{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VLWACQD3U4U2YXWLBIO4N3LNFF","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":"822b93f8bbb786f0d9395e33dc6c084598ce172d3053771f8f88567d1c2d9d2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-10-29T17:55:35Z","title_canon_sha256":"d36d389e58e11ca52509787329e43a40f03234c7d6f57458d6047d4a617016a1"},"schema_version":"1.0","source":{"id":"2110.15951","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.15951","created_at":"2026-07-05T04:24:23Z"},{"alias_kind":"arxiv_version","alias_value":"2110.15951v3","created_at":"2026-07-05T04:24:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.15951","created_at":"2026-07-05T04:24:23Z"},{"alias_kind":"pith_short_12","alias_value":"VLWACQD3U4U2","created_at":"2026-07-05T04:24:23Z"},{"alias_kind":"pith_short_16","alias_value":"VLWACQD3U4U2YXWL","created_at":"2026-07-05T04:24:23Z"},{"alias_kind":"pith_short_8","alias_value":"VLWACQD3","created_at":"2026-07-05T04:24:23Z"}],"graph_snapshots":[{"event_id":"sha256:fc66851171520cae90bd08fa6b86114322882564883e6656a3f2fcf82bdb338b","target":"graph","created_at":"2026-07-05T04:24:23Z","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/2110.15951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a formulation of the generalised uncertainty principle based on commutator $\\left[ {\\hat x}^i, {\\hat p}_j \\right]$ between position and momentum operators defined in a covariant manner using normal coordinates. We show how any such commutator can acquire corrections if the momentum space is curved. The correction is completely determined by the extrinsic curvature of the surface $p^2=$ constant in the momentum space, and results in non-commutativity of normal position coordinates $\\left[ {\\hat x}^i, {\\hat x}^j \\right] \\neq 0$. We then provide a construction for the momentum space ge","authors_text":"Dawood Kothawala, Raghvendra Singh","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-10-29T17:55:35Z","title":"Covariant formulation of Generalised Uncertainty Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.15951","kind":"arxiv","version":3},"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":"sha256:5a7eed9faf9730a086723d6b38599243877f43c0d1d9625d4e48254b6e6fa9e7","target":"record","created_at":"2026-07-05T04:24:23Z","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":"822b93f8bbb786f0d9395e33dc6c084598ce172d3053771f8f88567d1c2d9d2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-10-29T17:55:35Z","title_canon_sha256":"d36d389e58e11ca52509787329e43a40f03234c7d6f57458d6047d4a617016a1"},"schema_version":"1.0","source":{"id":"2110.15951","kind":"arxiv","version":3}},"canonical_sha256":"aaec01407ba729ac5ecb0a1dc6ed6d2973ad3e5f4e334f8f8d421a9e35b36be7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaec01407ba729ac5ecb0a1dc6ed6d2973ad3e5f4e334f8f8d421a9e35b36be7","first_computed_at":"2026-07-05T04:24:23.429484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:24:23.429484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xNrri1AOSdDhaI0Hj5EaoXCSfMxmqUc/qg5iOiE1Jn0YssSMpgiF+PZkVAi73iCpcr3XaM2fZ9xyAfTI9VnzAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:24:23.429874Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.15951","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a7eed9faf9730a086723d6b38599243877f43c0d1d9625d4e48254b6e6fa9e7","sha256:fc66851171520cae90bd08fa6b86114322882564883e6656a3f2fcf82bdb338b"],"state_sha256":"0fb516a9fead453667dc7d85e94cdde5aaaee8bc4a383af4ec74785d7a3f79aa"}