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We recall that, for $pq(p-q)\\neq 0$ and $x\\neq y$, the Stolarsky mean $S_{p,q}$ is defined by [S_{p,q}(x,y):=(\\dfrac{q(x^p-y^p)}{p(x^q-y^q)})^{\\frac1{p-q}}.] In the proof first we approximate the Stolarsky mean and we use the computer algebra system Maple V Release 9 to compute the Taylor exp"},"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":"1211.6100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-24T22:37:06Z","cross_cats_sorted":[],"title_canon_sha256":"5bc0289825319059c95ff562bf74727babddd5a528f4c0487936ac82f20daa83","abstract_canon_sha256":"bf069f99ed312fb7a02357b5b58a591abaa56c50692eb62673ef3fd5f957fe86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:06.069075Z","signature_b64":"0/kgmE8nVL5CWanSrWq69U/k3Z6TXtmkR/ZYdJI2a2204Avk5bUIBYdtgsr00QDAywlrZcYJVD36yASliDlGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fce561b0b49cb9966b160e0cdd90fe99540d94b0d614672723c999f230f0d05","last_reissued_at":"2026-05-18T03:39:06.068482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:06.068482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computer aided solution of the invariance equation for two-variable Stolarsky means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Szabolcs Baj\\'ak, Zsolt P\\'ales","submitted_at":"2012-11-24T22:37:06Z","abstract_excerpt":"We solve the so-called invariance equation in the class of two-variable Stolarsky means ${S_{p,q}:p,q\\in\\R}$, i.e., we find necessary and sufficient conditions on the 6 parameters $a,b,c,d,p,q$ such that the identity [S_{p,q}\\big(S_{a,b}(x,y),S_{c,d}(x,y)\\big)=S_{p,q}(x,y) \\qquad (x,y \\in \\R_+)] be valid. We recall that, for $pq(p-q)\\neq 0$ and $x\\neq y$, the Stolarsky mean $S_{p,q}$ is defined by [S_{p,q}(x,y):=(\\dfrac{q(x^p-y^p)}{p(x^q-y^q)})^{\\frac1{p-q}}.] In the proof first we approximate the Stolarsky mean and we use the computer algebra system Maple V Release 9 to compute the Taylor exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6100","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":"1211.6100","created_at":"2026-05-18T03:39:06.068576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.6100v2","created_at":"2026-05-18T03:39:06.068576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6100","created_at":"2026-05-18T03:39:06.068576+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7HFMGYLJHFZ","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7HFMGYLJHFZSZVR","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7HFMGYL","created_at":"2026-05-18T12:27:16.716162+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/N7HFMGYLJHFZSZVRMDQM3WIP5G","json":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G.json","graph_json":"https://pith.science/api/pith-number/N7HFMGYLJHFZSZVRMDQM3WIP5G/graph.json","events_json":"https://pith.science/api/pith-number/N7HFMGYLJHFZSZVRMDQM3WIP5G/events.json","paper":"https://pith.science/paper/N7HFMGYL"},"agent_actions":{"view_html":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G","download_json":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G.json","view_paper":"https://pith.science/paper/N7HFMGYL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.6100&json=true","fetch_graph":"https://pith.science/api/pith-number/N7HFMGYLJHFZSZVRMDQM3WIP5G/graph.json","fetch_events":"https://pith.science/api/pith-number/N7HFMGYLJHFZSZVRMDQM3WIP5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/action/storage_attestation","attest_author":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/action/author_attestation","sign_citation":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/action/citation_signature","submit_replication":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/action/replication_record"}},"created_at":"2026-05-18T03:39:06.068576+00:00","updated_at":"2026-05-18T03:39:06.068576+00:00"}