{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AFGN6YR44EWEX5OAAMOOJG7XND","short_pith_number":"pith:AFGN6YR4","schema_version":"1.0","canonical_sha256":"014cdf623ce12c4bf5c0031ce49bf768e86fe27670ed365be04c8f3760c52030","source":{"kind":"arxiv","id":"1603.00212","version":3},"attestation_state":"computed","paper":{"title":"Graphene with vacancies: supernumerary zero modes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.dis-nn","authors_text":"Ferdinand Evers, Gemma C. Solomon, Johannes Schindler, Norman Weik, Soumya Bera","submitted_at":"2016-03-01T10:13:03Z","abstract_excerpt":"The density of states, $\\varrho(E)$, of graphene is investigated within the tight binding (H\\\"uckel) approximation in the presence of vacancies. They induce a non-vanishing density of zero modes, $n_\\text{zm}$, that act as midgap states: $\\varrho(E)=n_\\text{zm}\\delta(E) + \\text{smooth}$. As is well known, the actual number of zero modes per sample can in principle exceed the sublattice imbalance: $N_\\text{zm}\\geq |N_\\text{A}-N_\\text{B}|$, where $N_\\text{A}$, $N_\\text{B}$ denote the number of carbon atoms in each sublattice. In this work, we establish a stronger relation that is valid in the th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.00212","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-03-01T10:13:03Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"860315bdc5d646d4c9e14416e0ee761a112349c91386f28f164e9e9b9ba88cea","abstract_canon_sha256":"042104a65fbf6d5092667bd065c3f0ed5b59174dddac1e5e135fa4ea7192444b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:17.048158Z","signature_b64":"e5OH3vkIWZW8tHvWq+qH6RYccp3Y8TrJeKs89pCeh13sH1aYAtHb9ScqlGz1s3bkAsQ1dkvoWWA//2u+o+57Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"014cdf623ce12c4bf5c0031ce49bf768e86fe27670ed365be04c8f3760c52030","last_reissued_at":"2026-05-18T01:07:17.047589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:17.047589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphene with vacancies: supernumerary zero modes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.dis-nn","authors_text":"Ferdinand Evers, Gemma C. Solomon, Johannes Schindler, Norman Weik, Soumya Bera","submitted_at":"2016-03-01T10:13:03Z","abstract_excerpt":"The density of states, $\\varrho(E)$, of graphene is investigated within the tight binding (H\\\"uckel) approximation in the presence of vacancies. They induce a non-vanishing density of zero modes, $n_\\text{zm}$, that act as midgap states: $\\varrho(E)=n_\\text{zm}\\delta(E) + \\text{smooth}$. As is well known, the actual number of zero modes per sample can in principle exceed the sublattice imbalance: $N_\\text{zm}\\geq |N_\\text{A}-N_\\text{B}|$, where $N_\\text{A}$, $N_\\text{B}$ denote the number of carbon atoms in each sublattice. In this work, we establish a stronger relation that is valid in the th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00212","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.00212","created_at":"2026-05-18T01:07:17.047669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.00212v3","created_at":"2026-05-18T01:07:17.047669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00212","created_at":"2026-05-18T01:07:17.047669+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFGN6YR44EWE","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFGN6YR44EWEX5OA","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFGN6YR4","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND","json":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND.json","graph_json":"https://pith.science/api/pith-number/AFGN6YR44EWEX5OAAMOOJG7XND/graph.json","events_json":"https://pith.science/api/pith-number/AFGN6YR44EWEX5OAAMOOJG7XND/events.json","paper":"https://pith.science/paper/AFGN6YR4"},"agent_actions":{"view_html":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND","download_json":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND.json","view_paper":"https://pith.science/paper/AFGN6YR4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.00212&json=true","fetch_graph":"https://pith.science/api/pith-number/AFGN6YR44EWEX5OAAMOOJG7XND/graph.json","fetch_events":"https://pith.science/api/pith-number/AFGN6YR44EWEX5OAAMOOJG7XND/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND/action/storage_attestation","attest_author":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND/action/author_attestation","sign_citation":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND/action/citation_signature","submit_replication":"https://pith.science/pith/AFGN6YR44EWEX5OAAMOOJG7XND/action/replication_record"}},"created_at":"2026-05-18T01:07:17.047669+00:00","updated_at":"2026-05-18T01:07:17.047669+00:00"}