{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:L5BHYZCT3LTPYUFK26M5LMO2V5","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":"df6af54173a806d983b129818d78e762df7e8cb0af9be8d87a84380af90cd59a","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2006-12-06T13:03:40Z","title_canon_sha256":"595f3df85175ba30bcba56c3ff0317c16878bedba6cdc34ff9ede6017a50b59b"},"schema_version":"1.0","source":{"id":"nlin/0612016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0612016","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0612016v1","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0612016","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"L5BHYZCT3LTP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"L5BHYZCT3LTPYUFK","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"L5BHYZCT","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:8dd72b2584a060d814bace6839bda8c4c121d25656e8b9330277f4300aea8812","target":"graph","created_at":"2026-05-18T04:09:56Z","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":"This supplement to the article \"Approximating multi-dimensional Hamiltonian flows by billiards\" contains the proofs of C$^{0}$ and C$^{r}$ - closeness theorems stated in the article.","authors_text":"A. Rapoport, D. Turaev, V. Rom-Kedar","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2006-12-06T13:03:40Z","title":"Supplement to the article \"Approximating multi-dimensional Hamiltonian flows by billiards\": Proof of C$^{0}$ and C$^{r}$ - closeness Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0612016","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:e2d52010110cce6184e6c434c2d100fb13bdb13ebf5e6f03991f69ac80183d4a","target":"record","created_at":"2026-05-18T04:09:56Z","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":"df6af54173a806d983b129818d78e762df7e8cb0af9be8d87a84380af90cd59a","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2006-12-06T13:03:40Z","title_canon_sha256":"595f3df85175ba30bcba56c3ff0317c16878bedba6cdc34ff9ede6017a50b59b"},"schema_version":"1.0","source":{"id":"nlin/0612016","kind":"arxiv","version":1}},"canonical_sha256":"5f427c6453dae6fc50aad799d5b1daaf580c88ffbaf5a98b8cbeb4ca2cb206e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f427c6453dae6fc50aad799d5b1daaf580c88ffbaf5a98b8cbeb4ca2cb206e8","first_computed_at":"2026-05-18T04:09:56.661788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:56.661788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8W7cAMJnZsxu3w/bqIrQAjE+f3KEcXFrWb3Khv4gZOTruB+ew5OqjyyEld3EbnllB0PwbL2Cdpx9fBfWY+59CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:56.662577Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0612016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2d52010110cce6184e6c434c2d100fb13bdb13ebf5e6f03991f69ac80183d4a","sha256:8dd72b2584a060d814bace6839bda8c4c121d25656e8b9330277f4300aea8812"],"state_sha256":"e6b1c159f1b809110671f6e2222ebfae3eb805158af8af3e38e520d9ad3defd8"}