{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MVQAGDF5FLRMCQ4I26FCRJEE76","short_pith_number":"pith:MVQAGDF5","canonical_record":{"source":{"id":"1601.04483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T11:55:35Z","cross_cats_sorted":[],"title_canon_sha256":"4d45184e845531744fb6671fccc7397da824febcdf82ac175ab9fbc540687233","abstract_canon_sha256":"392499027bd568ec62f9cb2ad5dc476daf87b78f17c457f73b7c23a79f663d7e"},"schema_version":"1.0"},"canonical_sha256":"6560030cbd2ae2c14388d78a28a484ffabc833a6195affa622e42410525e53e5","source":{"kind":"arxiv","id":"1601.04483","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04483","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04483v1","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04483","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"pith_short_12","alias_value":"MVQAGDF5FLRM","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVQAGDF5FLRMCQ4I","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVQAGDF5","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MVQAGDF5FLRMCQ4I26FCRJEE76","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T11:55:35Z","cross_cats_sorted":[],"title_canon_sha256":"4d45184e845531744fb6671fccc7397da824febcdf82ac175ab9fbc540687233","abstract_canon_sha256":"392499027bd568ec62f9cb2ad5dc476daf87b78f17c457f73b7c23a79f663d7e"},"schema_version":"1.0"},"canonical_sha256":"6560030cbd2ae2c14388d78a28a484ffabc833a6195affa622e42410525e53e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:44.913256Z","signature_b64":"+v91vWlMj9dJjLPTd6gmSLWY/8Q/CSfQkD0jhIWDd9XHUXgp9iaOHb9SAT8ivfvuXpCszBCI++3oxI9I+p95CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6560030cbd2ae2c14388d78a28a484ffabc833a6195affa622e42410525e53e5","last_reissued_at":"2026-05-18T01:22:44.912829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:44.912829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04483","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":"2026-05-18T01:22:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SwFcv0y+Xfud1S41EVXQjb4/UsaWMD91wtp5vHL84DU0N8N4ANoWhEmYFmyatoJTXXak+O74cLhUE1t7McHOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:27:48.672665Z"},"content_sha256":"37432211b62c2c34e1ec5492827271c4521ad80b9427508bdfcb4b0768374997","schema_version":"1.0","event_id":"sha256:37432211b62c2c34e1ec5492827271c4521ad80b9427508bdfcb4b0768374997"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MVQAGDF5FLRMCQ4I26FCRJEE76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial approximations to continuous functions and stochastic compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Linglong Yuan, Michael A. Zazanis, Takis Konstantopoulos","submitted_at":"2016-01-18T11:55:35Z","abstract_excerpt":"This paper presents a stochastic approach to theorems concerning the behavior of iterations of the Bernstein operator $B_n$ taking a continuous function $f \\in C[0,1]$ to a degree-$n$ polynomial when the number of iterations $k$ tends to infinity and $n$ is kept fixed or when $n$ tends to infinity as well. In the first instance, the underlying stochastic process is the so-called Wright-Fisher model, whereas, in the second instance, the underlying stochastic process is the Wright-Fisher diffusion. Both processes are probably the most basic ones in mathematical genetics. By using Markov chain th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04483","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":""},"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":"2026-05-18T01:22:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H853xChNQ+zkMZP9wnHLW/LGfwAUiIXJR1N7gSN3+ytBjwi6XdcLU4uYBnGIoQ4hq+fUT/OW/DfXfff1NOnkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:27:48.673014Z"},"content_sha256":"c53f03b1d25956a12599c08af3146682fe65b911abe8d87ec95e6ad1940fb566","schema_version":"1.0","event_id":"sha256:c53f03b1d25956a12599c08af3146682fe65b911abe8d87ec95e6ad1940fb566"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVQAGDF5FLRMCQ4I26FCRJEE76/bundle.json","state_url":"https://pith.science/pith/MVQAGDF5FLRMCQ4I26FCRJEE76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVQAGDF5FLRMCQ4I26FCRJEE76/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":"2026-06-25T12:27:48Z","links":{"resolver":"https://pith.science/pith/MVQAGDF5FLRMCQ4I26FCRJEE76","bundle":"https://pith.science/pith/MVQAGDF5FLRMCQ4I26FCRJEE76/bundle.json","state":"https://pith.science/pith/MVQAGDF5FLRMCQ4I26FCRJEE76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVQAGDF5FLRMCQ4I26FCRJEE76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MVQAGDF5FLRMCQ4I26FCRJEE76","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":"392499027bd568ec62f9cb2ad5dc476daf87b78f17c457f73b7c23a79f663d7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T11:55:35Z","title_canon_sha256":"4d45184e845531744fb6671fccc7397da824febcdf82ac175ab9fbc540687233"},"schema_version":"1.0","source":{"id":"1601.04483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04483","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04483v1","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04483","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"pith_short_12","alias_value":"MVQAGDF5FLRM","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVQAGDF5FLRMCQ4I","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVQAGDF5","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:c53f03b1d25956a12599c08af3146682fe65b911abe8d87ec95e6ad1940fb566","target":"graph","created_at":"2026-05-18T01:22:44Z","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 paper presents a stochastic approach to theorems concerning the behavior of iterations of the Bernstein operator $B_n$ taking a continuous function $f \\in C[0,1]$ to a degree-$n$ polynomial when the number of iterations $k$ tends to infinity and $n$ is kept fixed or when $n$ tends to infinity as well. In the first instance, the underlying stochastic process is the so-called Wright-Fisher model, whereas, in the second instance, the underlying stochastic process is the Wright-Fisher diffusion. Both processes are probably the most basic ones in mathematical genetics. By using Markov chain th","authors_text":"Linglong Yuan, Michael A. Zazanis, Takis Konstantopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T11:55:35Z","title":"Polynomial approximations to continuous functions and stochastic compositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04483","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":"sha256:37432211b62c2c34e1ec5492827271c4521ad80b9427508bdfcb4b0768374997","target":"record","created_at":"2026-05-18T01:22:44Z","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":"392499027bd568ec62f9cb2ad5dc476daf87b78f17c457f73b7c23a79f663d7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-18T11:55:35Z","title_canon_sha256":"4d45184e845531744fb6671fccc7397da824febcdf82ac175ab9fbc540687233"},"schema_version":"1.0","source":{"id":"1601.04483","kind":"arxiv","version":1}},"canonical_sha256":"6560030cbd2ae2c14388d78a28a484ffabc833a6195affa622e42410525e53e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6560030cbd2ae2c14388d78a28a484ffabc833a6195affa622e42410525e53e5","first_computed_at":"2026-05-18T01:22:44.912829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:44.912829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+v91vWlMj9dJjLPTd6gmSLWY/8Q/CSfQkD0jhIWDd9XHUXgp9iaOHb9SAT8ivfvuXpCszBCI++3oxI9I+p95CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:44.913256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37432211b62c2c34e1ec5492827271c4521ad80b9427508bdfcb4b0768374997","sha256:c53f03b1d25956a12599c08af3146682fe65b911abe8d87ec95e6ad1940fb566"],"state_sha256":"abb517ff85a57ab14b6a4677212ad2b64dde0563540009b298e9d1b0093b0d12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L9otd17Xj9MouJTZS9vcLm0nzrNGk8b6fwNfYPi6mMr9akD9HqgwSVlrkvqMPvvcBkaZg/2srYAKJGhhsjiMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:27:48.674942Z","bundle_sha256":"d231f11c2327483beb279577a91a761bd63336828a3eb1cfa08b10b94e83bb50"}}