{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:XKDFRGCFHIXQH6AYYCRSEPOEKL","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":"4d7307ffd849c403c2c2ecfd739485f0f9dfd99732278ce4e5b6fa5527dfd527","cross_cats_sorted":[],"license":"","primary_cat":"physics.ed-ph","submitted_at":"2006-08-27T15:20:55Z","title_canon_sha256":"a29904809b977c26102a9e9b617608db03d15aede92d7888f05b2267b4346d37"},"schema_version":"1.0","source":{"id":"physics/0608268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0608268","created_at":"2026-07-04T14:56:41Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0608268v1","created_at":"2026-07-04T14:56:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0608268","created_at":"2026-07-04T14:56:41Z"},{"alias_kind":"pith_short_12","alias_value":"XKDFRGCFHIXQ","created_at":"2026-07-04T14:56:41Z"},{"alias_kind":"pith_short_16","alias_value":"XKDFRGCFHIXQH6AY","created_at":"2026-07-04T14:56:41Z"},{"alias_kind":"pith_short_8","alias_value":"XKDFRGCF","created_at":"2026-07-04T14:56:41Z"}],"graph_snapshots":[{"event_id":"sha256:d139ed73b02f1d0ea7d21d1400e4a86b84fdd4a5fc6147a11c6dea3261bd9411","target":"graph","created_at":"2026-07-04T14:56:41Z","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/physics/0608268/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are used and interpreted. Research with university physics students in classes from algebra-based introductory physics indicates that the gap between what students think they are supposed to be doing and what their instructors expect them to do can cause","authors_text":"Edward F. Redish","cross_cats":[],"headline":"","license":"","primary_cat":"physics.ed-ph","submitted_at":"2006-08-27T15:20:55Z","title":"Problem Solving and the Use of Math in Physics Courses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0608268","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":"sha256:998658fd5aaa8d06e7a33b4a7028d9e4b562767cad736ea7c2d57e682b66689f","target":"record","created_at":"2026-07-04T14:56:41Z","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":"4d7307ffd849c403c2c2ecfd739485f0f9dfd99732278ce4e5b6fa5527dfd527","cross_cats_sorted":[],"license":"","primary_cat":"physics.ed-ph","submitted_at":"2006-08-27T15:20:55Z","title_canon_sha256":"a29904809b977c26102a9e9b617608db03d15aede92d7888f05b2267b4346d37"},"schema_version":"1.0","source":{"id":"physics/0608268","kind":"arxiv","version":1}},"canonical_sha256":"ba865898453a2f03f818c0a3223dc452e531cfd63cb458a6758f37c6ae4d5cec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba865898453a2f03f818c0a3223dc452e531cfd63cb458a6758f37c6ae4d5cec","first_computed_at":"2026-07-04T14:56:41.717364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:56:41.717364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"di9Lzjb/UC6hJzrklzOhUNJwte6lHr5Gf2bCFZIAnOREJLdE9Tvc10AcpMUymtnz/7gYvjKACpZF34Bmi+6pAA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:56:41.717819Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0608268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:998658fd5aaa8d06e7a33b4a7028d9e4b562767cad736ea7c2d57e682b66689f","sha256:d139ed73b02f1d0ea7d21d1400e4a86b84fdd4a5fc6147a11c6dea3261bd9411"],"state_sha256":"485fd2140669c6170918a72301c57c1d0aab2c676d4c8dc00cd18647a29753a1"}