{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:K6MMHOVLWH3BEXPJTGBCCAGUEN","short_pith_number":"pith:K6MMHOVL","schema_version":"1.0","canonical_sha256":"5798c3baabb1f6125de999822100d42367478ac6e73ac48155bf9e52e8148123","source":{"kind":"arxiv","id":"0711.4117","version":1},"attestation_state":"computed","paper":{"title":"A Simplified Calculation for the Fundamental Solution to the Heat Equation on the Heisenberg Group","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Boggess, Andrew Raich","submitted_at":"2007-11-26T21:03:40Z","abstract_excerpt":"Let $L = -1/4 (\\sum_{j=1}^n(X_j^2+Y_j^2)+i\\gamma T)$ where $\\gamma$ is a complex number, $X_j$, $Y_j$, and $T$ are the left invariant vector fields of the Heisenberg group structure for $R^n \\times R^n \\times R$. We explicitly compute the Fourier transform (in the spatial variables) of the fundamental solution of the Heat Equation $\\partial_s\\rho = -L\\rho$. As a consequence, we have a simplified computation of the Fourier transform of the fundamental solution of the $\\Box_b$-heat equation on the Heisenberg group and an explicit kernel of the heat equation associated to the weighted dbar-operat"},"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":"0711.4117","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-11-26T21:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"71b66b69015abdb0d83e34322fea9303f949663bd17af13edc70ba9d132933c6","abstract_canon_sha256":"c5a38bd58c146556185f46fdfdbd12aa803b408486c50c38882618f108a90d55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:09.500702Z","signature_b64":"JhMvGsqDD43Uus7BQEYj6KPlQUVowyEuwUbHSgt7dC0tUsnLYR2bLp7oiWch2YNIgHZIppTx7qPuM6181tvEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5798c3baabb1f6125de999822100d42367478ac6e73ac48155bf9e52e8148123","last_reissued_at":"2026-05-18T03:49:09.500254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:09.500254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Simplified Calculation for the Fundamental Solution to the Heat Equation on the Heisenberg Group","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Boggess, Andrew Raich","submitted_at":"2007-11-26T21:03:40Z","abstract_excerpt":"Let $L = -1/4 (\\sum_{j=1}^n(X_j^2+Y_j^2)+i\\gamma T)$ where $\\gamma$ is a complex number, $X_j$, $Y_j$, and $T$ are the left invariant vector fields of the Heisenberg group structure for $R^n \\times R^n \\times R$. We explicitly compute the Fourier transform (in the spatial variables) of the fundamental solution of the Heat Equation $\\partial_s\\rho = -L\\rho$. As a consequence, we have a simplified computation of the Fourier transform of the fundamental solution of the $\\Box_b$-heat equation on the Heisenberg group and an explicit kernel of the heat equation associated to the weighted dbar-operat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.4117","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":"0711.4117","created_at":"2026-05-18T03:49:09.500326+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.4117v1","created_at":"2026-05-18T03:49:09.500326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.4117","created_at":"2026-05-18T03:49:09.500326+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6MMHOVLWH3B","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6MMHOVLWH3BEXPJ","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6MMHOVL","created_at":"2026-05-18T12:25:55.427421+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/K6MMHOVLWH3BEXPJTGBCCAGUEN","json":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN.json","graph_json":"https://pith.science/api/pith-number/K6MMHOVLWH3BEXPJTGBCCAGUEN/graph.json","events_json":"https://pith.science/api/pith-number/K6MMHOVLWH3BEXPJTGBCCAGUEN/events.json","paper":"https://pith.science/paper/K6MMHOVL"},"agent_actions":{"view_html":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN","download_json":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN.json","view_paper":"https://pith.science/paper/K6MMHOVL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.4117&json=true","fetch_graph":"https://pith.science/api/pith-number/K6MMHOVLWH3BEXPJTGBCCAGUEN/graph.json","fetch_events":"https://pith.science/api/pith-number/K6MMHOVLWH3BEXPJTGBCCAGUEN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN/action/storage_attestation","attest_author":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN/action/author_attestation","sign_citation":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN/action/citation_signature","submit_replication":"https://pith.science/pith/K6MMHOVLWH3BEXPJTGBCCAGUEN/action/replication_record"}},"created_at":"2026-05-18T03:49:09.500326+00:00","updated_at":"2026-05-18T03:49:09.500326+00:00"}