{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EOK5VIXVZ4X4FLHVJOKKRZJFHP","short_pith_number":"pith:EOK5VIXV","schema_version":"1.0","canonical_sha256":"2395daa2f5cf2fc2acf54b94a8e5253bd5e270ba8497a4e73f41caa4b51921f6","source":{"kind":"arxiv","id":"1212.6684","version":1},"attestation_state":"computed","paper":{"title":"Waves in Honeycomb Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.AP","math.MP","quant-ph"],"primary_cat":"nlin.PS","authors_text":"Charles L. Fefferman, Michael I. Weinstein","submitted_at":"2012-12-30T03:32:30Z","abstract_excerpt":"We review recent work of the authors on the non-relativistic Schr\\\"odinger equation with a honeycomb lattice potential, $V$. In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_V=-\\Delta+V$ and (ii) the two-dimensional Dirac equations, as a large, but finite time, effective description of $e^{-iH_Vt}\\psi_0$, for data $\\psi_0$, which is spectrally localized at a Dirac point. We conclude with a formal derivation and discussion of the effective large time evolution for the nonlinear Schr\\\"odinger - Gross Pitaevskii equation "},"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":"1212.6684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-12-30T03:32:30Z","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.AP","math.MP","quant-ph"],"title_canon_sha256":"5514b97fb92910ddae34f75a95bc0964e5db3ee9ffc7293ba83e2b324d960d6f","abstract_canon_sha256":"8bf2e17b5b45bedad15d49eeb2aefb18e3af659d64af3185a325c5e5d6ddb7bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:31.216646Z","signature_b64":"+BAmTrFD8nPmlhxCOonlcc6mUS/IuGdjEVhi5d35U1+XeXZaP0wO6wH6y2ejFL+FyOKWZY9etlmm5r4ctLV5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2395daa2f5cf2fc2acf54b94a8e5253bd5e270ba8497a4e73f41caa4b51921f6","last_reissued_at":"2026-05-18T03:37:31.215890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:31.215890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Waves in Honeycomb Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.AP","math.MP","quant-ph"],"primary_cat":"nlin.PS","authors_text":"Charles L. Fefferman, Michael I. Weinstein","submitted_at":"2012-12-30T03:32:30Z","abstract_excerpt":"We review recent work of the authors on the non-relativistic Schr\\\"odinger equation with a honeycomb lattice potential, $V$. In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_V=-\\Delta+V$ and (ii) the two-dimensional Dirac equations, as a large, but finite time, effective description of $e^{-iH_Vt}\\psi_0$, for data $\\psi_0$, which is spectrally localized at a Dirac point. We conclude with a formal derivation and discussion of the effective large time evolution for the nonlinear Schr\\\"odinger - Gross Pitaevskii equation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6684","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.6684","created_at":"2026-05-18T03:37:31.216009+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6684v1","created_at":"2026-05-18T03:37:31.216009+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6684","created_at":"2026-05-18T03:37:31.216009+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOK5VIXVZ4X4","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOK5VIXVZ4X4FLHV","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOK5VIXV","created_at":"2026-05-18T12:27:04.183437+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/EOK5VIXVZ4X4FLHVJOKKRZJFHP","json":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP.json","graph_json":"https://pith.science/api/pith-number/EOK5VIXVZ4X4FLHVJOKKRZJFHP/graph.json","events_json":"https://pith.science/api/pith-number/EOK5VIXVZ4X4FLHVJOKKRZJFHP/events.json","paper":"https://pith.science/paper/EOK5VIXV"},"agent_actions":{"view_html":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP","download_json":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP.json","view_paper":"https://pith.science/paper/EOK5VIXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6684&json=true","fetch_graph":"https://pith.science/api/pith-number/EOK5VIXVZ4X4FLHVJOKKRZJFHP/graph.json","fetch_events":"https://pith.science/api/pith-number/EOK5VIXVZ4X4FLHVJOKKRZJFHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP/action/storage_attestation","attest_author":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP/action/author_attestation","sign_citation":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP/action/citation_signature","submit_replication":"https://pith.science/pith/EOK5VIXVZ4X4FLHVJOKKRZJFHP/action/replication_record"}},"created_at":"2026-05-18T03:37:31.216009+00:00","updated_at":"2026-05-18T03:37:31.216009+00:00"}