{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FY3JEZPL275PQRH45V4KE5BK47","short_pith_number":"pith:FY3JEZPL","canonical_record":{"source":{"id":"1602.00608","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-02-01T17:38:48Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"5e4fca609881c5a5cd4bc79df8647a1fc18cb8d1dfa117f2d0f8e60b8150915a","abstract_canon_sha256":"7ff70a527853aa0aa21bb1f671243aedd5171bbcd5645e8d1a2493142c82f77f"},"schema_version":"1.0"},"canonical_sha256":"2e369265ebd7faf844fced78a2742ae7d331eb9b8376d86ba9c3a87c9a740397","source":{"kind":"arxiv","id":"1602.00608","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00608","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00608v2","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00608","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"FY3JEZPL275P","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FY3JEZPL275PQRH4","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FY3JEZPL","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FY3JEZPL275PQRH45V4KE5BK47","target":"record","payload":{"canonical_record":{"source":{"id":"1602.00608","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-02-01T17:38:48Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"5e4fca609881c5a5cd4bc79df8647a1fc18cb8d1dfa117f2d0f8e60b8150915a","abstract_canon_sha256":"7ff70a527853aa0aa21bb1f671243aedd5171bbcd5645e8d1a2493142c82f77f"},"schema_version":"1.0"},"canonical_sha256":"2e369265ebd7faf844fced78a2742ae7d331eb9b8376d86ba9c3a87c9a740397","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:20.220578Z","signature_b64":"kc9iw7GL4GWFQZgBN5Q5WK5ifAu553V3dnYia2t2AEvjEQXAaqBJ17S29HypE0Z3+uTs/NqMePtxi9uGci+XBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e369265ebd7faf844fced78a2742ae7d331eb9b8376d86ba9c3a87c9a740397","last_reissued_at":"2026-05-18T00:48:20.219845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:20.219845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.00608","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6DbzA6+2sHg5q8Ojb/WqZcI6/tPuuJviZf4aOF3E9BospaY+3nY4rpbxe3SP8renM0kd9RdzOZey63GS3JCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:20:37.793220Z"},"content_sha256":"fa2c1360d58e84cd43db259186f782c69295bccc6dc55c8de596eb8ddb862295","schema_version":"1.0","event_id":"sha256:fa2c1360d58e84cd43db259186f782c69295bccc6dc55c8de596eb8ddb862295"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FY3JEZPL275PQRH45V4KE5BK47","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum theory of the Generalised Uncertainty Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"gr-qc","authors_text":"Jean-Philippe Bruneton, Julien Larena","submitted_at":"2016-02-01T17:38:48Z","abstract_excerpt":"We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \\delta_{ij} + g(P^2) P_i P_j $ for any functions $f$. However, we restrict our study to the case of commuting $X$'s. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00608","kind":"arxiv","version":2},"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":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8XvZ5MQ2aZeFKfDIOhqwfpC91suaHTvz9udZYDIM0TuKrhcSCFuO7L/xFCAP0ZSzFzQzGr5bVlN9XbVW3Gx9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:20:37.793708Z"},"content_sha256":"172cfd4bf73523e96e865bce7f288924a8ef9df61b65c3300361a3c7f0c20d35","schema_version":"1.0","event_id":"sha256:172cfd4bf73523e96e865bce7f288924a8ef9df61b65c3300361a3c7f0c20d35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FY3JEZPL275PQRH45V4KE5BK47/bundle.json","state_url":"https://pith.science/pith/FY3JEZPL275PQRH45V4KE5BK47/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FY3JEZPL275PQRH45V4KE5BK47/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":"2026-05-26T21:20:37Z","links":{"resolver":"https://pith.science/pith/FY3JEZPL275PQRH45V4KE5BK47","bundle":"https://pith.science/pith/FY3JEZPL275PQRH45V4KE5BK47/bundle.json","state":"https://pith.science/pith/FY3JEZPL275PQRH45V4KE5BK47/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FY3JEZPL275PQRH45V4KE5BK47/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FY3JEZPL275PQRH45V4KE5BK47","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":"7ff70a527853aa0aa21bb1f671243aedd5171bbcd5645e8d1a2493142c82f77f","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-02-01T17:38:48Z","title_canon_sha256":"5e4fca609881c5a5cd4bc79df8647a1fc18cb8d1dfa117f2d0f8e60b8150915a"},"schema_version":"1.0","source":{"id":"1602.00608","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00608","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00608v2","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00608","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"FY3JEZPL275P","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FY3JEZPL275PQRH4","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FY3JEZPL","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:172cfd4bf73523e96e865bce7f288924a8ef9df61b65c3300361a3c7f0c20d35","target":"graph","created_at":"2026-05-18T00:48:20Z","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":"We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \\delta_{ij} + g(P^2) P_i P_j $ for any functions $f$. However, we restrict our study to the case of commuting $X$'s. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heis","authors_text":"Jean-Philippe Bruneton, Julien Larena","cross_cats":["hep-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-02-01T17:38:48Z","title":"Quantum theory of the Generalised Uncertainty Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00608","kind":"arxiv","version":2},"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:fa2c1360d58e84cd43db259186f782c69295bccc6dc55c8de596eb8ddb862295","target":"record","created_at":"2026-05-18T00:48:20Z","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":"7ff70a527853aa0aa21bb1f671243aedd5171bbcd5645e8d1a2493142c82f77f","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-02-01T17:38:48Z","title_canon_sha256":"5e4fca609881c5a5cd4bc79df8647a1fc18cb8d1dfa117f2d0f8e60b8150915a"},"schema_version":"1.0","source":{"id":"1602.00608","kind":"arxiv","version":2}},"canonical_sha256":"2e369265ebd7faf844fced78a2742ae7d331eb9b8376d86ba9c3a87c9a740397","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e369265ebd7faf844fced78a2742ae7d331eb9b8376d86ba9c3a87c9a740397","first_computed_at":"2026-05-18T00:48:20.219845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:20.219845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kc9iw7GL4GWFQZgBN5Q5WK5ifAu553V3dnYia2t2AEvjEQXAaqBJ17S29HypE0Z3+uTs/NqMePtxi9uGci+XBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:20.220578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00608","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa2c1360d58e84cd43db259186f782c69295bccc6dc55c8de596eb8ddb862295","sha256:172cfd4bf73523e96e865bce7f288924a8ef9df61b65c3300361a3c7f0c20d35"],"state_sha256":"6038cf85c4ca1bbd4b0ede31b2793e1979a16dce3cc6e74a2a3d0a15f2d930b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrRzNVcb1+IbGnVXjvRyvLP+AvsEKUCsDhK19CakdT4GepRG949eTkKszBpq+/MM+Ky8MOkMdIMWq7a9C1qjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:20:37.796705Z","bundle_sha256":"8708e8fc14b904fb263c5cff6ad7abc881bce61a0528f0a80c63395d7ace0979"}}