98cb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ZJ6AEJOLRBZG76XX5KKWZRLLVD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simultaneous Border-Collision and Period-Doubling Bifurcations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David J.W. Simpson, James D. Meiss","submitted_at":"2009-05-22T17:23:33Z","abstract_excerpt":"We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of period-doubling bifurcations emanates non-tangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics are completely c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3730","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":"2026-05-18T02:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qU9P5LGYaFUyz2Nrui+tvgVR7YgTHepM2JLzkJWlEsEa7KmEJtds9HOv7NtDOdO7uerazdFVEONA0tlVenLBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:40:34.633368Z"},"content_sha256":"b7e3af128263a04e4e7b9f77c46550d374a56d6637bf09dcdcf8944da127ecf5","schema_version":"1.0","event_id":"sha256:b7e3af128263a04e4e7b9f77c46550d374a56d6637bf09dcdcf8944da127ecf5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJ6AEJOLRBZG76XX5KKWZRLLVD/bundle.json","state_url":"https://pith.science/pith/ZJ6AEJOLRBZG76XX5KKWZRLLVD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJ6AEJOLRBZG76XX5KKWZRLLVD/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":"2026-06-24T05:40:34Z","links":{"resolver":"https://pith.science/pith/ZJ6AEJOLRBZG76XX5KKWZRLLVD","bundle":"https://pith.science/pith/ZJ6AEJOLRBZG76XX5KKWZRLLVD/bundle.json","state":"https://pith.science/pith/ZJ6AEJOLRBZG76XX5KKWZRLLVD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJ6AEJOLRBZG76XX5KKWZRLLVD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZJ6AEJOLRBZG76XX5KKWZRLLVD","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":"90fa8fc45e1a77b77888703b98417fe94631cd56ba54d08e214f9d57bea2b4f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-22T17:23:33Z","title_canon_sha256":"33117870f3dc04424a05bb3e6007da3366271c26f0c6ff89e0430368030ee9e7"},"schema_version":"1.0","source":{"id":"0905.3730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3730","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3730v1","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3730","created_at":"2026-05-18T02:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ6AEJOLRBZG","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ6AEJOLRBZG76XX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ6AEJOL","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:b7e3af128263a04e4e7b9f77c46550d374a56d6637bf09dcdcf8944da127ecf5","target":"graph","created_at":"2026-05-18T02:13:37Z","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 unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of period-doubling bifurcations emanates non-tangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics are completely c","authors_text":"David J.W. Simpson, James D. Meiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-22T17:23:33Z","title":"Simultaneous Border-Collision and Period-Doubling Bifurcations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3730","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":"sha256:25f971bfcab29d09d309f56521dac302a9fc751dbba0465ff6de59d8c8c98cb5","target":"record","created_at":"2026-05-18T02:13:37Z","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":"90fa8fc45e1a77b77888703b98417fe94631cd56ba54d08e214f9d57bea2b4f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-22T17:23:33Z","title_canon_sha256":"33117870f3dc04424a05bb3e6007da3366271c26f0c6ff89e0430368030ee9e7"},"schema_version":"1.0","source":{"id":"0905.3730","kind":"arxiv","version":1}},"canonical_sha256":"ca7c0225cb88726ffaf7ea956cc56ba8f5eb4093cc3841c90b494d0bbe52611e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca7c0225cb88726ffaf7ea956cc56ba8f5eb4093cc3841c90b494d0bbe52611e","first_computed_at":"2026-05-18T02:13:37.951030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:37.951030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5TCvxYGwjYAMbNwQwAn3t+6T0vb/BOFk/0uJLKRjeTpxUIWOgX8eW6PH/i9TNv0U6YBuYATz23t0ZfB411F/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:37.951613Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25f971bfcab29d09d309f56521dac302a9fc751dbba0465ff6de59d8c8c98cb5","sha256:b7e3af128263a04e4e7b9f77c46550d374a56d6637bf09dcdcf8944da127ecf5"],"state_sha256":"edcb1ca6331dc1f78d37c4f61301c396ddb986bc82b2601afda9aed6e6ee931f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"We9nA1uJbHNtmD+zA3zWrLmZAGs9y/Iy/mMSqJvtXiphcF8db/neBXjNPfEvWOxc1pth0mhOrkSvkJH7mvDVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:40:34.635596Z","bundle_sha256":"caf3184726e30b75f0e602be2e9a0c9ecc9df9097266f79a92bc75f7896989de"}}