{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:KIXO436DG2GXX2KXWN66OU4PY7","short_pith_number":"pith:KIXO436D","canonical_record":{"source":{"id":"2308.10859","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-21T16:59:26Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","math.AP","math.MP"],"title_canon_sha256":"ff70f564b5bc7fd761b10c9aaef73034d3fed5ce2af1445d283fb43851a4dcab","abstract_canon_sha256":"5248c88a54a1373e7b8b046003b27a1b50593f52c7569f55c648bce702423a2a"},"schema_version":"1.0"},"canonical_sha256":"522eee6fc3368d7be957b37de7538fc7e18d828190b39236d107ff76664374c4","source":{"kind":"arxiv","id":"2308.10859","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.10859","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"2308.10859v1","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.10859","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"KIXO436DG2GX","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"pith_short_16","alias_value":"KIXO436DG2GXX2KX","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"pith_short_8","alias_value":"KIXO436D","created_at":"2026-07-05T06:43:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:KIXO436DG2GXX2KXWN66OU4PY7","target":"record","payload":{"canonical_record":{"source":{"id":"2308.10859","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-21T16:59:26Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","math.AP","math.MP"],"title_canon_sha256":"ff70f564b5bc7fd761b10c9aaef73034d3fed5ce2af1445d283fb43851a4dcab","abstract_canon_sha256":"5248c88a54a1373e7b8b046003b27a1b50593f52c7569f55c648bce702423a2a"},"schema_version":"1.0"},"canonical_sha256":"522eee6fc3368d7be957b37de7538fc7e18d828190b39236d107ff76664374c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:43:15.580099Z","signature_b64":"ap+l2Qx3i3vJ3swrjIxBy818vStzLeOL72lOyfRDHeyyMatjNGiKLOSVyoH58S35eSahXu3RcR9+jEiJJwHyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"522eee6fc3368d7be957b37de7538fc7e18d828190b39236d107ff76664374c4","last_reissued_at":"2026-07-05T06:43:15.579629Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:43:15.579629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.10859","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":"2026-07-05T06:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mu3/bh2MZ2o+rDxMth/QO9Wedup6QJkYBWLezGKXsRt4JETQ90axneItwNR28ucd9EzEA1AzK2yInOLBwkT0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:31:01.877899Z"},"content_sha256":"d66b51965031b340b5a3ea81622fd9d8728ac731bcd0bf140a282e1398bdc3f8","schema_version":"1.0","event_id":"sha256:d66b51965031b340b5a3ea81622fd9d8728ac731bcd0bf140a282e1398bdc3f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:KIXO436DG2GXX2KXWN66OU4PY7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chiral limit of twisted trilayer graphene","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.str-el","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Jens Wittsten, Mengxuan Yang, Simon Becker, Tristan Humbert","submitted_at":"2023-08-21T16:59:26Z","abstract_excerpt":"We initiate the mathematical study of the Bistritzer-MacDonald Hamiltonian for twisted trilayer graphene in the chiral limit (and beyond). We develop a spectral theoretic approach to investigate the presence of flat bands under specific magic parameters. This allows us to derive trace formulae that show that the tunnelling parameters that lead to flat bands are nowhere continuous as functions of the twisting angles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.10859","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/2308.10859/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":"2026-07-05T06:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z2Do6PpqJYh5sY3D1/yBy6SBjOeDVXIvEHxSw870h3Q8t0tstulCBWOwmmvMdTncDGBQodIdCYBUtJcF13ScCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:31:01.878264Z"},"content_sha256":"6d4a7514841e37bb8fc7c2ae404e123dd822bf336b250387b1d833ec00424f6a","schema_version":"1.0","event_id":"sha256:6d4a7514841e37bb8fc7c2ae404e123dd822bf336b250387b1d833ec00424f6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIXO436DG2GXX2KXWN66OU4PY7/bundle.json","state_url":"https://pith.science/pith/KIXO436DG2GXX2KXWN66OU4PY7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIXO436DG2GXX2KXWN66OU4PY7/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":"2026-07-06T10:31:01Z","links":{"resolver":"https://pith.science/pith/KIXO436DG2GXX2KXWN66OU4PY7","bundle":"https://pith.science/pith/KIXO436DG2GXX2KXWN66OU4PY7/bundle.json","state":"https://pith.science/pith/KIXO436DG2GXX2KXWN66OU4PY7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIXO436DG2GXX2KXWN66OU4PY7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KIXO436DG2GXX2KXWN66OU4PY7","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":"5248c88a54a1373e7b8b046003b27a1b50593f52c7569f55c648bce702423a2a","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-21T16:59:26Z","title_canon_sha256":"ff70f564b5bc7fd761b10c9aaef73034d3fed5ce2af1445d283fb43851a4dcab"},"schema_version":"1.0","source":{"id":"2308.10859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.10859","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"2308.10859v1","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.10859","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"KIXO436DG2GX","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"pith_short_16","alias_value":"KIXO436DG2GXX2KX","created_at":"2026-07-05T06:43:15Z"},{"alias_kind":"pith_short_8","alias_value":"KIXO436D","created_at":"2026-07-05T06:43:15Z"}],"graph_snapshots":[{"event_id":"sha256:6d4a7514841e37bb8fc7c2ae404e123dd822bf336b250387b1d833ec00424f6a","target":"graph","created_at":"2026-07-05T06:43:15Z","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/2308.10859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We initiate the mathematical study of the Bistritzer-MacDonald Hamiltonian for twisted trilayer graphene in the chiral limit (and beyond). We develop a spectral theoretic approach to investigate the presence of flat bands under specific magic parameters. This allows us to derive trace formulae that show that the tunnelling parameters that lead to flat bands are nowhere continuous as functions of the twisting angles.","authors_text":"Jens Wittsten, Mengxuan Yang, Simon Becker, Tristan Humbert","cross_cats":["cond-mat.mes-hall","cond-mat.str-el","math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-21T16:59:26Z","title":"Chiral limit of twisted trilayer graphene"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.10859","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:d66b51965031b340b5a3ea81622fd9d8728ac731bcd0bf140a282e1398bdc3f8","target":"record","created_at":"2026-07-05T06:43:15Z","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":"5248c88a54a1373e7b8b046003b27a1b50593f52c7569f55c648bce702423a2a","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.str-el","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-21T16:59:26Z","title_canon_sha256":"ff70f564b5bc7fd761b10c9aaef73034d3fed5ce2af1445d283fb43851a4dcab"},"schema_version":"1.0","source":{"id":"2308.10859","kind":"arxiv","version":1}},"canonical_sha256":"522eee6fc3368d7be957b37de7538fc7e18d828190b39236d107ff76664374c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"522eee6fc3368d7be957b37de7538fc7e18d828190b39236d107ff76664374c4","first_computed_at":"2026-07-05T06:43:15.579629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:43:15.579629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ap+l2Qx3i3vJ3swrjIxBy818vStzLeOL72lOyfRDHeyyMatjNGiKLOSVyoH58S35eSahXu3RcR9+jEiJJwHyAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:43:15.580099Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.10859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d66b51965031b340b5a3ea81622fd9d8728ac731bcd0bf140a282e1398bdc3f8","sha256:6d4a7514841e37bb8fc7c2ae404e123dd822bf336b250387b1d833ec00424f6a"],"state_sha256":"6bc311b96e2bde4d8837138ea1133ccabe1c8a8822b17d5f1469f738bd874315"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7ONjT8qyofm4BqDY8VzAPuMLjZLJFiZlR+zMBp1sN7RbrmsTWE/lKjj3ni3d99ML+zTNKlU5J8IfsKcw+B6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T10:31:01.880125Z","bundle_sha256":"4f3e8482ecfda5e072bac034a1ef1b78833e8f4c425462196fee52c7f6773f16"}}