{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZIJ55P6SMWFNQ24JRNHBD2BXJB","short_pith_number":"pith:ZIJ55P6S","schema_version":"1.0","canonical_sha256":"ca13debfd2658ad86b898b4e11e837487abe8452e4730325cc47a345aa38d69f","source":{"kind":"arxiv","id":"1509.08093","version":2},"attestation_state":"computed","paper":{"title":"Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.mes-hall","authors_text":"D. Ebert, K.G. Klimenko, P.B. Kolmakov, V.Ch. Zhukovsky","submitted_at":"2015-09-27T13:35:09Z","abstract_excerpt":"In this paper we consider a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene. Symmetry breaking in these models occurs due to a possible appearance of condensates. Special attention is paid to the symmetry properties of the appearing condensates in the framework of discrete chiral and $\\mathcal C$, $\\mathcal P$ and $\\mathcal T$ transformations. Moreover, boundary conditions corresponding to carbon nanotubes are considered and their relations with the effect of an"},"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":"1509.08093","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-09-27T13:35:09Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"a4be4ce092c5ca3259565efc89decb94393b422f6d98b1c5fca8c2f9bef0f3b6","abstract_canon_sha256":"8fc06b8189e90a689f4086c4447f920886bf0e19a986177abd306840bff51a66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:12.976776Z","signature_b64":"fSaoP62eAIX4bc7DFlTsEkDnm+Vo3X35e3nlesGPdSbAga1KABKMwsGhXbL/XHoAO0AuHGETCzRAqNz1+uW1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca13debfd2658ad86b898b4e11e837487abe8452e4730325cc47a345aa38d69f","last_reissued_at":"2026-05-18T01:08:12.976351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:12.976351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.mes-hall","authors_text":"D. Ebert, K.G. Klimenko, P.B. Kolmakov, V.Ch. Zhukovsky","submitted_at":"2015-09-27T13:35:09Z","abstract_excerpt":"In this paper we consider a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene. Symmetry breaking in these models occurs due to a possible appearance of condensates. Special attention is paid to the symmetry properties of the appearing condensates in the framework of discrete chiral and $\\mathcal C$, $\\mathcal P$ and $\\mathcal T$ transformations. Moreover, boundary conditions corresponding to carbon nanotubes are considered and their relations with the effect of an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08093","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.08093","created_at":"2026-05-18T01:08:12.976421+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08093v2","created_at":"2026-05-18T01:08:12.976421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08093","created_at":"2026-05-18T01:08:12.976421+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZIJ55P6SMWFN","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZIJ55P6SMWFNQ24J","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZIJ55P6S","created_at":"2026-05-18T12:29:52.810259+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/ZIJ55P6SMWFNQ24JRNHBD2BXJB","json":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB.json","graph_json":"https://pith.science/api/pith-number/ZIJ55P6SMWFNQ24JRNHBD2BXJB/graph.json","events_json":"https://pith.science/api/pith-number/ZIJ55P6SMWFNQ24JRNHBD2BXJB/events.json","paper":"https://pith.science/paper/ZIJ55P6S"},"agent_actions":{"view_html":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB","download_json":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB.json","view_paper":"https://pith.science/paper/ZIJ55P6S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08093&json=true","fetch_graph":"https://pith.science/api/pith-number/ZIJ55P6SMWFNQ24JRNHBD2BXJB/graph.json","fetch_events":"https://pith.science/api/pith-number/ZIJ55P6SMWFNQ24JRNHBD2BXJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB/action/storage_attestation","attest_author":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB/action/author_attestation","sign_citation":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB/action/citation_signature","submit_replication":"https://pith.science/pith/ZIJ55P6SMWFNQ24JRNHBD2BXJB/action/replication_record"}},"created_at":"2026-05-18T01:08:12.976421+00:00","updated_at":"2026-05-18T01:08:12.976421+00:00"}