{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ABOKDSALZGAYBYKVOK6YLTE4KJ","short_pith_number":"pith:ABOKDSAL","canonical_record":{"source":{"id":"1308.0713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-08-03T16:18:59Z","cross_cats_sorted":[],"title_canon_sha256":"a627b2c0ff40661e79e52387a4351b5c9caa5b8c8c06182e60a017447697acff","abstract_canon_sha256":"0346929370e2eb327d1b0781bb7f8790f6f658242fc3d7a0f43a14b6ec6b900f"},"schema_version":"1.0"},"canonical_sha256":"005ca1c80bc98180e15572bd85cc9c5250e41d43c21db7c5f2ce3b6bc9ac27d9","source":{"kind":"arxiv","id":"1308.0713","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0713","created_at":"2026-05-18T03:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0713v2","created_at":"2026-05-18T03:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0713","created_at":"2026-05-18T03:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"ABOKDSALZGAY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ABOKDSALZGAYBYKV","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ABOKDSAL","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ABOKDSALZGAYBYKVOK6YLTE4KJ","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-08-03T16:18:59Z","cross_cats_sorted":[],"title_canon_sha256":"a627b2c0ff40661e79e52387a4351b5c9caa5b8c8c06182e60a017447697acff","abstract_canon_sha256":"0346929370e2eb327d1b0781bb7f8790f6f658242fc3d7a0f43a14b6ec6b900f"},"schema_version":"1.0"},"canonical_sha256":"005ca1c80bc98180e15572bd85cc9c5250e41d43c21db7c5f2ce3b6bc9ac27d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:46.828376Z","signature_b64":"r/U1gQemYw+Xw7brx5jS2yXyTEWFT4ECIlP+LGzhN9yFayNJWMOnRR2/0+RS+KF8D5PkO3Ix+1giXHuX1gT9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"005ca1c80bc98180e15572bd85cc9c5250e41d43c21db7c5f2ce3b6bc9ac27d9","last_reissued_at":"2026-05-18T03:02:46.826775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:46.826775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0713","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":"2026-05-18T03:02:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AXxI5nRPneTsDHhsDEPtXP3nlMvsej3R1OEgZkJblw/ealUPhEaUN4rr07qbipW5gpSwPHiB041E1euksXkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:12:48.272618Z"},"content_sha256":"f6f43eb0a19dfc9a373156b2ebee15946c38823cf52d6d5abff95f90bed684b8","schema_version":"1.0","event_id":"sha256:f6f43eb0a19dfc9a373156b2ebee15946c38823cf52d6d5abff95f90bed684b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ABOKDSALZGAYBYKVOK6YLTE4KJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optical properties of the Hofstadter butterfly in the Moir\\'{e} superlattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Mikito Koshino, Pilkyung Moon","submitted_at":"2013-08-03T16:18:59Z","abstract_excerpt":"We investigate the optical absorption spectrum and the selection rule for the Hofstadter butterfly in twisted bilayer graphene under magnetic fields. We demonstrate that the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. We find that the optical selection rule has a nested self-similar structure as well, and it is governed by the conservation of the total angular momentum summed over different hierarchies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0713","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":"2026-05-18T03:02:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzsl0oIWnjnUwQe/oizizVsnDiXoLUsNFsoDQYVQ5PL6C7MW9MNgzt5nG5Zzh1rjr0cPdPliSikQm7/LrYTfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:12:48.273248Z"},"content_sha256":"92eae208bf759f5c38465296c4666fc1452e9677fa25d4eacb0b299d6a7839e2","schema_version":"1.0","event_id":"sha256:92eae208bf759f5c38465296c4666fc1452e9677fa25d4eacb0b299d6a7839e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABOKDSALZGAYBYKVOK6YLTE4KJ/bundle.json","state_url":"https://pith.science/pith/ABOKDSALZGAYBYKVOK6YLTE4KJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABOKDSALZGAYBYKVOK6YLTE4KJ/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":"2026-06-06T08:12:48Z","links":{"resolver":"https://pith.science/pith/ABOKDSALZGAYBYKVOK6YLTE4KJ","bundle":"https://pith.science/pith/ABOKDSALZGAYBYKVOK6YLTE4KJ/bundle.json","state":"https://pith.science/pith/ABOKDSALZGAYBYKVOK6YLTE4KJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABOKDSALZGAYBYKVOK6YLTE4KJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ABOKDSALZGAYBYKVOK6YLTE4KJ","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":"0346929370e2eb327d1b0781bb7f8790f6f658242fc3d7a0f43a14b6ec6b900f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-08-03T16:18:59Z","title_canon_sha256":"a627b2c0ff40661e79e52387a4351b5c9caa5b8c8c06182e60a017447697acff"},"schema_version":"1.0","source":{"id":"1308.0713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0713","created_at":"2026-05-18T03:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0713v2","created_at":"2026-05-18T03:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0713","created_at":"2026-05-18T03:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"ABOKDSALZGAY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ABOKDSALZGAYBYKV","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ABOKDSAL","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:92eae208bf759f5c38465296c4666fc1452e9677fa25d4eacb0b299d6a7839e2","target":"graph","created_at":"2026-05-18T03:02:46Z","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 investigate the optical absorption spectrum and the selection rule for the Hofstadter butterfly in twisted bilayer graphene under magnetic fields. We demonstrate that the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. We find that the optical selection rule has a nested self-similar structure as well, and it is governed by the conservation of the total angular momentum summed over different hierarchies.","authors_text":"Mikito Koshino, Pilkyung Moon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-08-03T16:18:59Z","title":"Optical properties of the Hofstadter butterfly in the Moir\\'{e} superlattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0713","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:f6f43eb0a19dfc9a373156b2ebee15946c38823cf52d6d5abff95f90bed684b8","target":"record","created_at":"2026-05-18T03:02:46Z","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":"0346929370e2eb327d1b0781bb7f8790f6f658242fc3d7a0f43a14b6ec6b900f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-08-03T16:18:59Z","title_canon_sha256":"a627b2c0ff40661e79e52387a4351b5c9caa5b8c8c06182e60a017447697acff"},"schema_version":"1.0","source":{"id":"1308.0713","kind":"arxiv","version":2}},"canonical_sha256":"005ca1c80bc98180e15572bd85cc9c5250e41d43c21db7c5f2ce3b6bc9ac27d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"005ca1c80bc98180e15572bd85cc9c5250e41d43c21db7c5f2ce3b6bc9ac27d9","first_computed_at":"2026-05-18T03:02:46.826775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:46.826775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r/U1gQemYw+Xw7brx5jS2yXyTEWFT4ECIlP+LGzhN9yFayNJWMOnRR2/0+RS+KF8D5PkO3Ix+1giXHuX1gT9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:46.828376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6f43eb0a19dfc9a373156b2ebee15946c38823cf52d6d5abff95f90bed684b8","sha256:92eae208bf759f5c38465296c4666fc1452e9677fa25d4eacb0b299d6a7839e2"],"state_sha256":"a55cdee1a710c515cbb69c25afa3200dbcb759bc05455e73f951909fb96cfacd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7AWRJFriAhrj4qECCDxNbNXSFKrygpW4fI5OTpUPFImOqV2dh/YGBUcHRfwjSaQhFJDMkoKc7sd/vexTBnttBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:12:48.277418Z","bundle_sha256":"b769abd3a94ff01faf8cdb4400b2c9ddda807c527ee8ea5c3b43d54af332f71d"}}