{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4JMN4VNIWARTZVW7OE3AXTBAOS","short_pith_number":"pith:4JMN4VNI","canonical_record":{"source":{"id":"1706.08623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-26T23:07:57Z","cross_cats_sorted":[],"title_canon_sha256":"b1bb27ea8b48faaeea1a51e4795d57b3ed9bb79d86eff1b4e54e4e8c0aeb968c","abstract_canon_sha256":"4c95acac6e44bf554a5824890291f7759d259d68e1eef3b7fc657ce1a82ec6af"},"schema_version":"1.0"},"canonical_sha256":"e258de55a8b0233cd6df71360bcc207483dd1c9baee552f27b3b6bdd13636818","source":{"kind":"arxiv","id":"1706.08623","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08623","created_at":"2026-05-18T00:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08623v2","created_at":"2026-05-18T00:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08623","created_at":"2026-05-18T00:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"4JMN4VNIWART","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JMN4VNIWARTZVW7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JMN4VNI","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4JMN4VNIWARTZVW7OE3AXTBAOS","target":"record","payload":{"canonical_record":{"source":{"id":"1706.08623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-26T23:07:57Z","cross_cats_sorted":[],"title_canon_sha256":"b1bb27ea8b48faaeea1a51e4795d57b3ed9bb79d86eff1b4e54e4e8c0aeb968c","abstract_canon_sha256":"4c95acac6e44bf554a5824890291f7759d259d68e1eef3b7fc657ce1a82ec6af"},"schema_version":"1.0"},"canonical_sha256":"e258de55a8b0233cd6df71360bcc207483dd1c9baee552f27b3b6bdd13636818","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:45.386665Z","signature_b64":"rnQMywPJZakO9bH1XGjUhvL5ZCFR0mqh+2ja4Wc6UdOXaSC3DC4dcSp7+rQQKMFDZ4MYOapMahCTy8nEUk42BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e258de55a8b0233cd6df71360bcc207483dd1c9baee552f27b3b6bdd13636818","last_reissued_at":"2026-05-18T00:04:45.385976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:45.385976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.08623","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2QEnAwoKlZ39MQceZA0ZFYN1niNpgWSyi4p1+mFIVdfGcWar82si/JbKPnYBiIBkAbFWdKzuKrCOQaVUaN0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:56:17.757087Z"},"content_sha256":"28df167c6f2f1077a3b94ab922ec1974ff3798a3088e5a8c674e41a5a25f786a","schema_version":"1.0","event_id":"sha256:28df167c6f2f1077a3b94ab922ec1974ff3798a3088e5a8c674e41a5a25f786a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4JMN4VNIWARTZVW7OE3AXTBAOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carl P. Dettmann, Dmitry Turaev, Vitaly Fain","submitted_at":"2017-06-26T23:07:57Z","abstract_excerpt":"We study billiard dynamics inside an ellipse for which the axes lengths are changed periodically in time and an $O(\\delta)$-small quartic polynomial deformation is added to the boundary. In this situation the energy of the particle in the billiard is no longer conserved. We show a Fermi acceleration in such system: there exists a billiard trajectory on which the energy tends to infinity. The construction is based on the analysis of dynamics in the phase space near a homoclinic intersection of the stable and unstable manifolds of the normally hyperbolic invariant cylinder $\\Lambda$, parameteris"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08623","kind":"arxiv","version":2},"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":"2026-05-18T00:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6zNL2mlJfhM80F1mYFB9vWCco//xckdef0q6OxwT+/JNoNbnijc/fdYtC13/NM74OYH6LpL1oGTVt/9vwmnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:56:17.757445Z"},"content_sha256":"3117fcfa46dfc8cfe26456b8cc298f88fd29e429df79afcdac52ab8ea7fe60f1","schema_version":"1.0","event_id":"sha256:3117fcfa46dfc8cfe26456b8cc298f88fd29e429df79afcdac52ab8ea7fe60f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JMN4VNIWARTZVW7OE3AXTBAOS/bundle.json","state_url":"https://pith.science/pith/4JMN4VNIWARTZVW7OE3AXTBAOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JMN4VNIWARTZVW7OE3AXTBAOS/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":"2026-05-28T21:56:17Z","links":{"resolver":"https://pith.science/pith/4JMN4VNIWARTZVW7OE3AXTBAOS","bundle":"https://pith.science/pith/4JMN4VNIWARTZVW7OE3AXTBAOS/bundle.json","state":"https://pith.science/pith/4JMN4VNIWARTZVW7OE3AXTBAOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JMN4VNIWARTZVW7OE3AXTBAOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4JMN4VNIWARTZVW7OE3AXTBAOS","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":"4c95acac6e44bf554a5824890291f7759d259d68e1eef3b7fc657ce1a82ec6af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-26T23:07:57Z","title_canon_sha256":"b1bb27ea8b48faaeea1a51e4795d57b3ed9bb79d86eff1b4e54e4e8c0aeb968c"},"schema_version":"1.0","source":{"id":"1706.08623","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08623","created_at":"2026-05-18T00:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08623v2","created_at":"2026-05-18T00:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08623","created_at":"2026-05-18T00:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"4JMN4VNIWART","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JMN4VNIWARTZVW7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JMN4VNI","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:3117fcfa46dfc8cfe26456b8cc298f88fd29e429df79afcdac52ab8ea7fe60f1","target":"graph","created_at":"2026-05-18T00:04:45Z","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 study billiard dynamics inside an ellipse for which the axes lengths are changed periodically in time and an $O(\\delta)$-small quartic polynomial deformation is added to the boundary. In this situation the energy of the particle in the billiard is no longer conserved. We show a Fermi acceleration in such system: there exists a billiard trajectory on which the energy tends to infinity. The construction is based on the analysis of dynamics in the phase space near a homoclinic intersection of the stable and unstable manifolds of the normally hyperbolic invariant cylinder $\\Lambda$, parameteris","authors_text":"Carl P. Dettmann, Dmitry Turaev, Vitaly Fain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-26T23:07:57Z","title":"Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08623","kind":"arxiv","version":2},"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":"sha256:28df167c6f2f1077a3b94ab922ec1974ff3798a3088e5a8c674e41a5a25f786a","target":"record","created_at":"2026-05-18T00:04:45Z","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":"4c95acac6e44bf554a5824890291f7759d259d68e1eef3b7fc657ce1a82ec6af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-26T23:07:57Z","title_canon_sha256":"b1bb27ea8b48faaeea1a51e4795d57b3ed9bb79d86eff1b4e54e4e8c0aeb968c"},"schema_version":"1.0","source":{"id":"1706.08623","kind":"arxiv","version":2}},"canonical_sha256":"e258de55a8b0233cd6df71360bcc207483dd1c9baee552f27b3b6bdd13636818","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e258de55a8b0233cd6df71360bcc207483dd1c9baee552f27b3b6bdd13636818","first_computed_at":"2026-05-18T00:04:45.385976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:45.385976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rnQMywPJZakO9bH1XGjUhvL5ZCFR0mqh+2ja4Wc6UdOXaSC3DC4dcSp7+rQQKMFDZ4MYOapMahCTy8nEUk42BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:45.386665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08623","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28df167c6f2f1077a3b94ab922ec1974ff3798a3088e5a8c674e41a5a25f786a","sha256:3117fcfa46dfc8cfe26456b8cc298f88fd29e429df79afcdac52ab8ea7fe60f1"],"state_sha256":"cdd7604ecb05c63f97e1b0f0e184a1b9b7a663240465485b9330f870061bf44b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q96zjWI4p7nyA5D8RMVGul+CJ4U5km5bkZz5YZI/sLa0/RfTIp7X8BQLJJvjsxNL+TITiInV+A2/+0DIxp3oBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:56:17.759463Z","bundle_sha256":"23b95fd4a2aef8e3eb33a4ae7238d24623e805a86dc74e3e0aeb6cd0da36811a"}}