{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:566ZF7UDV7UCCITP3MHIUIRJYG","short_pith_number":"pith:566ZF7UD","canonical_record":{"source":{"id":"2606.26809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-06-25T09:50:34Z","cross_cats_sorted":[],"title_canon_sha256":"fc5672ac2b3cc44dadf5ea486c73fcbd351f4a8a291f1ee9b5cfbbfa63fc7f21","abstract_canon_sha256":"5903dec9c9835beb04b90a56db06522483c76ebff280c46f35564799a702a9cf"},"schema_version":"1.0"},"canonical_sha256":"efbd92fe83afe821226fdb0e8a2229c1bef5ed7b80428281e303efa129ac145f","source":{"kind":"arxiv","id":"2606.26809","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26809","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26809v1","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26809","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"566ZF7UDV7UC","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"pith_short_16","alias_value":"566ZF7UDV7UCCITP","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"pith_short_8","alias_value":"566ZF7UD","created_at":"2026-06-26T01:16:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:566ZF7UDV7UCCITP3MHIUIRJYG","target":"record","payload":{"canonical_record":{"source":{"id":"2606.26809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-06-25T09:50:34Z","cross_cats_sorted":[],"title_canon_sha256":"fc5672ac2b3cc44dadf5ea486c73fcbd351f4a8a291f1ee9b5cfbbfa63fc7f21","abstract_canon_sha256":"5903dec9c9835beb04b90a56db06522483c76ebff280c46f35564799a702a9cf"},"schema_version":"1.0"},"canonical_sha256":"efbd92fe83afe821226fdb0e8a2229c1bef5ed7b80428281e303efa129ac145f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:00.431285Z","signature_b64":"GI1LWN446YinTfNc2OFSP0SDETnMFveJWpNLXLa+YTz+OENgQUfI+Y8hzIc7Kusga/UqcWjDo/8puNmWvnWQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efbd92fe83afe821226fdb0e8a2229c1bef5ed7b80428281e303efa129ac145f","last_reissued_at":"2026-06-26T01:16:00.430885Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:00.430885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.26809","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":"2026-06-26T01:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0yhqsha5nkLOTTFZLvlnErlqZ8dyUWI5hZsjcqSitPtkZiFgJP3lfckl7gIgVqr5Gj+MhFLRm/XG883K3sGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:03:09.816597Z"},"content_sha256":"24a793435eb0de66a5b8d54f10eafe356a3b7b65de8959e35b97e131b029ac71","schema_version":"1.0","event_id":"sha256:24a793435eb0de66a5b8d54f10eafe356a3b7b65de8959e35b97e131b029ac71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:566ZF7UDV7UCCITP3MHIUIRJYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Educational Proof Assistant Waterproof in an Introductory Proof Course: Proof Construction and Learning Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Jim Portegies, Johan Commelin, Pim Otte, Rogier Bos","submitted_at":"2026-06-25T09:50:34Z","abstract_excerpt":"We study the use of an educational proof assistant in an introductory proof course through a quasi-experiment in a varied setting: multiple teachers, students with different study programs, and a mixed Dutch-English language environment. First-year university students are known to struggle with writing proofs. Waterproof is a proof assistant that is designed to support the transfer of skills to paper proofs by working with controlled natural language. We focus on the students' ability to construct valid mathematical proofs, and on their learning process. We study this through in-class observat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26809","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/2606.26809/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":"2026-06-26T01:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGpJNSGkn4fj0PN6PAEbRCVBauC5gUchq8Qz0+ryPDLiORur1Bo9L1Ei0bExyg5NIKl/rQw+i27P9zE6sJxdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:03:09.816962Z"},"content_sha256":"e5293680eb6636bcdce3ae22c36af3e1911b5ceb5e2f9d37bb774a9bd98ea446","schema_version":"1.0","event_id":"sha256:e5293680eb6636bcdce3ae22c36af3e1911b5ceb5e2f9d37bb774a9bd98ea446"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/566ZF7UDV7UCCITP3MHIUIRJYG/bundle.json","state_url":"https://pith.science/pith/566ZF7UDV7UCCITP3MHIUIRJYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/566ZF7UDV7UCCITP3MHIUIRJYG/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":"2026-06-27T10:03:09Z","links":{"resolver":"https://pith.science/pith/566ZF7UDV7UCCITP3MHIUIRJYG","bundle":"https://pith.science/pith/566ZF7UDV7UCCITP3MHIUIRJYG/bundle.json","state":"https://pith.science/pith/566ZF7UDV7UCCITP3MHIUIRJYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/566ZF7UDV7UCCITP3MHIUIRJYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:566ZF7UDV7UCCITP3MHIUIRJYG","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":"5903dec9c9835beb04b90a56db06522483c76ebff280c46f35564799a702a9cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-06-25T09:50:34Z","title_canon_sha256":"fc5672ac2b3cc44dadf5ea486c73fcbd351f4a8a291f1ee9b5cfbbfa63fc7f21"},"schema_version":"1.0","source":{"id":"2606.26809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26809","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26809v1","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26809","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"566ZF7UDV7UC","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"pith_short_16","alias_value":"566ZF7UDV7UCCITP","created_at":"2026-06-26T01:16:00Z"},{"alias_kind":"pith_short_8","alias_value":"566ZF7UD","created_at":"2026-06-26T01:16:00Z"}],"graph_snapshots":[{"event_id":"sha256:e5293680eb6636bcdce3ae22c36af3e1911b5ceb5e2f9d37bb774a9bd98ea446","target":"graph","created_at":"2026-06-26T01:16:00Z","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/2606.26809/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the use of an educational proof assistant in an introductory proof course through a quasi-experiment in a varied setting: multiple teachers, students with different study programs, and a mixed Dutch-English language environment. First-year university students are known to struggle with writing proofs. Waterproof is a proof assistant that is designed to support the transfer of skills to paper proofs by working with controlled natural language. We focus on the students' ability to construct valid mathematical proofs, and on their learning process. We study this through in-class observat","authors_text":"Jim Portegies, Johan Commelin, Pim Otte, Rogier Bos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-06-25T09:50:34Z","title":"The Educational Proof Assistant Waterproof in an Introductory Proof Course: Proof Construction and Learning Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26809","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":"sha256:24a793435eb0de66a5b8d54f10eafe356a3b7b65de8959e35b97e131b029ac71","target":"record","created_at":"2026-06-26T01:16:00Z","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":"5903dec9c9835beb04b90a56db06522483c76ebff280c46f35564799a702a9cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-06-25T09:50:34Z","title_canon_sha256":"fc5672ac2b3cc44dadf5ea486c73fcbd351f4a8a291f1ee9b5cfbbfa63fc7f21"},"schema_version":"1.0","source":{"id":"2606.26809","kind":"arxiv","version":1}},"canonical_sha256":"efbd92fe83afe821226fdb0e8a2229c1bef5ed7b80428281e303efa129ac145f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efbd92fe83afe821226fdb0e8a2229c1bef5ed7b80428281e303efa129ac145f","first_computed_at":"2026-06-26T01:16:00.430885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:00.430885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GI1LWN446YinTfNc2OFSP0SDETnMFveJWpNLXLa+YTz+OENgQUfI+Y8hzIc7Kusga/UqcWjDo/8puNmWvnWQCg==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:00.431285Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24a793435eb0de66a5b8d54f10eafe356a3b7b65de8959e35b97e131b029ac71","sha256:e5293680eb6636bcdce3ae22c36af3e1911b5ceb5e2f9d37bb774a9bd98ea446"],"state_sha256":"4cfe639b2649b7222d1e07fd6ee0396f39e25f5a909c4b36ec4d53ca292713d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPHV2K4aNX046r89U11o2SQeY7jjiLrFEikxX30p1rCUq4gHrYJU3qm0tqsSHhhGlKuqlYnlb0IfrwvD9ECJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:03:09.818944Z","bundle_sha256":"35a37081e750c05f16099625c4adf5a1e9745271edfe9e363c3a1a1e66db20f2"}}