{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:LQBB4CVSBJJ7NMNTLGNKJ6BOER","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":"7a22fe963e1aca49320f525e08e8e24a9e2dbda068cad106be2480371f8fe47e","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2002-08-27T15:45:45Z","title_canon_sha256":"6b2140e57dabb907f5417d542dd346762dad0eed2a0efdb16f10f6d5464ac440"},"schema_version":"1.0","source":{"id":"nlin/0208037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0208037","created_at":"2026-05-18T03:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0208037v1","created_at":"2026-05-18T03:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0208037","created_at":"2026-05-18T03:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"LQBB4CVSBJJ7","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"LQBB4CVSBJJ7NMNT","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"LQBB4CVS","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:6a6982bbd4e255ce1a3c4401aba836f989df88e88db4cf689c5c4e80bb15bb04","target":"graph","created_at":"2026-05-18T03:56:58Z","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 perform fractal analysis on a closed classical hard-wall billiard, the circular billiard with a straight cut, assuming there are two openings on the boundary. We use a two-dimensional set of initial conditions that produce all possible trajectories of a particle injected from one opening, and numerically compute the fractal dimension of singular points of a function that maps an initial condition to the number of collisions with the wall before the exit. We introduce a simplified box-counting algorithm, which uses points from a rectangular grid inside the two-dimensional set of the initial ","authors_text":"Suhan Ree","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2002-08-27T15:45:45Z","title":"Fractal analysis on a closed classical hard-wall billiard using a simplified box-counting algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0208037","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":"sha256:41e69e644adb9eeaa9874ecbe35f52f9251bfbcfdd599856795865c281d0dd15","target":"record","created_at":"2026-05-18T03:56:58Z","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":"7a22fe963e1aca49320f525e08e8e24a9e2dbda068cad106be2480371f8fe47e","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2002-08-27T15:45:45Z","title_canon_sha256":"6b2140e57dabb907f5417d542dd346762dad0eed2a0efdb16f10f6d5464ac440"},"schema_version":"1.0","source":{"id":"nlin/0208037","kind":"arxiv","version":1}},"canonical_sha256":"5c021e0ab20a53f6b1b3599aa4f82e2475093c5686bc92b84dda924e95b2b9ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c021e0ab20a53f6b1b3599aa4f82e2475093c5686bc92b84dda924e95b2b9ca","first_computed_at":"2026-05-18T03:56:58.528738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:58.528738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yX8pqwe+giKYHgfNwbgNmg5mFNAKelHTei+gMsRFyp1vnXYnSmT7NA8Y22UAqp+tFzDlZZyg4FqgERTyI4iUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:58.529661Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0208037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41e69e644adb9eeaa9874ecbe35f52f9251bfbcfdd599856795865c281d0dd15","sha256:6a6982bbd4e255ce1a3c4401aba836f989df88e88db4cf689c5c4e80bb15bb04"],"state_sha256":"1cd9d616e9bc7c27d6790dfe2904915d730cb9e35fe9b80017b20a1243db633d"}