{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:FDWA5CB27QRGRT7P52WIP2XIMQ","short_pith_number":"pith:FDWA5CB2","canonical_record":{"source":{"id":"nlin/0508024","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2005-08-17T13:04:38Z","cross_cats_sorted":[],"title_canon_sha256":"b5d5f91514a9092420945d2d71ff481dcd4a1227ccd450ddeb250ede374678da","abstract_canon_sha256":"5c05d0519ed4916b9e4ded255ed18448d689264d41d742287bbd127fa0e032f1"},"schema_version":"1.0"},"canonical_sha256":"28ec0e883afc2268cfefeeac87eae8642eaa776c88a6d59ec704730d5b1f2d7b","source":{"kind":"arxiv","id":"nlin/0508024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0508024","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0508024v1","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0508024","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"FDWA5CB27QRG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"FDWA5CB27QRGRT7P","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"FDWA5CB2","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:FDWA5CB27QRGRT7P52WIP2XIMQ","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0508024","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2005-08-17T13:04:38Z","cross_cats_sorted":[],"title_canon_sha256":"b5d5f91514a9092420945d2d71ff481dcd4a1227ccd450ddeb250ede374678da","abstract_canon_sha256":"5c05d0519ed4916b9e4ded255ed18448d689264d41d742287bbd127fa0e032f1"},"schema_version":"1.0"},"canonical_sha256":"28ec0e883afc2268cfefeeac87eae8642eaa776c88a6d59ec704730d5b1f2d7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:18.568021Z","signature_b64":"Bp6ZPMX0q8ppWMk7AyP8aBuQzw5oxLaBKQ8xVJcFNhsTBAcxwxqEoPZjhExxUwnPQVXPEC3OUfzPOT0YVSjGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28ec0e883afc2268cfefeeac87eae8642eaa776c88a6d59ec704730d5b1f2d7b","last_reissued_at":"2026-05-18T01:38:18.567233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:18.567233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0508024","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":"2026-05-18T01:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XEeWYAJ3r0gJ/sa/XROqch/gd80frtUAqu5mTj71gJPVaOKDQ2SVDfpNdpeN/wxQDFMSKSPCP+3N8UFoXw6sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:05:25.053781Z"},"content_sha256":"05c5c968496546c55acd76cd37c68a3ed6e35d109d8c4df5188e769dbb599856","schema_version":"1.0","event_id":"sha256:05c5c968496546c55acd76cd37c68a3ed6e35d109d8c4df5188e769dbb599856"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:FDWA5CB27QRGRT7P52WIP2XIMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resonance- and Chaos-Assisted Tunneling","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Christopher Eltschka, Denis Ullmo, Peter Schlagheck","submitted_at":"2005-08-17T13:04:38Z","abstract_excerpt":"We consider dynamical tunneling between two symmetry-related regular islands that are separated in phase space by a chaotic sea. Such tunneling processes are dominantly governed by nonlinear resonances, which induce a coupling mechanism between ``regular'' quantum states within and ``chaotic'' states outside the islands. By means of a random matrix ansatz for the chaotic part of the Hamiltonian, one can show that the corresponding coupling matrix element directly determines the level splitting between the symmetric and the antisymmetric eigenstates of the pair of islands. We show in detail how"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0508024","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":"2026-05-18T01:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5WmffG5svfxBK4WES5Z+oa0Ny3QqPuVvroPh//cL3vz+DVCALwujaQGN9dAt4W7wqHlcei6NC+k9Y0USkfGgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:05:25.054111Z"},"content_sha256":"9b406dd30321d6ecb114811070adfc9c31edf586512cb15d1d973aa5b7a8d0a5","schema_version":"1.0","event_id":"sha256:9b406dd30321d6ecb114811070adfc9c31edf586512cb15d1d973aa5b7a8d0a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FDWA5CB27QRGRT7P52WIP2XIMQ/bundle.json","state_url":"https://pith.science/pith/FDWA5CB27QRGRT7P52WIP2XIMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FDWA5CB27QRGRT7P52WIP2XIMQ/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":"2026-06-20T05:05:25Z","links":{"resolver":"https://pith.science/pith/FDWA5CB27QRGRT7P52WIP2XIMQ","bundle":"https://pith.science/pith/FDWA5CB27QRGRT7P52WIP2XIMQ/bundle.json","state":"https://pith.science/pith/FDWA5CB27QRGRT7P52WIP2XIMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FDWA5CB27QRGRT7P52WIP2XIMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:FDWA5CB27QRGRT7P52WIP2XIMQ","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":"5c05d0519ed4916b9e4ded255ed18448d689264d41d742287bbd127fa0e032f1","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2005-08-17T13:04:38Z","title_canon_sha256":"b5d5f91514a9092420945d2d71ff481dcd4a1227ccd450ddeb250ede374678da"},"schema_version":"1.0","source":{"id":"nlin/0508024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0508024","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0508024v1","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0508024","created_at":"2026-05-18T01:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"FDWA5CB27QRG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"FDWA5CB27QRGRT7P","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"FDWA5CB2","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:9b406dd30321d6ecb114811070adfc9c31edf586512cb15d1d973aa5b7a8d0a5","target":"graph","created_at":"2026-05-18T01:38:18Z","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 consider dynamical tunneling between two symmetry-related regular islands that are separated in phase space by a chaotic sea. Such tunneling processes are dominantly governed by nonlinear resonances, which induce a coupling mechanism between ``regular'' quantum states within and ``chaotic'' states outside the islands. By means of a random matrix ansatz for the chaotic part of the Hamiltonian, one can show that the corresponding coupling matrix element directly determines the level splitting between the symmetric and the antisymmetric eigenstates of the pair of islands. We show in detail how","authors_text":"Christopher Eltschka, Denis Ullmo, Peter Schlagheck","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2005-08-17T13:04:38Z","title":"Resonance- and Chaos-Assisted Tunneling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0508024","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":"sha256:05c5c968496546c55acd76cd37c68a3ed6e35d109d8c4df5188e769dbb599856","target":"record","created_at":"2026-05-18T01:38:18Z","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":"5c05d0519ed4916b9e4ded255ed18448d689264d41d742287bbd127fa0e032f1","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2005-08-17T13:04:38Z","title_canon_sha256":"b5d5f91514a9092420945d2d71ff481dcd4a1227ccd450ddeb250ede374678da"},"schema_version":"1.0","source":{"id":"nlin/0508024","kind":"arxiv","version":1}},"canonical_sha256":"28ec0e883afc2268cfefeeac87eae8642eaa776c88a6d59ec704730d5b1f2d7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28ec0e883afc2268cfefeeac87eae8642eaa776c88a6d59ec704730d5b1f2d7b","first_computed_at":"2026-05-18T01:38:18.567233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:18.567233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bp6ZPMX0q8ppWMk7AyP8aBuQzw5oxLaBKQ8xVJcFNhsTBAcxwxqEoPZjhExxUwnPQVXPEC3OUfzPOT0YVSjGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:18.568021Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0508024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05c5c968496546c55acd76cd37c68a3ed6e35d109d8c4df5188e769dbb599856","sha256:9b406dd30321d6ecb114811070adfc9c31edf586512cb15d1d973aa5b7a8d0a5"],"state_sha256":"2cb4d14a2d72e1cfd8dcf5728ae5d96a35997e32b919bf33189aee6a421af4dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XwfiIXgjF/eYxZ1NPV1LgRmeVykdfEerzOJOUYn8sNoZnDNckY49xXLG/TQUvywFE8q655ddKpzuDB24BrTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:05:25.055900Z","bundle_sha256":"3da2fbfd2d57918fbc0c195bb6a0541eb37800ee389b2a1e7bf0aff7186fe655"}}