{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R2MGAR4KDNCAVKNVNPHWWM7SKW","short_pith_number":"pith:R2MGAR4K","canonical_record":{"source":{"id":"1701.01409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:19:13Z","cross_cats_sorted":[],"title_canon_sha256":"6351e354b4ee610f2b1ca7813c45492ba176b47b899210ec2bbabee80abf6b06","abstract_canon_sha256":"1b612b97b172792ac831f078309a71da9d5302203dc2c2c73772e135eafc7bfb"},"schema_version":"1.0"},"canonical_sha256":"8e9860478a1b440aa9b56bcf6b33f255af0baa3a4a85b7dd144108f14ceb9bcc","source":{"kind":"arxiv","id":"1701.01409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01409","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01409v1","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01409","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"R2MGAR4KDNCA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2MGAR4KDNCAVKNV","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2MGAR4K","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R2MGAR4KDNCAVKNVNPHWWM7SKW","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:19:13Z","cross_cats_sorted":[],"title_canon_sha256":"6351e354b4ee610f2b1ca7813c45492ba176b47b899210ec2bbabee80abf6b06","abstract_canon_sha256":"1b612b97b172792ac831f078309a71da9d5302203dc2c2c73772e135eafc7bfb"},"schema_version":"1.0"},"canonical_sha256":"8e9860478a1b440aa9b56bcf6b33f255af0baa3a4a85b7dd144108f14ceb9bcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:19.765230Z","signature_b64":"r7z9+ykqcNy3laJkwHCp1BRFPkPPU/cD29mrRtuKlpiIqOLhbv6XrTH/ZpKHjXMvWwXGPDkt/bXSCdr9IzPrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e9860478a1b440aa9b56bcf6b33f255af0baa3a4a85b7dd144108f14ceb9bcc","last_reissued_at":"2026-05-18T00:53:19.764737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:19.764737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01409","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":"2026-05-18T00:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UbQxTSn5jk2fgPi4TtcQgW3cwzFr22vgKaXrIYsz05hn8hURet0EzXErAgXFFTnSQ+iKRsvTrLJ4f2wxIyuLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:13:36.719784Z"},"content_sha256":"f4b3cf7c375e45fabdb8777efe7ab23b056efebe9476d2341c5a16fdc3982dee","schema_version":"1.0","event_id":"sha256:f4b3cf7c375e45fabdb8777efe7ab23b056efebe9476d2341c5a16fdc3982dee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R2MGAR4KDNCAVKNVNPHWWM7SKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Student difficulties with determining expectation values in quantum mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.ed-ph","authors_text":"Chandralekha Singh, Emily Marshman","submitted_at":"2017-01-05T18:19:13Z","abstract_excerpt":"The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01409","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":"2026-05-18T00:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"++ZiV2i0IrvmGsov5sGJm+l7ZDpvIRuj68vhF9mzSZ87uG30BLN/Z4L2bB7tUIBxeGIC40UDW5TzWSDCr/jAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:13:36.720135Z"},"content_sha256":"5fa4b695f1429dcb62573c658bae0e61d07e7c97af7942bf9fbe184dbf6fc264","schema_version":"1.0","event_id":"sha256:5fa4b695f1429dcb62573c658bae0e61d07e7c97af7942bf9fbe184dbf6fc264"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R2MGAR4KDNCAVKNVNPHWWM7SKW/bundle.json","state_url":"https://pith.science/pith/R2MGAR4KDNCAVKNVNPHWWM7SKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R2MGAR4KDNCAVKNVNPHWWM7SKW/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":"2026-06-02T06:13:36Z","links":{"resolver":"https://pith.science/pith/R2MGAR4KDNCAVKNVNPHWWM7SKW","bundle":"https://pith.science/pith/R2MGAR4KDNCAVKNVNPHWWM7SKW/bundle.json","state":"https://pith.science/pith/R2MGAR4KDNCAVKNVNPHWWM7SKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R2MGAR4KDNCAVKNVNPHWWM7SKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R2MGAR4KDNCAVKNVNPHWWM7SKW","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":"1b612b97b172792ac831f078309a71da9d5302203dc2c2c73772e135eafc7bfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:19:13Z","title_canon_sha256":"6351e354b4ee610f2b1ca7813c45492ba176b47b899210ec2bbabee80abf6b06"},"schema_version":"1.0","source":{"id":"1701.01409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01409","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01409v1","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01409","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"R2MGAR4KDNCA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2MGAR4KDNCAVKNV","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2MGAR4K","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:5fa4b695f1429dcb62573c658bae0e61d07e7c97af7942bf9fbe184dbf6fc264","target":"graph","created_at":"2026-05-18T00:53:19Z","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 expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.","authors_text":"Chandralekha Singh, Emily Marshman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:19:13Z","title":"Student difficulties with determining expectation values in quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01409","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:f4b3cf7c375e45fabdb8777efe7ab23b056efebe9476d2341c5a16fdc3982dee","target":"record","created_at":"2026-05-18T00:53:19Z","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":"1b612b97b172792ac831f078309a71da9d5302203dc2c2c73772e135eafc7bfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:19:13Z","title_canon_sha256":"6351e354b4ee610f2b1ca7813c45492ba176b47b899210ec2bbabee80abf6b06"},"schema_version":"1.0","source":{"id":"1701.01409","kind":"arxiv","version":1}},"canonical_sha256":"8e9860478a1b440aa9b56bcf6b33f255af0baa3a4a85b7dd144108f14ceb9bcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e9860478a1b440aa9b56bcf6b33f255af0baa3a4a85b7dd144108f14ceb9bcc","first_computed_at":"2026-05-18T00:53:19.764737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:19.764737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r7z9+ykqcNy3laJkwHCp1BRFPkPPU/cD29mrRtuKlpiIqOLhbv6XrTH/ZpKHjXMvWwXGPDkt/bXSCdr9IzPrAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:19.765230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4b3cf7c375e45fabdb8777efe7ab23b056efebe9476d2341c5a16fdc3982dee","sha256:5fa4b695f1429dcb62573c658bae0e61d07e7c97af7942bf9fbe184dbf6fc264"],"state_sha256":"d5adcdf465205a8f0cefdf8553516e15979c8663e19c9dea79d6a3063f5a6d54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c3Wcu6RQSdAOKKUVOWl3bmoBADV4VxA31wq9EBXwFyQ08PlyyMw4YJuV4UpUmGn29wuE8uMQg8WSfURuO4ozDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:13:36.722428Z","bundle_sha256":"8cfdb1268f2ff3d655d868dce55d9f6ba50fb10b49cc98e20b8894ffeefd263a"}}