{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LHH4MPZTHUMRVMQWWSNAXGGJGT","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":"da8c9e81e9306090ee019fa6c317f4c81ffd0a91bc755962089a7582a826ce42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2014-07-15T06:15:21Z","title_canon_sha256":"d0cdf0a163fcd8ffad6967f398c50140c1b730e19a6642e1fa8bd2a298f9165a"},"schema_version":"1.0","source":{"id":"1407.3888","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3888","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3888v2","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3888","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"LHH4MPZTHUMR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LHH4MPZTHUMRVMQW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LHH4MPZT","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:3fbbcaaa4b34e3aec23798ab0593ce5f1f58405075eca0bf1ce67a44cfa28c65","target":"graph","created_at":"2026-05-18T02:41:25Z","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":"Expanding our knowledge of student difficulties in advanced undergraduate electromagnetism is essential if we are to develop effective instructional interventions. Drawing on an analysis of course materials, in-class observations and responses to conceptual questions, we document specific resources employed by students when reasoning about the divergence of a vector field. One common student error, which persisted in our course despite explicit instruction, is to misinterpret any \"spreading out\" of field lines in a diagram as representing a place of non-zero divergence. Some of these student d","authors_text":"Cecilia Astolfi, Charles Baily","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2014-07-15T06:15:21Z","title":"Student Reasoning About the Divergence of a Vector Field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3888","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":"sha256:407171f51280bfdd02fdd04be693f3330be80852df7fd39e05c09dc4a091fbfb","target":"record","created_at":"2026-05-18T02:41:25Z","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":"da8c9e81e9306090ee019fa6c317f4c81ffd0a91bc755962089a7582a826ce42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2014-07-15T06:15:21Z","title_canon_sha256":"d0cdf0a163fcd8ffad6967f398c50140c1b730e19a6642e1fa8bd2a298f9165a"},"schema_version":"1.0","source":{"id":"1407.3888","kind":"arxiv","version":2}},"canonical_sha256":"59cfc63f333d191ab216b49a0b98c934ec5b17bd474b5b3bc546aee6b6d4082c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59cfc63f333d191ab216b49a0b98c934ec5b17bd474b5b3bc546aee6b6d4082c","first_computed_at":"2026-05-18T02:41:25.849491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:25.849491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClEz6Gy9vMnM8cG1szEc3leKdOfbX5uGPc/+iNJ5v2UXEdvYYrp/HlY7k3wobQ2yDBxB+oaNWkd8wm8Ir8vOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:25.850021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3888","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:407171f51280bfdd02fdd04be693f3330be80852df7fd39e05c09dc4a091fbfb","sha256:3fbbcaaa4b34e3aec23798ab0593ce5f1f58405075eca0bf1ce67a44cfa28c65"],"state_sha256":"6cf9c4956faaefb84c1b7d77cf7cd334b83fc3eb9deb711e6fce584eee6a81ff"}