{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TLHE3NC4J3SYII3S6E63OR5I2C","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":"47d8a8f4018865505f6d5aa71af71f545a70e051293195b4a3a00670e400e248","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-05-14T10:10:10Z","title_canon_sha256":"63574252e7a39625d28b90467a38fa1e069d04ee286b732a7974eb2a19a27c84"},"schema_version":"1.0","source":{"id":"1905.05494","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05494","created_at":"2026-07-05T05:43:06Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05494v3","created_at":"2026-07-05T05:43:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05494","created_at":"2026-07-05T05:43:06Z"},{"alias_kind":"pith_short_12","alias_value":"TLHE3NC4J3SY","created_at":"2026-07-05T05:43:06Z"},{"alias_kind":"pith_short_16","alias_value":"TLHE3NC4J3SYII3S","created_at":"2026-07-05T05:43:06Z"},{"alias_kind":"pith_short_8","alias_value":"TLHE3NC4","created_at":"2026-07-05T05:43:06Z"}],"graph_snapshots":[{"event_id":"sha256:00a8244795cf563b895e1ebf90ab12310c995770d1a7295285a35e12469bb960","target":"graph","created_at":"2026-07-05T05:43:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1905.05494/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We tackle the problem of efficiently approximating the volume of convex polytopes, when these are given in three different representations: H-polytopes, which have been studied extensively, V-polytopes, and zonotopes (Z-polytopes). We design a novel practical Multiphase Monte Carlo algorithm that leverages random walks based on billiard trajectories, as well as a new empirical convergence tests and a simulated annealing schedule of adaptive convex bodies. After tuning several parameters of our proposed method, we present a detailed experimental evaluation of our tuned algorithm using a rich da","authors_text":"Apostolos Chalkis, Ioannis Z. Emiris, Vissarion Fisikopoulos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-05-14T10:10:10Z","title":"A practical algorithm for volume estimation based on billiard trajectories and simulated annealing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05494","kind":"arxiv","version":3},"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":"sha256:46f27e45508f70c668f4def1f9087498ed2c38c556d5975a90e6d03147044017","target":"record","created_at":"2026-07-05T05:43:06Z","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":"47d8a8f4018865505f6d5aa71af71f545a70e051293195b4a3a00670e400e248","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-05-14T10:10:10Z","title_canon_sha256":"63574252e7a39625d28b90467a38fa1e069d04ee286b732a7974eb2a19a27c84"},"schema_version":"1.0","source":{"id":"1905.05494","kind":"arxiv","version":3}},"canonical_sha256":"9ace4db45c4ee5842372f13db747a8d0bdb9e6928097b69fccc85d24fbf8d12a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ace4db45c4ee5842372f13db747a8d0bdb9e6928097b69fccc85d24fbf8d12a","first_computed_at":"2026-07-05T05:43:06.120939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:43:06.120939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g8e+FE3Rqa+9oBMj6Ms8gm/6clc9C2iETvu+XpTRDGW0G/las8nTdeQcT2OwiCqM2gZwBZC7uaUrPamCXiItDA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:43:06.121354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05494","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46f27e45508f70c668f4def1f9087498ed2c38c556d5975a90e6d03147044017","sha256:00a8244795cf563b895e1ebf90ab12310c995770d1a7295285a35e12469bb960"],"state_sha256":"64584e0b8b42d40d8b494d410b481220edc1b5295f8a10a02258d19478bcf118"}