{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MXUDKPRCWYB67S2OWTVZF4XPE5","short_pith_number":"pith:MXUDKPRC","canonical_record":{"source":{"id":"1208.2359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-11T15:21:56Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"8765aceb54a76b064580a4f9339debb08a0adbbc1d72b3325ca19a5154e981a5","abstract_canon_sha256":"b576a60f23021b6b5c92f63b6e35108e29d24529f06b21e1505d1320bd1a3a08"},"schema_version":"1.0"},"canonical_sha256":"65e8353e22b603efcb4eb4eb92f2ef275c56e11337b6b53d04809bf851f0f5ef","source":{"kind":"arxiv","id":"1208.2359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2359","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2359v1","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2359","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"MXUDKPRCWYB6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXUDKPRCWYB67S2O","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXUDKPRC","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MXUDKPRCWYB67S2OWTVZF4XPE5","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-11T15:21:56Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"8765aceb54a76b064580a4f9339debb08a0adbbc1d72b3325ca19a5154e981a5","abstract_canon_sha256":"b576a60f23021b6b5c92f63b6e35108e29d24529f06b21e1505d1320bd1a3a08"},"schema_version":"1.0"},"canonical_sha256":"65e8353e22b603efcb4eb4eb92f2ef275c56e11337b6b53d04809bf851f0f5ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:58.068927Z","signature_b64":"rpxWDDp97mIuC0yoGgeBe0tVce9nhLaUQVnsQxE0ND3eYX+raKAkQpf6wQjnCG4gCk46a3+HZyQ5m3SDpAYjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65e8353e22b603efcb4eb4eb92f2ef275c56e11337b6b53d04809bf851f0f5ef","last_reissued_at":"2026-05-18T03:48:58.068187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:58.068187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2359","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":"2026-05-18T03:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IHMYRP7YKnG22pLm+eoSirXsLm3uQiXYkBqZ+o4i4GNv8L8v63ySZF3A5aFFVmGuXtdKopTJK+UZvQrO41KAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:37:59.236924Z"},"content_sha256":"5f6fa86350f38848d08c3017358dbf71f3f91f88be64d73a74377d8348ab984c","schema_version":"1.0","event_id":"sha256:5f6fa86350f38848d08c3017358dbf71f3f91f88be64d73a74377d8348ab984c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MXUDKPRCWYB67S2OWTVZF4XPE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac theory on a space with linear Lie type fuzziness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"hep-th","authors_text":"A. H. Fatollahi, A. Shariati, M. Khorrami","submitted_at":"2012-08-11T15:21:56Z","abstract_excerpt":"A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is compact, the real space exhibits lattice characteristics (as the eigenvalues of space operators are discrete), and the similarity of such a \\emph{lattice} with ordinary lattices is manifested, among other things, in a phenomenon resembling the famous \\emph{fermion doubling} problem. A projection is introduced to make the dynamical number of spinors equal to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2359","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":"2026-05-18T03:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5GnnAU5fTdOvPhcJ7OWBnJSz1mo2LiLnUmrt4c7jPWdN0xX1MYasm1BC/ZHCm5VpqELseY7106NgNr8Mv6BKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:37:59.237293Z"},"content_sha256":"2c8d82dc5ece8e85222cc459f70ef8fb66ae9b2f6eafa6f41094f97c5ea2d083","schema_version":"1.0","event_id":"sha256:2c8d82dc5ece8e85222cc459f70ef8fb66ae9b2f6eafa6f41094f97c5ea2d083"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXUDKPRCWYB67S2OWTVZF4XPE5/bundle.json","state_url":"https://pith.science/pith/MXUDKPRCWYB67S2OWTVZF4XPE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXUDKPRCWYB67S2OWTVZF4XPE5/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":"2026-06-01T02:37:59Z","links":{"resolver":"https://pith.science/pith/MXUDKPRCWYB67S2OWTVZF4XPE5","bundle":"https://pith.science/pith/MXUDKPRCWYB67S2OWTVZF4XPE5/bundle.json","state":"https://pith.science/pith/MXUDKPRCWYB67S2OWTVZF4XPE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXUDKPRCWYB67S2OWTVZF4XPE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MXUDKPRCWYB67S2OWTVZF4XPE5","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":"b576a60f23021b6b5c92f63b6e35108e29d24529f06b21e1505d1320bd1a3a08","cross_cats_sorted":["hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-11T15:21:56Z","title_canon_sha256":"8765aceb54a76b064580a4f9339debb08a0adbbc1d72b3325ca19a5154e981a5"},"schema_version":"1.0","source":{"id":"1208.2359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2359","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2359v1","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2359","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"MXUDKPRCWYB6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXUDKPRCWYB67S2O","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXUDKPRC","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:2c8d82dc5ece8e85222cc459f70ef8fb66ae9b2f6eafa6f41094f97c5ea2d083","target":"graph","created_at":"2026-05-18T03:48:58Z","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":"A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is compact, the real space exhibits lattice characteristics (as the eigenvalues of space operators are discrete), and the similarity of such a \\emph{lattice} with ordinary lattices is manifested, among other things, in a phenomenon resembling the famous \\emph{fermion doubling} problem. A projection is introduced to make the dynamical number of spinors equal to t","authors_text":"A. H. Fatollahi, A. Shariati, M. Khorrami","cross_cats":["hep-lat"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-11T15:21:56Z","title":"Dirac theory on a space with linear Lie type fuzziness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2359","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":"sha256:5f6fa86350f38848d08c3017358dbf71f3f91f88be64d73a74377d8348ab984c","target":"record","created_at":"2026-05-18T03:48:58Z","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":"b576a60f23021b6b5c92f63b6e35108e29d24529f06b21e1505d1320bd1a3a08","cross_cats_sorted":["hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-11T15:21:56Z","title_canon_sha256":"8765aceb54a76b064580a4f9339debb08a0adbbc1d72b3325ca19a5154e981a5"},"schema_version":"1.0","source":{"id":"1208.2359","kind":"arxiv","version":1}},"canonical_sha256":"65e8353e22b603efcb4eb4eb92f2ef275c56e11337b6b53d04809bf851f0f5ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65e8353e22b603efcb4eb4eb92f2ef275c56e11337b6b53d04809bf851f0f5ef","first_computed_at":"2026-05-18T03:48:58.068187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:58.068187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rpxWDDp97mIuC0yoGgeBe0tVce9nhLaUQVnsQxE0ND3eYX+raKAkQpf6wQjnCG4gCk46a3+HZyQ5m3SDpAYjAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:58.068927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f6fa86350f38848d08c3017358dbf71f3f91f88be64d73a74377d8348ab984c","sha256:2c8d82dc5ece8e85222cc459f70ef8fb66ae9b2f6eafa6f41094f97c5ea2d083"],"state_sha256":"eb5669b85e5e804adb45d2dc1f26dd2433acc99060050ec6e52adc7334469fda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SPshKni6Z+m5H7jC8/ZCJ0wh0QTooFKRI7uixkeIQlxwVmt3b69EAKFBUdDiOxRbbTkssS669q/ypIkdSNnqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:37:59.239419Z","bundle_sha256":"85770e61dbe9f74b26a519b1aa0179afb56aff11ccbae7d54ca2f54940ddc16e"}}