{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XJQDTGCK7N6FWHWRNWQFDAYQI3","short_pith_number":"pith:XJQDTGCK","schema_version":"1.0","canonical_sha256":"ba6039984afb7c5b1ed16da051831046f19b4b8a6792bfe74b86b08967bb742f","source":{"kind":"arxiv","id":"1311.4972","version":2},"attestation_state":"computed","paper":{"title":"Fermi acceleration in chaotic shape-preserving billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Benjamin Batisti\\'c","submitted_at":"2013-11-20T07:40:33Z","abstract_excerpt":"We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law $v = n^{\\beta}$ with respect to the number of collisions n. If the shape of the chaotic time-dependent billiard is not preserved it is well known that the acceleration exponent is $\\beta = 1/2$. We show, on the other hand, that if the shape of the billiard is preserved then the only possible values of $\\beta$ are $1/4$, $1/6$ and in a special case $0$. We show that the va"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.4972","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-11-20T07:40:33Z","cross_cats_sorted":[],"title_canon_sha256":"3e7a81f6fbbd8b5e705787b3d29e0941bfc41a9be4dbb7b64a9cd6e4050492d2","abstract_canon_sha256":"d6b7f33c3eb751804b44c8335d5a2a1c93eae5b458a3a9e5b89cecd5f3a4b789"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:22.625483Z","signature_b64":"XTzpCWQHD5BgY6ia2pde4AtwGjyp1fKpWVUN69rv5i7iw3H/Xvp+2VognE90RgDndY5hrT62xmuFtUguDAuTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba6039984afb7c5b1ed16da051831046f19b4b8a6792bfe74b86b08967bb742f","last_reissued_at":"2026-05-18T01:46:22.624683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:22.624683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fermi acceleration in chaotic shape-preserving billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Benjamin Batisti\\'c","submitted_at":"2013-11-20T07:40:33Z","abstract_excerpt":"We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law $v = n^{\\beta}$ with respect to the number of collisions n. If the shape of the chaotic time-dependent billiard is not preserved it is well known that the acceleration exponent is $\\beta = 1/2$. We show, on the other hand, that if the shape of the billiard is preserved then the only possible values of $\\beta$ are $1/4$, $1/6$ and in a special case $0$. We show that the va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4972","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.4972","created_at":"2026-05-18T01:46:22.624747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4972v2","created_at":"2026-05-18T01:46:22.624747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4972","created_at":"2026-05-18T01:46:22.624747+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJQDTGCK7N6F","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJQDTGCK7N6FWHWR","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJQDTGCK","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3","json":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3.json","graph_json":"https://pith.science/api/pith-number/XJQDTGCK7N6FWHWRNWQFDAYQI3/graph.json","events_json":"https://pith.science/api/pith-number/XJQDTGCK7N6FWHWRNWQFDAYQI3/events.json","paper":"https://pith.science/paper/XJQDTGCK"},"agent_actions":{"view_html":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3","download_json":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3.json","view_paper":"https://pith.science/paper/XJQDTGCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4972&json=true","fetch_graph":"https://pith.science/api/pith-number/XJQDTGCK7N6FWHWRNWQFDAYQI3/graph.json","fetch_events":"https://pith.science/api/pith-number/XJQDTGCK7N6FWHWRNWQFDAYQI3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3/action/storage_attestation","attest_author":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3/action/author_attestation","sign_citation":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3/action/citation_signature","submit_replication":"https://pith.science/pith/XJQDTGCK7N6FWHWRNWQFDAYQI3/action/replication_record"}},"created_at":"2026-05-18T01:46:22.624747+00:00","updated_at":"2026-05-18T01:46:22.624747+00:00"}