{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7SJCQDKLBKKJRU2KYPW6TKSR5D","short_pith_number":"pith:7SJCQDKL","canonical_record":{"source":{"id":"1101.4094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-01-21T09:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"fd7acf2481dd98bdcc47118202da45ce4f6fe7a84b863da9f8e5b2867bc0d404","abstract_canon_sha256":"95cc07abb195a9e2431064a453da39a79192e756230f96db360c9b968a8b85c7"},"schema_version":"1.0"},"canonical_sha256":"fc92280d4b0a9498d34ac3ede9aa51e8f9dd42452faa4a1125907d9169972667","source":{"kind":"arxiv","id":"1101.4094","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4094","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4094v1","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4094","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"7SJCQDKLBKKJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7SJCQDKLBKKJRU2K","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7SJCQDKL","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7SJCQDKLBKKJRU2KYPW6TKSR5D","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-01-21T09:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"fd7acf2481dd98bdcc47118202da45ce4f6fe7a84b863da9f8e5b2867bc0d404","abstract_canon_sha256":"95cc07abb195a9e2431064a453da39a79192e756230f96db360c9b968a8b85c7"},"schema_version":"1.0"},"canonical_sha256":"fc92280d4b0a9498d34ac3ede9aa51e8f9dd42452faa4a1125907d9169972667","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:50.794793Z","signature_b64":"3D15KG1h21TTXY/+aSeoqSaFTbyqJxREJLLgLLA0c0CW0dNZLb43JKpOjzuQUG6mkEqtGKSvpNlx2FUeFY99CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc92280d4b0a9498d34ac3ede9aa51e8f9dd42452faa4a1125907d9169972667","last_reissued_at":"2026-05-18T02:22:50.794261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:50.794261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4094","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":"2026-05-18T02:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CNcas+UPyqKk68vH/M76bIAC2b8KVh3RPQt7ixKoZ99f24w7M1gjXEb/TYKI3KkLQ6amEO/D9tjX/7BJg5kdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:05:25.548073Z"},"content_sha256":"ce58e78c43426a7432f41b1b2d4abc96ffb466f114093efd01ff2d6fa140e23d","schema_version":"1.0","event_id":"sha256:ce58e78c43426a7432f41b1b2d4abc96ffb466f114093efd01ff2d6fa140e23d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7SJCQDKLBKKJRU2KYPW6TKSR5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kronig-Penney model on bilayer graphene: spectrum and transmission periodic in the strength of the barriers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"F. M. Peeters, M. Barbier, P. Vasilopoulos","submitted_at":"2011-01-21T09:34:01Z","abstract_excerpt":"We show that the transmission through single and double {\\delta}-function potential barriers of strength P in bilayer graphene is periodic in P with period {\\pi}. For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behaviour is found for the conductance. The spectrum of a periodic succession of {\\delta}-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2{\\pi}. For P smaller than a critical value, the spectrum exhibits two Dirac points while for P larger than this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4094","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":"2026-05-18T02:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XM40YMS+1M1IbZwXsOWU7YaivuelpfRxR3BJNolth9oYFHQzSSlKuIlj+8S1t72pAHZ0Q2T65aI1MaApsH4jAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:05:25.548801Z"},"content_sha256":"f8112e4d9e44bde3713edae48cf2833288213df46ba3b8f2fe462dad27136b73","schema_version":"1.0","event_id":"sha256:f8112e4d9e44bde3713edae48cf2833288213df46ba3b8f2fe462dad27136b73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SJCQDKLBKKJRU2KYPW6TKSR5D/bundle.json","state_url":"https://pith.science/pith/7SJCQDKLBKKJRU2KYPW6TKSR5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SJCQDKLBKKJRU2KYPW6TKSR5D/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":"2026-06-08T17:05:25Z","links":{"resolver":"https://pith.science/pith/7SJCQDKLBKKJRU2KYPW6TKSR5D","bundle":"https://pith.science/pith/7SJCQDKLBKKJRU2KYPW6TKSR5D/bundle.json","state":"https://pith.science/pith/7SJCQDKLBKKJRU2KYPW6TKSR5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SJCQDKLBKKJRU2KYPW6TKSR5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7SJCQDKLBKKJRU2KYPW6TKSR5D","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":"95cc07abb195a9e2431064a453da39a79192e756230f96db360c9b968a8b85c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-01-21T09:34:01Z","title_canon_sha256":"fd7acf2481dd98bdcc47118202da45ce4f6fe7a84b863da9f8e5b2867bc0d404"},"schema_version":"1.0","source":{"id":"1101.4094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4094","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4094v1","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4094","created_at":"2026-05-18T02:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"7SJCQDKLBKKJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7SJCQDKLBKKJRU2K","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7SJCQDKL","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:f8112e4d9e44bde3713edae48cf2833288213df46ba3b8f2fe462dad27136b73","target":"graph","created_at":"2026-05-18T02:22:50Z","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 show that the transmission through single and double {\\delta}-function potential barriers of strength P in bilayer graphene is periodic in P with period {\\pi}. For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behaviour is found for the conductance. The spectrum of a periodic succession of {\\delta}-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2{\\pi}. For P smaller than a critical value, the spectrum exhibits two Dirac points while for P larger than this","authors_text":"F. M. Peeters, M. Barbier, P. Vasilopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-01-21T09:34:01Z","title":"Kronig-Penney model on bilayer graphene: spectrum and transmission periodic in the strength of the barriers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4094","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:ce58e78c43426a7432f41b1b2d4abc96ffb466f114093efd01ff2d6fa140e23d","target":"record","created_at":"2026-05-18T02:22:50Z","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":"95cc07abb195a9e2431064a453da39a79192e756230f96db360c9b968a8b85c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2011-01-21T09:34:01Z","title_canon_sha256":"fd7acf2481dd98bdcc47118202da45ce4f6fe7a84b863da9f8e5b2867bc0d404"},"schema_version":"1.0","source":{"id":"1101.4094","kind":"arxiv","version":1}},"canonical_sha256":"fc92280d4b0a9498d34ac3ede9aa51e8f9dd42452faa4a1125907d9169972667","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc92280d4b0a9498d34ac3ede9aa51e8f9dd42452faa4a1125907d9169972667","first_computed_at":"2026-05-18T02:22:50.794261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:50.794261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3D15KG1h21TTXY/+aSeoqSaFTbyqJxREJLLgLLA0c0CW0dNZLb43JKpOjzuQUG6mkEqtGKSvpNlx2FUeFY99CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:50.794793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce58e78c43426a7432f41b1b2d4abc96ffb466f114093efd01ff2d6fa140e23d","sha256:f8112e4d9e44bde3713edae48cf2833288213df46ba3b8f2fe462dad27136b73"],"state_sha256":"1d00b3dd966ebbaa067466ddb593ad2f6da52126adbed58964070842a91e337d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oCHmTZRyJ5zkZHXyoLRwSg689If4pgL2KTwN6/Sq1/DqZ/MFpJuJ+vtu1UEJh1yR4kyjLtzkks1hbh/D4NPKAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:05:25.552566Z","bundle_sha256":"1579a6d4f3b202159837c38b96f7e71df265612a8bf20dc16be8d988408995e8"}}