{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YLGFZ66PINEKWXA5MKC3QHXHYP","short_pith_number":"pith:YLGFZ66P","canonical_record":{"source":{"id":"1204.2723","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T13:49:58Z","cross_cats_sorted":[],"title_canon_sha256":"360ea80b3257167ea0e5ed668dd2a5cc027879b3e4656c9ecb50e90c65b05012","abstract_canon_sha256":"8dc15fa253f0f6c0b868928e234c1aa99d9c357b54c185b8d4063b586e3609bc"},"schema_version":"1.0"},"canonical_sha256":"c2cc5cfbcf4348ab5c1d6285b81ee7c3c20b4ae1b6d42e8ebac966dc4079ae6c","source":{"kind":"arxiv","id":"1204.2723","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2723","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2723v2","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2723","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"pith_short_12","alias_value":"YLGFZ66PINEK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YLGFZ66PINEKWXA5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YLGFZ66P","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YLGFZ66PINEKWXA5MKC3QHXHYP","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2723","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T13:49:58Z","cross_cats_sorted":[],"title_canon_sha256":"360ea80b3257167ea0e5ed668dd2a5cc027879b3e4656c9ecb50e90c65b05012","abstract_canon_sha256":"8dc15fa253f0f6c0b868928e234c1aa99d9c357b54c185b8d4063b586e3609bc"},"schema_version":"1.0"},"canonical_sha256":"c2cc5cfbcf4348ab5c1d6285b81ee7c3c20b4ae1b6d42e8ebac966dc4079ae6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:47.254734Z","signature_b64":"xbMQtFuaP/wvdTkaqJtB8JANO65v4PoVUFl421ftugwbEhp1L2lAVoz2kKIXGEinI/Ugk3fYnFp7bA9/2YZgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2cc5cfbcf4348ab5c1d6285b81ee7c3c20b4ae1b6d42e8ebac966dc4079ae6c","last_reissued_at":"2026-05-18T03:46:47.253918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:47.253918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2723","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPeFoeFiFxSrKw9AtMN0PzF/eXMkM+4avQy4xECYllcqIGiHBdFeUfggqCMGsOFvxIUAOpXIfr5jrKvFb7HLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:13:35.394570Z"},"content_sha256":"45eb544e085903a4ff5a51f2143b31857134c3bf785a4add9af17317beb7e2fe","schema_version":"1.0","event_id":"sha256:45eb544e085903a4ff5a51f2143b31857134c3bf785a4add9af17317beb7e2fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YLGFZ66PINEKWXA5MKC3QHXHYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the composition and decomposition of positive linear operators III: A non-trivial decomposition of the Bernstein operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexandru Lupa\\c{s}, Heiner Gonska, Ioan Ra\\c{s}a, Margareta Heilmann","submitted_at":"2012-04-12T13:49:58Z","abstract_excerpt":"The central problem in this technical report is the question if the classical Bernstein operator can be decomposed into nontrivial building blocks where one of the factors is the genuine Beta operator introduced by M\\\"uhlbach and Lupa\\c{s}. We collect several properties of the Beta operator such as injectivity, the eigenstructure and the images of the monomials under its inverse. Moreover, we give a decomposition of the form $B_n = \\bar{\\mathbb{B}}_n \\circ F_n $ where $F_n$ is a nonpositive linear operator having quite interesting properties. We study the images of the monomials under $F_n$, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2723","kind":"arxiv","version":2},"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":"2026-05-18T03:46:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TvAA24q9RjAkZeVzvgnqrw4zckckz3sLTjER7Vnl+7Colx/GOzVHhOAMrjwUPp2NoS2QgLm3KCI9WuPmBsnuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:13:35.394911Z"},"content_sha256":"3d9b67dc4563322fad76f0507ca3a37958f7d048de4b896dba4970128d4c947f","schema_version":"1.0","event_id":"sha256:3d9b67dc4563322fad76f0507ca3a37958f7d048de4b896dba4970128d4c947f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLGFZ66PINEKWXA5MKC3QHXHYP/bundle.json","state_url":"https://pith.science/pith/YLGFZ66PINEKWXA5MKC3QHXHYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLGFZ66PINEKWXA5MKC3QHXHYP/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":"2026-06-23T09:13:35Z","links":{"resolver":"https://pith.science/pith/YLGFZ66PINEKWXA5MKC3QHXHYP","bundle":"https://pith.science/pith/YLGFZ66PINEKWXA5MKC3QHXHYP/bundle.json","state":"https://pith.science/pith/YLGFZ66PINEKWXA5MKC3QHXHYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLGFZ66PINEKWXA5MKC3QHXHYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YLGFZ66PINEKWXA5MKC3QHXHYP","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":"8dc15fa253f0f6c0b868928e234c1aa99d9c357b54c185b8d4063b586e3609bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T13:49:58Z","title_canon_sha256":"360ea80b3257167ea0e5ed668dd2a5cc027879b3e4656c9ecb50e90c65b05012"},"schema_version":"1.0","source":{"id":"1204.2723","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2723","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2723v2","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2723","created_at":"2026-05-18T03:46:47Z"},{"alias_kind":"pith_short_12","alias_value":"YLGFZ66PINEK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YLGFZ66PINEKWXA5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YLGFZ66P","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:3d9b67dc4563322fad76f0507ca3a37958f7d048de4b896dba4970128d4c947f","target":"graph","created_at":"2026-05-18T03:46:47Z","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":"The central problem in this technical report is the question if the classical Bernstein operator can be decomposed into nontrivial building blocks where one of the factors is the genuine Beta operator introduced by M\\\"uhlbach and Lupa\\c{s}. We collect several properties of the Beta operator such as injectivity, the eigenstructure and the images of the monomials under its inverse. Moreover, we give a decomposition of the form $B_n = \\bar{\\mathbb{B}}_n \\circ F_n $ where $F_n$ is a nonpositive linear operator having quite interesting properties. We study the images of the monomials under $F_n$, i","authors_text":"Alexandru Lupa\\c{s}, Heiner Gonska, Ioan Ra\\c{s}a, Margareta Heilmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T13:49:58Z","title":"On the composition and decomposition of positive linear operators III: A non-trivial decomposition of the Bernstein operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2723","kind":"arxiv","version":2},"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":"sha256:45eb544e085903a4ff5a51f2143b31857134c3bf785a4add9af17317beb7e2fe","target":"record","created_at":"2026-05-18T03:46:47Z","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":"8dc15fa253f0f6c0b868928e234c1aa99d9c357b54c185b8d4063b586e3609bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T13:49:58Z","title_canon_sha256":"360ea80b3257167ea0e5ed668dd2a5cc027879b3e4656c9ecb50e90c65b05012"},"schema_version":"1.0","source":{"id":"1204.2723","kind":"arxiv","version":2}},"canonical_sha256":"c2cc5cfbcf4348ab5c1d6285b81ee7c3c20b4ae1b6d42e8ebac966dc4079ae6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2cc5cfbcf4348ab5c1d6285b81ee7c3c20b4ae1b6d42e8ebac966dc4079ae6c","first_computed_at":"2026-05-18T03:46:47.253918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:47.253918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xbMQtFuaP/wvdTkaqJtB8JANO65v4PoVUFl421ftugwbEhp1L2lAVoz2kKIXGEinI/Ugk3fYnFp7bA9/2YZgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:47.254734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2723","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45eb544e085903a4ff5a51f2143b31857134c3bf785a4add9af17317beb7e2fe","sha256:3d9b67dc4563322fad76f0507ca3a37958f7d048de4b896dba4970128d4c947f"],"state_sha256":"8203325299ef4505e1a5df77686d244f1898716bef920fae6fa47a1738448ecb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H047LLyVtTRqp9R2D7BFQSR2G3fhqtaNgLZJRkiR3d+odLkqtrEKTTdUNkW2ryqM3ZiL/OZf1pBWwCHJAmdwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T09:13:35.399437Z","bundle_sha256":"7dc7f1e87b35e26abe662092e3c7ba22ef21a59758c72667a11935072f7dc798"}}