{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4KZNQDHNOUBRSCF4TAYMG47BGM","short_pith_number":"pith:4KZNQDHN","canonical_record":{"source":{"id":"1701.01411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"295e4e1b6ad2b0d705e7a1006dbbf9119cbac65303a2fbe4442bf95f5dd89c2a","abstract_canon_sha256":"61ce1107351f44464a2634358bdd5c656029ac7c019e27ec58a1de3a4fd675d2"},"schema_version":"1.0"},"canonical_sha256":"e2b2d80ced75031908bc9830c373e1332cef9aa848747cb1b889e8c28ba8330e","source":{"kind":"arxiv","id":"1701.01411","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01411","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01411v1","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01411","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"4KZNQDHNOUBR","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4KZNQDHNOUBRSCF4","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4KZNQDHN","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4KZNQDHNOUBRSCF4TAYMG47BGM","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"295e4e1b6ad2b0d705e7a1006dbbf9119cbac65303a2fbe4442bf95f5dd89c2a","abstract_canon_sha256":"61ce1107351f44464a2634358bdd5c656029ac7c019e27ec58a1de3a4fd675d2"},"schema_version":"1.0"},"canonical_sha256":"e2b2d80ced75031908bc9830c373e1332cef9aa848747cb1b889e8c28ba8330e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:19.747951Z","signature_b64":"GewrT6XoYu+2f6rnOVHzM43W/dd/XGKKp8V2Qno94BOtrP9onOAoiRrMx7wiZG3J/1PL8HsyNVWxLTsPo6mYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2b2d80ced75031908bc9830c373e1332cef9aa848747cb1b889e8c28ba8330e","last_reissued_at":"2026-05-18T00:53:19.747214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:19.747214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01411","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":"Typq+ZMelm9b7hs3ihoSYGNfbZAs4O2dNlGjLAL0anrX1bbiZFd4pQkqe/Ao/QTBR8bicaNPqbUJn3O8hhepCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:46:19.900883Z"},"content_sha256":"afc57bd16272186ae92dfab89cb856eb2f5a9b9fd9dd7cf400983a70508b381f","schema_version":"1.0","event_id":"sha256:afc57bd16272186ae92dfab89cb856eb2f5a9b9fd9dd7cf400983a70508b381f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4KZNQDHNOUBRSCF4TAYMG47BGM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Student difficulties with representations of quantum operators corresponding to observables","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":"2017-01-05T18:21:33Z","abstract_excerpt":"Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01411","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":"xz2hoGerOM+YMe78jjEKP7PijWih5PvJpu+VMVSHCu1Y4KKViSpBZUlhVVb0GWwLxEoTBKAC1cTcCmurlxJEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:46:19.901475Z"},"content_sha256":"34d7ef42f4e7bfd7717ec5a08512e33483473cdef96efbb0bd50577a7f1c4efd","schema_version":"1.0","event_id":"sha256:34d7ef42f4e7bfd7717ec5a08512e33483473cdef96efbb0bd50577a7f1c4efd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KZNQDHNOUBRSCF4TAYMG47BGM/bundle.json","state_url":"https://pith.science/pith/4KZNQDHNOUBRSCF4TAYMG47BGM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KZNQDHNOUBRSCF4TAYMG47BGM/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":"2026-05-28T05:46:19Z","links":{"resolver":"https://pith.science/pith/4KZNQDHNOUBRSCF4TAYMG47BGM","bundle":"https://pith.science/pith/4KZNQDHNOUBRSCF4TAYMG47BGM/bundle.json","state":"https://pith.science/pith/4KZNQDHNOUBRSCF4TAYMG47BGM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KZNQDHNOUBRSCF4TAYMG47BGM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4KZNQDHNOUBRSCF4TAYMG47BGM","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":"61ce1107351f44464a2634358bdd5c656029ac7c019e27ec58a1de3a4fd675d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:21:33Z","title_canon_sha256":"295e4e1b6ad2b0d705e7a1006dbbf9119cbac65303a2fbe4442bf95f5dd89c2a"},"schema_version":"1.0","source":{"id":"1701.01411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01411","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01411v1","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01411","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"4KZNQDHNOUBR","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4KZNQDHNOUBRSCF4","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4KZNQDHN","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:34d7ef42f4e7bfd7717ec5a08512e33483473cdef96efbb0bd50577a7f1c4efd","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":"Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.","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":"2017-01-05T18:21:33Z","title":"Student difficulties with representations of quantum operators corresponding to observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01411","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:afc57bd16272186ae92dfab89cb856eb2f5a9b9fd9dd7cf400983a70508b381f","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":"61ce1107351f44464a2634358bdd5c656029ac7c019e27ec58a1de3a4fd675d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2017-01-05T18:21:33Z","title_canon_sha256":"295e4e1b6ad2b0d705e7a1006dbbf9119cbac65303a2fbe4442bf95f5dd89c2a"},"schema_version":"1.0","source":{"id":"1701.01411","kind":"arxiv","version":1}},"canonical_sha256":"e2b2d80ced75031908bc9830c373e1332cef9aa848747cb1b889e8c28ba8330e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2b2d80ced75031908bc9830c373e1332cef9aa848747cb1b889e8c28ba8330e","first_computed_at":"2026-05-18T00:53:19.747214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:19.747214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GewrT6XoYu+2f6rnOVHzM43W/dd/XGKKp8V2Qno94BOtrP9onOAoiRrMx7wiZG3J/1PL8HsyNVWxLTsPo6mYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:19.747951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afc57bd16272186ae92dfab89cb856eb2f5a9b9fd9dd7cf400983a70508b381f","sha256:34d7ef42f4e7bfd7717ec5a08512e33483473cdef96efbb0bd50577a7f1c4efd"],"state_sha256":"d3d80000c0cc4aad74b37f21d93321912c48671aeff683374cafd9559454959a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wp+txe+1Z0KdXnSotEbySy4hNuJfGGI9PADS5iRGIOotJ0WSzzRfwKTs0soxRqLDcTwlzpZg7V2E6GXIweXTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:46:19.904185Z","bundle_sha256":"1779726d77bdf03c9d20f6ad2bbad36f3c40541da45f4393ace871fdafc72d65"}}