{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7FP63BKAQNGDWF2W25ZCGXN5U6","short_pith_number":"pith:7FP63BKA","canonical_record":{"source":{"id":"2507.09277","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"hep-th","submitted_at":"2025-07-12T13:15:53Z","cross_cats_sorted":[],"title_canon_sha256":"6ef1b9b4d292b683389b36722d608b22452faf55ccf36682dcc6c9fb20629a25","abstract_canon_sha256":"b542ad230c54ce8ac6a810437d7378f4a712b13fcc689d90333761f0f83e1617"},"schema_version":"1.0"},"canonical_sha256":"f95fed8540834c3b1756d772235dbda79bf613aa6e992d4618085c57f02a9a03","source":{"kind":"arxiv","id":"2507.09277","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.09277","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"2507.09277v1","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09277","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"7FP63BKAQNGD","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"pith_short_16","alias_value":"7FP63BKAQNGDWF2W","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"pith_short_8","alias_value":"7FP63BKA","created_at":"2026-07-05T11:36:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7FP63BKAQNGDWF2W25ZCGXN5U6","target":"record","payload":{"canonical_record":{"source":{"id":"2507.09277","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"hep-th","submitted_at":"2025-07-12T13:15:53Z","cross_cats_sorted":[],"title_canon_sha256":"6ef1b9b4d292b683389b36722d608b22452faf55ccf36682dcc6c9fb20629a25","abstract_canon_sha256":"b542ad230c54ce8ac6a810437d7378f4a712b13fcc689d90333761f0f83e1617"},"schema_version":"1.0"},"canonical_sha256":"f95fed8540834c3b1756d772235dbda79bf613aa6e992d4618085c57f02a9a03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:06.643111Z","signature_b64":"ef6z9U1ZSJ59VbCTGEfODlKKCVL8q7ERyj5H4Y68xs19UEvIsH0ZUoCxnrJpkXkaNBXoCZGvT2BSHG7azHU/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f95fed8540834c3b1756d772235dbda79bf613aa6e992d4618085c57f02a9a03","last_reissued_at":"2026-07-05T11:36:06.642693Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:06.642693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.09277","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":"2026-07-05T11:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQVs2US2s03nHyOVIPShnppD4+izC2qGK8ED228vSzOdJyNlBpkyKF3GgSsZ5mVfjEx0cYwFFLrByR7bNq5EDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:22:18.731339Z"},"content_sha256":"46b7315b6d49b2c9c5f30f28df13a5d6d5cb8e0f0f7caf453190f840cea68905","schema_version":"1.0","event_id":"sha256:46b7315b6d49b2c9c5f30f28df13a5d6d5cb8e0f0f7caf453190f840cea68905"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7FP63BKAQNGDWF2W25ZCGXN5U6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauge Invariant and Generic Formulation of Magnetic Translations and so(3,1) Curtright-Zachos Generators","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Haru-Tada Sato","submitted_at":"2025-07-12T13:15:53Z","abstract_excerpt":"We propose a gauge-invariant formulation of magnetic translation (GMT) operators, eliminating the gauge dependence that conventional definitions suffer from due to specific gauge choices. We extend this framework by incorporating so(3,1) conformal symmetry, demonstrating how GMT operators can be naturally embedded within this algebraic structure. We then show the fundamental role of sim(2) duality between pseudo-dilatation and pseudo-angular momentum operators in constructing GMT operators. A key result of this approach is the derivation of the Curtright-Zachos (CZ) generators from gauge-invar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09277","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/2507.09277/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":"2026-07-05T11:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtulzUH1L7ICQzQeOgkJ+fh4Np7o92EvkbnEf+lp2OTWm5qmovbHXsJiI5b6/XpuEhufGbXdjLQHxfKADQJvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:22:18.732273Z"},"content_sha256":"d5526f8a54362b83c345d72f456af469f11d0600e508fd9ee131c3db0e9de363","schema_version":"1.0","event_id":"sha256:d5526f8a54362b83c345d72f456af469f11d0600e508fd9ee131c3db0e9de363"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FP63BKAQNGDWF2W25ZCGXN5U6/bundle.json","state_url":"https://pith.science/pith/7FP63BKAQNGDWF2W25ZCGXN5U6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FP63BKAQNGDWF2W25ZCGXN5U6/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":"2026-08-09T07:22:18Z","links":{"resolver":"https://pith.science/pith/7FP63BKAQNGDWF2W25ZCGXN5U6","bundle":"https://pith.science/pith/7FP63BKAQNGDWF2W25ZCGXN5U6/bundle.json","state":"https://pith.science/pith/7FP63BKAQNGDWF2W25ZCGXN5U6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FP63BKAQNGDWF2W25ZCGXN5U6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7FP63BKAQNGDWF2W25ZCGXN5U6","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":"b542ad230c54ce8ac6a810437d7378f4a712b13fcc689d90333761f0f83e1617","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"hep-th","submitted_at":"2025-07-12T13:15:53Z","title_canon_sha256":"6ef1b9b4d292b683389b36722d608b22452faf55ccf36682dcc6c9fb20629a25"},"schema_version":"1.0","source":{"id":"2507.09277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.09277","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"2507.09277v1","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09277","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"7FP63BKAQNGD","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"pith_short_16","alias_value":"7FP63BKAQNGDWF2W","created_at":"2026-07-05T11:36:06Z"},{"alias_kind":"pith_short_8","alias_value":"7FP63BKA","created_at":"2026-07-05T11:36:06Z"}],"graph_snapshots":[{"event_id":"sha256:d5526f8a54362b83c345d72f456af469f11d0600e508fd9ee131c3db0e9de363","target":"graph","created_at":"2026-07-05T11:36:06Z","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/2507.09277/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a gauge-invariant formulation of magnetic translation (GMT) operators, eliminating the gauge dependence that conventional definitions suffer from due to specific gauge choices. We extend this framework by incorporating so(3,1) conformal symmetry, demonstrating how GMT operators can be naturally embedded within this algebraic structure. We then show the fundamental role of sim(2) duality between pseudo-dilatation and pseudo-angular momentum operators in constructing GMT operators. A key result of this approach is the derivation of the Curtright-Zachos (CZ) generators from gauge-invar","authors_text":"Haru-Tada Sato","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"hep-th","submitted_at":"2025-07-12T13:15:53Z","title":"Gauge Invariant and Generic Formulation of Magnetic Translations and so(3,1) Curtright-Zachos Generators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09277","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":"sha256:46b7315b6d49b2c9c5f30f28df13a5d6d5cb8e0f0f7caf453190f840cea68905","target":"record","created_at":"2026-07-05T11:36:06Z","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":"b542ad230c54ce8ac6a810437d7378f4a712b13fcc689d90333761f0f83e1617","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"hep-th","submitted_at":"2025-07-12T13:15:53Z","title_canon_sha256":"6ef1b9b4d292b683389b36722d608b22452faf55ccf36682dcc6c9fb20629a25"},"schema_version":"1.0","source":{"id":"2507.09277","kind":"arxiv","version":1}},"canonical_sha256":"f95fed8540834c3b1756d772235dbda79bf613aa6e992d4618085c57f02a9a03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f95fed8540834c3b1756d772235dbda79bf613aa6e992d4618085c57f02a9a03","first_computed_at":"2026-07-05T11:36:06.642693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:06.642693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ef6z9U1ZSJ59VbCTGEfODlKKCVL8q7ERyj5H4Y68xs19UEvIsH0ZUoCxnrJpkXkaNBXoCZGvT2BSHG7azHU/Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:06.643111Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.09277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46b7315b6d49b2c9c5f30f28df13a5d6d5cb8e0f0f7caf453190f840cea68905","sha256:d5526f8a54362b83c345d72f456af469f11d0600e508fd9ee131c3db0e9de363"],"state_sha256":"27b459cb1a1860be04ebb7637fa61aee4f7eaec174bda879d7d29988514331d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zOCv9A5WUMht/9avZhyU6QKIFJ2Rycrfx9CKF3/61bIWUbJdA7XvwfiH2r1EUlIK+l7W3ASIvA0p+Q51u5qcAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:22:18.737993Z","bundle_sha256":"1849a9e8afcfc8d2cf67eda14ba32afd4050d29649d9e2d966d2b113f72dc893"}}