{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JMMSZ5SARR7RDBCIB5ZQGJW3TD","short_pith_number":"pith:JMMSZ5SA","schema_version":"1.0","canonical_sha256":"4b192cf6408c7f1184480f730326db98ee2817990ffd83567c4c76675994da4f","source":{"kind":"arxiv","id":"1309.7579","version":1},"attestation_state":"computed","paper":{"title":"A Structure result for bricks in Heisenberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fran\\c{c}ois Hennecart, Norbert Hegyv\\'ari","submitted_at":"2013-09-29T12:00:49Z","abstract_excerpt":"We show that for a sufficiently big \\textit{brick} $B$ of the $(2n+1)$-dimensional Heisenberg group $H_n$ over the finite field $\\mathbb{F}_p$, the product set $B\\cdot B$ contains at least $|B|/p$ many cosets of some non trivial subgroup of $H_n$."},"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":"1309.7579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-29T12:00:49Z","cross_cats_sorted":[],"title_canon_sha256":"4dd935e293abc34cdeb6882f4daa0b2589e341d2bf8a222ecc0024659f3692d9","abstract_canon_sha256":"18931dba2e574cb51644e5e0ca7a4f371a8e15d3a4cb668cc40c082b87c92255"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:56.509262Z","signature_b64":"PMxj+IxYLRtCax1Uf/OACUaU7qKazlL/F9m48jX+WsgG9lU8qm38NyCLbevhuxHCa6D5Cmf8SWYElCGMDuDbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b192cf6408c7f1184480f730326db98ee2817990ffd83567c4c76675994da4f","last_reissued_at":"2026-05-18T03:11:56.508624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:56.508624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Structure result for bricks in Heisenberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fran\\c{c}ois Hennecart, Norbert Hegyv\\'ari","submitted_at":"2013-09-29T12:00:49Z","abstract_excerpt":"We show that for a sufficiently big \\textit{brick} $B$ of the $(2n+1)$-dimensional Heisenberg group $H_n$ over the finite field $\\mathbb{F}_p$, the product set $B\\cdot B$ contains at least $|B|/p$ many cosets of some non trivial subgroup of $H_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7579","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":"1309.7579","created_at":"2026-05-18T03:11:56.508721+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7579v1","created_at":"2026-05-18T03:11:56.508721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7579","created_at":"2026-05-18T03:11:56.508721+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMMSZ5SARR7R","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMMSZ5SARR7RDBCI","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMMSZ5SA","created_at":"2026-05-18T12:27:49.015174+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/JMMSZ5SARR7RDBCIB5ZQGJW3TD","json":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD.json","graph_json":"https://pith.science/api/pith-number/JMMSZ5SARR7RDBCIB5ZQGJW3TD/graph.json","events_json":"https://pith.science/api/pith-number/JMMSZ5SARR7RDBCIB5ZQGJW3TD/events.json","paper":"https://pith.science/paper/JMMSZ5SA"},"agent_actions":{"view_html":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD","download_json":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD.json","view_paper":"https://pith.science/paper/JMMSZ5SA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7579&json=true","fetch_graph":"https://pith.science/api/pith-number/JMMSZ5SARR7RDBCIB5ZQGJW3TD/graph.json","fetch_events":"https://pith.science/api/pith-number/JMMSZ5SARR7RDBCIB5ZQGJW3TD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD/action/storage_attestation","attest_author":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD/action/author_attestation","sign_citation":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD/action/citation_signature","submit_replication":"https://pith.science/pith/JMMSZ5SARR7RDBCIB5ZQGJW3TD/action/replication_record"}},"created_at":"2026-05-18T03:11:56.508721+00:00","updated_at":"2026-05-18T03:11:56.508721+00:00"}