{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W65JWUZU4EZM2BYR2MOFCYFSYI","short_pith_number":"pith:W65JWUZU","canonical_record":{"source":{"id":"1309.7284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-09-27T16:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"54ca4ec459698246217c4e24bb52403b3bb414c48fccda4acb8cc02909c3921d","abstract_canon_sha256":"983c431b4ef70b64108a8f2bf057e44073c0b6b427bb3ff3d5214ab91968f77c"},"schema_version":"1.0"},"canonical_sha256":"b7ba9b5334e132cd0711d31c5160b2c20f344f2517fe9372f82f5b92a65abad0","source":{"kind":"arxiv","id":"1309.7284","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7284","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7284v1","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7284","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"W65JWUZU4EZM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W65JWUZU4EZM2BYR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W65JWUZU","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W65JWUZU4EZM2BYR2MOFCYFSYI","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-09-27T16:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"54ca4ec459698246217c4e24bb52403b3bb414c48fccda4acb8cc02909c3921d","abstract_canon_sha256":"983c431b4ef70b64108a8f2bf057e44073c0b6b427bb3ff3d5214ab91968f77c"},"schema_version":"1.0"},"canonical_sha256":"b7ba9b5334e132cd0711d31c5160b2c20f344f2517fe9372f82f5b92a65abad0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:48.549896Z","signature_b64":"aM0g/WZyZPFQtYodYAjKA3TNu7ftDu8JBrl/nxjBYV7oP/9A5pHgkfTIB4Iv9R87fBn3l2QOozKjzSc/7fX4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7ba9b5334e132cd0711d31c5160b2c20f344f2517fe9372f82f5b92a65abad0","last_reissued_at":"2026-05-18T02:51:48.549432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:48.549432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7284","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":"2026-05-18T02:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9kvNFf1mrLi/ilvC7+U8k3k/Weo+M9XxjkQbxYrq//GJUhYL6FVWIFJSN1IhzhWpiewCU9dEp9g79N7uIew1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:12:16.078426Z"},"content_sha256":"764b9519692a3db04730140038253e904769dab03a4d6aaac6b9398868eec015","schema_version":"1.0","event_id":"sha256:764b9519692a3db04730140038253e904769dab03a4d6aaac6b9398868eec015"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W65JWUZU4EZM2BYR2MOFCYFSYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Pouria Pedram","submitted_at":"2013-09-27T16:11:00Z","abstract_excerpt":"We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to $\\hbar\\sqrt{\\beta}$ and a maximal momentum proportional to $1/\\sqrt{\\beta}$, where $\\beta$ is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7284","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":"2026-05-18T02:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ae7TCZM3jk6V38xhX/QXyRuLeGQf+kxntWMZJTG18EyNHjPojiekjU1VZRMQX5JZaLZdhhl2Hvfv6n3un678Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:12:16.078768Z"},"content_sha256":"b2e68b2da9bf8d578434d42bc443bbefaaa2b906e658baaee228ed1291a0ebe9","schema_version":"1.0","event_id":"sha256:b2e68b2da9bf8d578434d42bc443bbefaaa2b906e658baaee228ed1291a0ebe9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W65JWUZU4EZM2BYR2MOFCYFSYI/bundle.json","state_url":"https://pith.science/pith/W65JWUZU4EZM2BYR2MOFCYFSYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W65JWUZU4EZM2BYR2MOFCYFSYI/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":"2026-06-20T06:12:16Z","links":{"resolver":"https://pith.science/pith/W65JWUZU4EZM2BYR2MOFCYFSYI","bundle":"https://pith.science/pith/W65JWUZU4EZM2BYR2MOFCYFSYI/bundle.json","state":"https://pith.science/pith/W65JWUZU4EZM2BYR2MOFCYFSYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W65JWUZU4EZM2BYR2MOFCYFSYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W65JWUZU4EZM2BYR2MOFCYFSYI","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":"983c431b4ef70b64108a8f2bf057e44073c0b6b427bb3ff3d5214ab91968f77c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-09-27T16:11:00Z","title_canon_sha256":"54ca4ec459698246217c4e24bb52403b3bb414c48fccda4acb8cc02909c3921d"},"schema_version":"1.0","source":{"id":"1309.7284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7284","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7284v1","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7284","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"W65JWUZU4EZM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W65JWUZU4EZM2BYR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W65JWUZU","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:b2e68b2da9bf8d578434d42bc443bbefaaa2b906e658baaee228ed1291a0ebe9","target":"graph","created_at":"2026-05-18T02:51:48Z","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 find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to $\\hbar\\sqrt{\\beta}$ and a maximal momentum proportional to $1/\\sqrt{\\beta}$, where $\\beta$ is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spe","authors_text":"Pouria Pedram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-09-27T16:11:00Z","title":"Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7284","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":"sha256:764b9519692a3db04730140038253e904769dab03a4d6aaac6b9398868eec015","target":"record","created_at":"2026-05-18T02:51:48Z","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":"983c431b4ef70b64108a8f2bf057e44073c0b6b427bb3ff3d5214ab91968f77c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-09-27T16:11:00Z","title_canon_sha256":"54ca4ec459698246217c4e24bb52403b3bb414c48fccda4acb8cc02909c3921d"},"schema_version":"1.0","source":{"id":"1309.7284","kind":"arxiv","version":1}},"canonical_sha256":"b7ba9b5334e132cd0711d31c5160b2c20f344f2517fe9372f82f5b92a65abad0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7ba9b5334e132cd0711d31c5160b2c20f344f2517fe9372f82f5b92a65abad0","first_computed_at":"2026-05-18T02:51:48.549432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:48.549432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aM0g/WZyZPFQtYodYAjKA3TNu7ftDu8JBrl/nxjBYV7oP/9A5pHgkfTIB4Iv9R87fBn3l2QOozKjzSc/7fX4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:48.549896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:764b9519692a3db04730140038253e904769dab03a4d6aaac6b9398868eec015","sha256:b2e68b2da9bf8d578434d42bc443bbefaaa2b906e658baaee228ed1291a0ebe9"],"state_sha256":"f610e5002087083ac37a22219f96a5a686b76aa0131e9fe0a185f63b9c45067d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTR/0oqJLOw4hd/T0UJgVC+Oy/7ZeKWq1KHrYzs3P7B1hHtzn0H/2FSNcCRhEhMkavf+pAlKtrDMsua22rFmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:12:16.080691Z","bundle_sha256":"39ec2b5cf470cc86fbde713d4855dd437c905c1f06b83bf7a579bcd35534e598"}}