{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N3J5S67P7OBQGAJRKKULT3775C","short_pith_number":"pith:N3J5S67P","canonical_record":{"source":{"id":"1406.1773","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-06T18:58:36Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"1fbba2ccd21198821cfd8f8af2dd318a4050e55e1aaa95c45f9bb0c487323964","abstract_canon_sha256":"20b493988285d37e33f9429ecacaaac86c88b23f042e23eb7585819b924eb706"},"schema_version":"1.0"},"canonical_sha256":"6ed3d97beffb8303013152a8b9efffe890b956e997ae6550047073cea722e324","source":{"kind":"arxiv","id":"1406.1773","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1773","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1773v2","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1773","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"N3J5S67P7OBQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N3J5S67P7OBQGAJR","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N3J5S67P","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N3J5S67P7OBQGAJRKKULT3775C","target":"record","payload":{"canonical_record":{"source":{"id":"1406.1773","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-06T18:58:36Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"1fbba2ccd21198821cfd8f8af2dd318a4050e55e1aaa95c45f9bb0c487323964","abstract_canon_sha256":"20b493988285d37e33f9429ecacaaac86c88b23f042e23eb7585819b924eb706"},"schema_version":"1.0"},"canonical_sha256":"6ed3d97beffb8303013152a8b9efffe890b956e997ae6550047073cea722e324","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:17.102332Z","signature_b64":"vIZAuLN2KrsC5lSv2h+4Ldgvfu0bZKNolsL8cZOk6bNwci54R7ajRxlnjxP1FMpUoWO1MnMmZD0kb+7+3suzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ed3d97beffb8303013152a8b9efffe890b956e997ae6550047073cea722e324","last_reissued_at":"2026-05-18T02:44:17.101838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:17.101838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.1773","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":"2026-05-18T02:44:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r6b4W2JpBui/n37yYvHaEwiIA9MKZoYRQaICmhLokt7f4RdP7tozbtpUqXjZafakmJsfOdK2FBtpzScUZjd6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:39:52.653086Z"},"content_sha256":"c3469d17d3dc28d0b3157ebe2fbf764bb58093dc52937cfbeec520b15a3ee062","schema_version":"1.0","event_id":"sha256:c3469d17d3dc28d0b3157ebe2fbf764bb58093dc52937cfbeec520b15a3ee062"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N3J5S67P7OBQGAJRKKULT3775C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamical polarization in ABC-stacked multilayer graphene in a magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.str-el","authors_text":"E.V. Gorbar, O.O. Sobol, V.P. Gusynin","submitted_at":"2014-06-06T18:58:36Z","abstract_excerpt":"In the continuum low energy model, we calculate the one-loop dynamical polarization functions in ABC-stacked (rhombohedral) $n$-layer graphene in a magnetic field. Neglecting the trigonal warping effects, they are derived as functions of wavevector and frequency at finite chemical potential, temperature, band gap, and the width of Landau levels. The analytic results are given in terms of digamma functions and generalized Laguerre polynomials and have the form of double sums over Landau levels. Various particular limits for polarization functions (static, clean, etc.) are discussed. The intrala"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1773","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":"2026-05-18T02:44:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1jgXIzxTsWljUfjWHcozQyHdKTZHXOirLM4ZE3Q22BqWsZgA+MUD5+2XXUBNb+dJt1LakJ4fihdULWMMnTzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:39:52.653453Z"},"content_sha256":"66c2d180f37b6123bdd4b436644ec0bfa99c59989915a5710051f596a2a0f8af","schema_version":"1.0","event_id":"sha256:66c2d180f37b6123bdd4b436644ec0bfa99c59989915a5710051f596a2a0f8af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3J5S67P7OBQGAJRKKULT3775C/bundle.json","state_url":"https://pith.science/pith/N3J5S67P7OBQGAJRKKULT3775C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3J5S67P7OBQGAJRKKULT3775C/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":"2026-05-31T15:39:52Z","links":{"resolver":"https://pith.science/pith/N3J5S67P7OBQGAJRKKULT3775C","bundle":"https://pith.science/pith/N3J5S67P7OBQGAJRKKULT3775C/bundle.json","state":"https://pith.science/pith/N3J5S67P7OBQGAJRKKULT3775C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3J5S67P7OBQGAJRKKULT3775C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N3J5S67P7OBQGAJRKKULT3775C","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":"20b493988285d37e33f9429ecacaaac86c88b23f042e23eb7585819b924eb706","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-06T18:58:36Z","title_canon_sha256":"1fbba2ccd21198821cfd8f8af2dd318a4050e55e1aaa95c45f9bb0c487323964"},"schema_version":"1.0","source":{"id":"1406.1773","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1773","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1773v2","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1773","created_at":"2026-05-18T02:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"N3J5S67P7OBQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N3J5S67P7OBQGAJR","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N3J5S67P","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:66c2d180f37b6123bdd4b436644ec0bfa99c59989915a5710051f596a2a0f8af","target":"graph","created_at":"2026-05-18T02:44:17Z","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":"In the continuum low energy model, we calculate the one-loop dynamical polarization functions in ABC-stacked (rhombohedral) $n$-layer graphene in a magnetic field. Neglecting the trigonal warping effects, they are derived as functions of wavevector and frequency at finite chemical potential, temperature, band gap, and the width of Landau levels. The analytic results are given in terms of digamma functions and generalized Laguerre polynomials and have the form of double sums over Landau levels. Various particular limits for polarization functions (static, clean, etc.) are discussed. The intrala","authors_text":"E.V. Gorbar, O.O. Sobol, V.P. Gusynin","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-06T18:58:36Z","title":"Dynamical polarization in ABC-stacked multilayer graphene in a magnetic field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1773","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:c3469d17d3dc28d0b3157ebe2fbf764bb58093dc52937cfbeec520b15a3ee062","target":"record","created_at":"2026-05-18T02:44:17Z","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":"20b493988285d37e33f9429ecacaaac86c88b23f042e23eb7585819b924eb706","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-06T18:58:36Z","title_canon_sha256":"1fbba2ccd21198821cfd8f8af2dd318a4050e55e1aaa95c45f9bb0c487323964"},"schema_version":"1.0","source":{"id":"1406.1773","kind":"arxiv","version":2}},"canonical_sha256":"6ed3d97beffb8303013152a8b9efffe890b956e997ae6550047073cea722e324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ed3d97beffb8303013152a8b9efffe890b956e997ae6550047073cea722e324","first_computed_at":"2026-05-18T02:44:17.101838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:17.101838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vIZAuLN2KrsC5lSv2h+4Ldgvfu0bZKNolsL8cZOk6bNwci54R7ajRxlnjxP1FMpUoWO1MnMmZD0kb+7+3suzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:17.102332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1773","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3469d17d3dc28d0b3157ebe2fbf764bb58093dc52937cfbeec520b15a3ee062","sha256:66c2d180f37b6123bdd4b436644ec0bfa99c59989915a5710051f596a2a0f8af"],"state_sha256":"dd22d7ad09c86a3e8fe5b865908749fc7b44adda95ae4340bcd6b5b70c672984"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2vF4A8kZHL9SnNdoiTf9Z2qqlSi4nyLB+qLrYdNVLWcHPYx65QlDzLBe92WF2nOM0g+CZtmGI/S5rjlvamDoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:39:52.655716Z","bundle_sha256":"42db05dcdf07bf02425de3444a8e0fa85dba40fd3ff1a26a54c68e3e3c9b9e57"}}