{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AAMEJOXO2LIA5SMPSUUMQB6MUP","short_pith_number":"pith:AAMEJOXO","schema_version":"1.0","canonical_sha256":"001844baeed2d00ec98f9528c807cca3e2b1c04e03d34c6604d6dbebe02d3580","source":{"kind":"arxiv","id":"1412.7905","version":1},"attestation_state":"computed","paper":{"title":"Anti Lie-Trotter formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"F. Hiai, K.M.R. Audenaert","submitted_at":"2014-12-26T07:22:15Z","abstract_excerpt":"Let $A$ and $B$ be positive semidefinite matrices. The limit of the expression $Z_p:=(A^{p/2}B^pA^{p/2})^{1/p}$ as $p$ tends to $0$ is given by the well known Lie-Trotter-Kato formula. A similar formula holds for the limit of $G_p:=(A^p\\,\\#\\,B^p)^{2/p}$ as $p$ tends to $0$, where $X\\,\\#\\,Y$ is the geometric mean of $X$ and $Y$. In this paper we study the complementary limit of $Z_p$ and $G_p$ as $p$ tends to $\\infty$, with the ultimate goal of finding an explicit formula, which we call the anti Lie-Trotter formula. We show that the limit of $Z_p$ exists and find an explicit formula in a specia"},"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":"1412.7905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-26T07:22:15Z","cross_cats_sorted":[],"title_canon_sha256":"3c1ce3ea6075b989192ff18ab4dd074463e2b0b14341b410b9740297e852ca72","abstract_canon_sha256":"39a41a5f642b9146785d2c63524fb3bdf79d86c8e2f88da224b314ae1a6b212d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:24.777531Z","signature_b64":"aSiOQ6IKjqWFGR3qUNNuhQS7dnUC2ahxAMuTnKzxlFKPyWmeHBEQcRRtVvF9xo2S+QgKHagVkj1vJhrwuH71DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"001844baeed2d00ec98f9528c807cca3e2b1c04e03d34c6604d6dbebe02d3580","last_reissued_at":"2026-05-18T02:30:24.776956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:24.776956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anti Lie-Trotter formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"F. Hiai, K.M.R. Audenaert","submitted_at":"2014-12-26T07:22:15Z","abstract_excerpt":"Let $A$ and $B$ be positive semidefinite matrices. The limit of the expression $Z_p:=(A^{p/2}B^pA^{p/2})^{1/p}$ as $p$ tends to $0$ is given by the well known Lie-Trotter-Kato formula. A similar formula holds for the limit of $G_p:=(A^p\\,\\#\\,B^p)^{2/p}$ as $p$ tends to $0$, where $X\\,\\#\\,Y$ is the geometric mean of $X$ and $Y$. In this paper we study the complementary limit of $Z_p$ and $G_p$ as $p$ tends to $\\infty$, with the ultimate goal of finding an explicit formula, which we call the anti Lie-Trotter formula. We show that the limit of $Z_p$ exists and find an explicit formula in a specia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7905","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":"1412.7905","created_at":"2026-05-18T02:30:24.777026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7905v1","created_at":"2026-05-18T02:30:24.777026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7905","created_at":"2026-05-18T02:30:24.777026+00:00"},{"alias_kind":"pith_short_12","alias_value":"AAMEJOXO2LIA","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AAMEJOXO2LIA5SMP","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AAMEJOXO","created_at":"2026-05-18T12:28:19.803747+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/AAMEJOXO2LIA5SMPSUUMQB6MUP","json":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP.json","graph_json":"https://pith.science/api/pith-number/AAMEJOXO2LIA5SMPSUUMQB6MUP/graph.json","events_json":"https://pith.science/api/pith-number/AAMEJOXO2LIA5SMPSUUMQB6MUP/events.json","paper":"https://pith.science/paper/AAMEJOXO"},"agent_actions":{"view_html":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP","download_json":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP.json","view_paper":"https://pith.science/paper/AAMEJOXO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7905&json=true","fetch_graph":"https://pith.science/api/pith-number/AAMEJOXO2LIA5SMPSUUMQB6MUP/graph.json","fetch_events":"https://pith.science/api/pith-number/AAMEJOXO2LIA5SMPSUUMQB6MUP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP/action/storage_attestation","attest_author":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP/action/author_attestation","sign_citation":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP/action/citation_signature","submit_replication":"https://pith.science/pith/AAMEJOXO2LIA5SMPSUUMQB6MUP/action/replication_record"}},"created_at":"2026-05-18T02:30:24.777026+00:00","updated_at":"2026-05-18T02:30:24.777026+00:00"}