{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AQWU6K227LHMXCLQNPE2SIU4UC","short_pith_number":"pith:AQWU6K22","canonical_record":{"source":{"id":"2607.16440","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2026-07-17T18:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"358e63f8ad64f56b49a040ba165d5437ed1ba6a79af3e3f92bf0108ab91fb934","abstract_canon_sha256":"2fd39f6e0105efa7793b4c6237ae7c9aa4ed9120f8d446b83aeb68072ca66043"},"schema_version":"1.0"},"canonical_sha256":"042d4f2b5afacecb89706bc9a9229ca0a3628cd4c583228271b2ae6a3803c8aa","source":{"kind":"arxiv","id":"2607.16440","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16440","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16440v1","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16440","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"AQWU6K227LHM","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"pith_short_16","alias_value":"AQWU6K227LHMXCLQ","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"pith_short_8","alias_value":"AQWU6K22","created_at":"2026-07-21T00:20:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AQWU6K227LHMXCLQNPE2SIU4UC","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16440","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2026-07-17T18:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"358e63f8ad64f56b49a040ba165d5437ed1ba6a79af3e3f92bf0108ab91fb934","abstract_canon_sha256":"2fd39f6e0105efa7793b4c6237ae7c9aa4ed9120f8d446b83aeb68072ca66043"},"schema_version":"1.0"},"canonical_sha256":"042d4f2b5afacecb89706bc9a9229ca0a3628cd4c583228271b2ae6a3803c8aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T00:20:18.736266Z","signature_b64":"+6v2NtEWplSoWx75MT05598rvPgAhZ8LxGpeqakRWzxcAroTQSm/mD1W/Qi3OuB55TN/q1x1Q/VOJxPJXdKYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"042d4f2b5afacecb89706bc9a9229ca0a3628cd4c583228271b2ae6a3803c8aa","last_reissued_at":"2026-07-21T00:20:18.735380Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T00:20:18.735380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16440","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":"2026-07-21T00:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZX/FTsIInzkgWxefyGLFDDNGtutCGeI3qTXK7XDWPIMKYJJQEXWUNqUdp8t84eCrTqL90RtPjzRpFP6rS/8yAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:31:08.114904Z"},"content_sha256":"411ae9c5ac03a7b5fe80f250da5c01c7523a1377233550d166704d9c7cc53528","schema_version":"1.0","event_id":"sha256:411ae9c5ac03a7b5fe80f250da5c01c7523a1377233550d166704d9c7cc53528"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AQWU6K227LHMXCLQNPE2SIU4UC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measurement Symmetry and Heisenberg Geometry: Embedding Classical Test Theory in a Noncommutative Representation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.OT","authors_text":"William R. Nugent","submitted_at":"2026-07-17T18:36:59Z","abstract_excerpt":"Classical measurement theory is traditionally formulated in an algebraic framework. However, it is fundamentally commutative and does not naturally represent noncommutative measurement phenomena identified in the social sciences. This study investigates whether the transformation structure of classical measurement theory preserves a canonical noncommutative geometry. A measurement state vector is introduced, and transformations relating various forms of equivalence (parallelism) between measures are expressed as a Lie matrix group. A faithful matrix representation of the Heisenberg group is in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16440","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/2607.16440/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":"2026-07-21T00:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Tn89vpqBXZzcEWyL7ymRePw/HNOJC/z94DQwGOzNzBzKcOqBkp8Xhyv+e75T++0skCc3eT/6obiSIGN/HqMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:31:08.115408Z"},"content_sha256":"43d899df88f796d1f7c836c587f89751a8b2f1282c2694cdf971717ad8be4cf3","schema_version":"1.0","event_id":"sha256:43d899df88f796d1f7c836c587f89751a8b2f1282c2694cdf971717ad8be4cf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQWU6K227LHMXCLQNPE2SIU4UC/bundle.json","state_url":"https://pith.science/pith/AQWU6K227LHMXCLQNPE2SIU4UC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQWU6K227LHMXCLQNPE2SIU4UC/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":"2026-08-04T21:31:08Z","links":{"resolver":"https://pith.science/pith/AQWU6K227LHMXCLQNPE2SIU4UC","bundle":"https://pith.science/pith/AQWU6K227LHMXCLQNPE2SIU4UC/bundle.json","state":"https://pith.science/pith/AQWU6K227LHMXCLQNPE2SIU4UC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQWU6K227LHMXCLQNPE2SIU4UC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AQWU6K227LHMXCLQNPE2SIU4UC","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":"2fd39f6e0105efa7793b4c6237ae7c9aa4ed9120f8d446b83aeb68072ca66043","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2026-07-17T18:36:59Z","title_canon_sha256":"358e63f8ad64f56b49a040ba165d5437ed1ba6a79af3e3f92bf0108ab91fb934"},"schema_version":"1.0","source":{"id":"2607.16440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16440","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16440v1","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16440","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"AQWU6K227LHM","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"pith_short_16","alias_value":"AQWU6K227LHMXCLQ","created_at":"2026-07-21T00:20:18Z"},{"alias_kind":"pith_short_8","alias_value":"AQWU6K22","created_at":"2026-07-21T00:20:18Z"}],"graph_snapshots":[{"event_id":"sha256:43d899df88f796d1f7c836c587f89751a8b2f1282c2694cdf971717ad8be4cf3","target":"graph","created_at":"2026-07-21T00:20:18Z","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/2607.16440/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classical measurement theory is traditionally formulated in an algebraic framework. However, it is fundamentally commutative and does not naturally represent noncommutative measurement phenomena identified in the social sciences. This study investigates whether the transformation structure of classical measurement theory preserves a canonical noncommutative geometry. A measurement state vector is introduced, and transformations relating various forms of equivalence (parallelism) between measures are expressed as a Lie matrix group. A faithful matrix representation of the Heisenberg group is in","authors_text":"William R. Nugent","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2026-07-17T18:36:59Z","title":"Measurement Symmetry and Heisenberg Geometry: Embedding Classical Test Theory in a Noncommutative Representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16440","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":"sha256:411ae9c5ac03a7b5fe80f250da5c01c7523a1377233550d166704d9c7cc53528","target":"record","created_at":"2026-07-21T00:20:18Z","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":"2fd39f6e0105efa7793b4c6237ae7c9aa4ed9120f8d446b83aeb68072ca66043","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2026-07-17T18:36:59Z","title_canon_sha256":"358e63f8ad64f56b49a040ba165d5437ed1ba6a79af3e3f92bf0108ab91fb934"},"schema_version":"1.0","source":{"id":"2607.16440","kind":"arxiv","version":1}},"canonical_sha256":"042d4f2b5afacecb89706bc9a9229ca0a3628cd4c583228271b2ae6a3803c8aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"042d4f2b5afacecb89706bc9a9229ca0a3628cd4c583228271b2ae6a3803c8aa","first_computed_at":"2026-07-21T00:20:18.735380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T00:20:18.735380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+6v2NtEWplSoWx75MT05598rvPgAhZ8LxGpeqakRWzxcAroTQSm/mD1W/Qi3OuB55TN/q1x1Q/VOJxPJXdKYDw==","signature_status":"signed_v1","signed_at":"2026-07-21T00:20:18.736266Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:411ae9c5ac03a7b5fe80f250da5c01c7523a1377233550d166704d9c7cc53528","sha256:43d899df88f796d1f7c836c587f89751a8b2f1282c2694cdf971717ad8be4cf3"],"state_sha256":"dd30f702b75f639a424fcba745faa9a54c3e0aa1b1b9a263d178c39f05984842"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKMp/4y46V/piFDBtP9kmkUrIFWkVa0EIHg2cMPtDXsh+Z5T4evQPKJ3/Wi1acd1JmM80EdefnStl8hm3+LuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T21:31:08.120989Z","bundle_sha256":"905f1494f9f64fcbfc87303e219a811e03f764113e62bce2e677e55c22892cfa"}}