{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KBQCYWVB2YD2KPGGN22RHDLBBS","short_pith_number":"pith:KBQCYWVB","canonical_record":{"source":{"id":"1511.01875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-05T19:59:57Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"ec9002b2224128bb7e8f145c023d5bd081c9eb89fa0647fb1e73932cce4a00ad","abstract_canon_sha256":"21a5214f34fbafd52352c58db9d99832823a7607124478d8b748b6cc6513796f"},"schema_version":"1.0"},"canonical_sha256":"50602c5aa1d607a53cc66eb5138d610c9376ab4540255f26a1848ac92092acf4","source":{"kind":"arxiv","id":"1511.01875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01875","created_at":"2026-05-18T01:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01875v1","created_at":"2026-05-18T01:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01875","created_at":"2026-05-18T01:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"KBQCYWVB2YD2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KBQCYWVB2YD2KPGG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KBQCYWVB","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KBQCYWVB2YD2KPGGN22RHDLBBS","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-05T19:59:57Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"ec9002b2224128bb7e8f145c023d5bd081c9eb89fa0647fb1e73932cce4a00ad","abstract_canon_sha256":"21a5214f34fbafd52352c58db9d99832823a7607124478d8b748b6cc6513796f"},"schema_version":"1.0"},"canonical_sha256":"50602c5aa1d607a53cc66eb5138d610c9376ab4540255f26a1848ac92092acf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:41.771376Z","signature_b64":"h/3YtwTr9ujNhbrrVU2vur5EOOWkz9CS9iwycIa2yihgOwMs6oTIzBaYm2f6Mo2/gUe1oRxY5HHKeBi6CZG5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50602c5aa1d607a53cc66eb5138d610c9376ab4540255f26a1848ac92092acf4","last_reissued_at":"2026-05-18T01:18:41.770760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:41.770760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01875","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":"2026-05-18T01:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IansE4Vrct/BZAauNUqw6UA8/LNMF8V8wKJVJKk7gk3vCKHnXXUnECgeBfnArE2RWQmDY4Jo3wfNUa4GCC5WAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:07:25.901900Z"},"content_sha256":"de7869b90f4cd033ea17c1e3986add969e8801e1748aa8850b73989403ee498b","schema_version":"1.0","event_id":"sha256:de7869b90f4cd033ea17c1e3986add969e8801e1748aa8850b73989403ee498b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KBQCYWVB2YD2KPGGN22RHDLBBS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete Flavour Symmetries from the Heisenberg Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"E.G. Floratos, G.K. Leontaris","submitted_at":"2015-11-05T19:59:57Z","abstract_excerpt":"Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01875","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":"2026-05-18T01:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbumK0iIwob+FDLFpV60+VPadFyEkadFmXKu+o7VNsBlwvyJey5Gd0EEo3GA58ZQiPLroTI0mujifUsRS4FoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:07:25.902245Z"},"content_sha256":"2aa8873e6d1a37c6bcbbc0b569f886e3aa2bdf26feda0c8b78a4ad53b14e6a52","schema_version":"1.0","event_id":"sha256:2aa8873e6d1a37c6bcbbc0b569f886e3aa2bdf26feda0c8b78a4ad53b14e6a52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBQCYWVB2YD2KPGGN22RHDLBBS/bundle.json","state_url":"https://pith.science/pith/KBQCYWVB2YD2KPGGN22RHDLBBS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBQCYWVB2YD2KPGGN22RHDLBBS/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":"2026-06-30T22:07:25Z","links":{"resolver":"https://pith.science/pith/KBQCYWVB2YD2KPGGN22RHDLBBS","bundle":"https://pith.science/pith/KBQCYWVB2YD2KPGGN22RHDLBBS/bundle.json","state":"https://pith.science/pith/KBQCYWVB2YD2KPGGN22RHDLBBS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBQCYWVB2YD2KPGGN22RHDLBBS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KBQCYWVB2YD2KPGGN22RHDLBBS","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":"21a5214f34fbafd52352c58db9d99832823a7607124478d8b748b6cc6513796f","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-05T19:59:57Z","title_canon_sha256":"ec9002b2224128bb7e8f145c023d5bd081c9eb89fa0647fb1e73932cce4a00ad"},"schema_version":"1.0","source":{"id":"1511.01875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01875","created_at":"2026-05-18T01:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01875v1","created_at":"2026-05-18T01:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01875","created_at":"2026-05-18T01:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"KBQCYWVB2YD2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KBQCYWVB2YD2KPGG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KBQCYWVB","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:2aa8873e6d1a37c6bcbbc0b569f886e3aa2bdf26feda0c8b78a4ad53b14e6a52","target":"graph","created_at":"2026-05-18T01:18:41Z","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":"Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the","authors_text":"E.G. Floratos, G.K. Leontaris","cross_cats":["hep-ph","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-05T19:59:57Z","title":"Discrete Flavour Symmetries from the Heisenberg Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01875","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:de7869b90f4cd033ea17c1e3986add969e8801e1748aa8850b73989403ee498b","target":"record","created_at":"2026-05-18T01:18:41Z","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":"21a5214f34fbafd52352c58db9d99832823a7607124478d8b748b6cc6513796f","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-05T19:59:57Z","title_canon_sha256":"ec9002b2224128bb7e8f145c023d5bd081c9eb89fa0647fb1e73932cce4a00ad"},"schema_version":"1.0","source":{"id":"1511.01875","kind":"arxiv","version":1}},"canonical_sha256":"50602c5aa1d607a53cc66eb5138d610c9376ab4540255f26a1848ac92092acf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50602c5aa1d607a53cc66eb5138d610c9376ab4540255f26a1848ac92092acf4","first_computed_at":"2026-05-18T01:18:41.770760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:41.770760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h/3YtwTr9ujNhbrrVU2vur5EOOWkz9CS9iwycIa2yihgOwMs6oTIzBaYm2f6Mo2/gUe1oRxY5HHKeBi6CZG5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:41.771376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de7869b90f4cd033ea17c1e3986add969e8801e1748aa8850b73989403ee498b","sha256:2aa8873e6d1a37c6bcbbc0b569f886e3aa2bdf26feda0c8b78a4ad53b14e6a52"],"state_sha256":"9c48f95c5daf8f03bf7e8b3194d3fab98a848721ea8f3352522f9609de3a643e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xhFbF6hPLhdXQNXj7LXr9Fs8riHASRamjsXfCn0MbQp/XThbZKSk357foZfF3kpp8cWm6tSwvuBmQyypNrhUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:07:25.904241Z","bundle_sha256":"e7ffacd409ad8dc2e9cd785ebb77b2824729322f4ad4736bd85a1f744320bbf5"}}