{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZIBMWLNG4EESEUYH3REQXKZFKN","short_pith_number":"pith:ZIBMWLNG","canonical_record":{"source":{"id":"2606.23841","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-22T18:23:31Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"bebe020dc30e3495adcc67e76d2b0456a9cb7f0e7a563eaf4ef92e631acbae92","abstract_canon_sha256":"58fcf1150adf97022f0ed9913a71ce255b01bfe44d2fb3154af013318668f406"},"schema_version":"1.0"},"canonical_sha256":"ca02cb2da6e109225307dc490bab25536cdf3164a067c6f4cff56ca33c07904d","source":{"kind":"arxiv","id":"2606.23841","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23841","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23841v1","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23841","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZIBMWLNG4EES","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_16","alias_value":"ZIBMWLNG4EESEUYH","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_8","alias_value":"ZIBMWLNG","created_at":"2026-06-24T00:14:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZIBMWLNG4EESEUYH3REQXKZFKN","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23841","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-22T18:23:31Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"bebe020dc30e3495adcc67e76d2b0456a9cb7f0e7a563eaf4ef92e631acbae92","abstract_canon_sha256":"58fcf1150adf97022f0ed9913a71ce255b01bfe44d2fb3154af013318668f406"},"schema_version":"1.0"},"canonical_sha256":"ca02cb2da6e109225307dc490bab25536cdf3164a067c6f4cff56ca33c07904d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T00:14:28.373675Z","signature_b64":"BNcxwx0Nsp11A8ejK98WoGdeuE1TsoamuRcx2XwlBXzuVxUuLhP7tc/32hjEmhoSHDrkY+n83yBlpNt9PkVuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca02cb2da6e109225307dc490bab25536cdf3164a067c6f4cff56ca33c07904d","last_reissued_at":"2026-06-24T00:14:28.373253Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T00:14:28.373253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23841","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-24T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ovl8QZuT2tE8q1BFAtL+9CqoAe7n3ZWUYUZDw/uxnw8doMxnZjSCioNNtwPQi32wzt/He84b62Hl02Gaya/xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T23:43:16.367494Z"},"content_sha256":"8da15c459b24a2febd2d70b569b6057f0bd2f03cdf9b0ad626e79156f74daf46","schema_version":"1.0","event_id":"sha256:8da15c459b24a2febd2d70b569b6057f0bd2f03cdf9b0ad626e79156f74daf46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZIBMWLNG4EESEUYH3REQXKZFKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational Framework for B\\'ezier Distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.OC","authors_text":"Andr\\'es L. Medaglia, Esteban Leiva, Luis F. Zuluaga","submitted_at":"2026-06-22T18:23:31Z","abstract_excerpt":"Flexible continuous univariate distributions with bounded support are essential for accurate input modeling in stochastic simulation and decision analysis. Although B\\'ezier distributions provide a powerful family capable of representing complex shapes, their adoption has been hindered by the lack of efficient fitting procedures and modern software implementations. This paper develops a computational framework for fitting B\\'ezier distributions to empirical data via both minimum error and maximum likelihood estimation, leveraging first-order optimization methods and exploiting the geometry of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23841","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23841/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-24T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RorY0E9xWF6z/L8dDCVGTLXjsJtjSGYHpu24qcwycgzka9gC2v16D2p1NNXXAUo6zbvIWHYFfCHEpLYMh4tSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T23:43:16.368066Z"},"content_sha256":"fd123243b30e901a171258383b10d9b3b6a082fcef5b0796f49ded179d05209b","schema_version":"1.0","event_id":"sha256:fd123243b30e901a171258383b10d9b3b6a082fcef5b0796f49ded179d05209b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIBMWLNG4EESEUYH3REQXKZFKN/bundle.json","state_url":"https://pith.science/pith/ZIBMWLNG4EESEUYH3REQXKZFKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIBMWLNG4EESEUYH3REQXKZFKN/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":"2026-07-31T23:43:16Z","links":{"resolver":"https://pith.science/pith/ZIBMWLNG4EESEUYH3REQXKZFKN","bundle":"https://pith.science/pith/ZIBMWLNG4EESEUYH3REQXKZFKN/bundle.json","state":"https://pith.science/pith/ZIBMWLNG4EESEUYH3REQXKZFKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIBMWLNG4EESEUYH3REQXKZFKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZIBMWLNG4EESEUYH3REQXKZFKN","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":"58fcf1150adf97022f0ed9913a71ce255b01bfe44d2fb3154af013318668f406","cross_cats_sorted":["stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-22T18:23:31Z","title_canon_sha256":"bebe020dc30e3495adcc67e76d2b0456a9cb7f0e7a563eaf4ef92e631acbae92"},"schema_version":"1.0","source":{"id":"2606.23841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23841","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23841v1","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23841","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZIBMWLNG4EES","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_16","alias_value":"ZIBMWLNG4EESEUYH","created_at":"2026-06-24T00:14:28Z"},{"alias_kind":"pith_short_8","alias_value":"ZIBMWLNG","created_at":"2026-06-24T00:14:28Z"}],"graph_snapshots":[{"event_id":"sha256:fd123243b30e901a171258383b10d9b3b6a082fcef5b0796f49ded179d05209b","target":"graph","created_at":"2026-06-24T00:14:28Z","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/2606.23841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Flexible continuous univariate distributions with bounded support are essential for accurate input modeling in stochastic simulation and decision analysis. Although B\\'ezier distributions provide a powerful family capable of representing complex shapes, their adoption has been hindered by the lack of efficient fitting procedures and modern software implementations. This paper develops a computational framework for fitting B\\'ezier distributions to empirical data via both minimum error and maximum likelihood estimation, leveraging first-order optimization methods and exploiting the geometry of ","authors_text":"Andr\\'es L. Medaglia, Esteban Leiva, Luis F. Zuluaga","cross_cats":["stat.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-22T18:23:31Z","title":"Computational Framework for B\\'ezier Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23841","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":"sha256:8da15c459b24a2febd2d70b569b6057f0bd2f03cdf9b0ad626e79156f74daf46","target":"record","created_at":"2026-06-24T00:14:28Z","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":"58fcf1150adf97022f0ed9913a71ce255b01bfe44d2fb3154af013318668f406","cross_cats_sorted":["stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-22T18:23:31Z","title_canon_sha256":"bebe020dc30e3495adcc67e76d2b0456a9cb7f0e7a563eaf4ef92e631acbae92"},"schema_version":"1.0","source":{"id":"2606.23841","kind":"arxiv","version":1}},"canonical_sha256":"ca02cb2da6e109225307dc490bab25536cdf3164a067c6f4cff56ca33c07904d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca02cb2da6e109225307dc490bab25536cdf3164a067c6f4cff56ca33c07904d","first_computed_at":"2026-06-24T00:14:28.373253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T00:14:28.373253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BNcxwx0Nsp11A8ejK98WoGdeuE1TsoamuRcx2XwlBXzuVxUuLhP7tc/32hjEmhoSHDrkY+n83yBlpNt9PkVuBg==","signature_status":"signed_v1","signed_at":"2026-06-24T00:14:28.373675Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da15c459b24a2febd2d70b569b6057f0bd2f03cdf9b0ad626e79156f74daf46","sha256:fd123243b30e901a171258383b10d9b3b6a082fcef5b0796f49ded179d05209b"],"state_sha256":"fd55a5e01ac803478ad8d8c4bb2a6d3893b4cdea727f566229cf356f65384f49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FqW5GCmxR9Z7NpcY/s1bjmZGKtl3Rt7X92CJy4OJtZS9t16IeU5lTMullDtDJ+3wXBL/ALkb76Dw3Qm1MF/nBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T23:43:16.372087Z","bundle_sha256":"533d0c1dde9987f9c5c13b75135725ca28c0164c597d8dd6ff598ec9ad0883cd"}}