{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:N7HFMGYLJHFZSZVRMDQM3WIP5G","short_pith_number":"pith:N7HFMGYL","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"},"canonical_sha256":"6fce561b0b49cb9966b160e0cdd90fe99540d94b0d614672723c999f230f0d05","source":{"kind":"arxiv","id":"1211.6100","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6100","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6100v2","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6100","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"N7HFMGYLJHFZ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N7HFMGYLJHFZSZVR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N7HFMGYL","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:N7HFMGYLJHFZSZVRMDQM3WIP5G","target":"record","payload":{"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"},"canonical_sha256":"6fce561b0b49cb9966b160e0cdd90fe99540d94b0d614672723c999f230f0d05","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"},"source_kind":"arxiv","source_id":"1211.6100","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zO4REC+CZjeFeEqjwNQEAEXLirsDigYlM1dN2T8Sz5mCuiiIGf3PkNna2OW3LPfbrFjBEVGovwnVhqyVGvzzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:12:35.075541Z"},"content_sha256":"765324e6c0bc55598c91a00c36942f086bd2b33bb68614ee82cc44d1087472f2","schema_version":"1.0","event_id":"sha256:765324e6c0bc55598c91a00c36942f086bd2b33bb68614ee82cc44d1087472f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:N7HFMGYLJHFZSZVRMDQM3WIP5G","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DAU28pCtiFhM9iSWwbhLN4GUgL/4pXpRydLoM0Kv57maWNZQcJaY1/KNLCuGlrJfDWCI+WQ0WsuwWeug/MYfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:12:35.076180Z"},"content_sha256":"169b72eb73371573f78d0dc5fe4d3f9f76dfa9b18fc57734d88aa1191d27f08c","schema_version":"1.0","event_id":"sha256:169b72eb73371573f78d0dc5fe4d3f9f76dfa9b18fc57734d88aa1191d27f08c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/bundle.json","state_url":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T08:12:35Z","links":{"resolver":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G","bundle":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/bundle.json","state":"https://pith.science/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7HFMGYLJHFZSZVRMDQM3WIP5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N7HFMGYLJHFZSZVRMDQM3WIP5G","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf069f99ed312fb7a02357b5b58a591abaa56c50692eb62673ef3fd5f957fe86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-24T22:37:06Z","title_canon_sha256":"5bc0289825319059c95ff562bf74727babddd5a528f4c0487936ac82f20daa83"},"schema_version":"1.0","source":{"id":"1211.6100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6100","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6100v2","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6100","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"N7HFMGYLJHFZ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N7HFMGYLJHFZSZVR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N7HFMGYL","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:169b72eb73371573f78d0dc5fe4d3f9f76dfa9b18fc57734d88aa1191d27f08c","target":"graph","created_at":"2026-05-18T03:39:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Szabolcs Baj\\'ak, Zsolt P\\'ales","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-24T22:37:06Z","title":"Computer aided solution of the invariance equation for two-variable Stolarsky means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6100","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:765324e6c0bc55598c91a00c36942f086bd2b33bb68614ee82cc44d1087472f2","target":"record","created_at":"2026-05-18T03:39:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf069f99ed312fb7a02357b5b58a591abaa56c50692eb62673ef3fd5f957fe86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-24T22:37:06Z","title_canon_sha256":"5bc0289825319059c95ff562bf74727babddd5a528f4c0487936ac82f20daa83"},"schema_version":"1.0","source":{"id":"1211.6100","kind":"arxiv","version":2}},"canonical_sha256":"6fce561b0b49cb9966b160e0cdd90fe99540d94b0d614672723c999f230f0d05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fce561b0b49cb9966b160e0cdd90fe99540d94b0d614672723c999f230f0d05","first_computed_at":"2026-05-18T03:39:06.068482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:06.068482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/kgmE8nVL5CWanSrWq69U/k3Z6TXtmkR/ZYdJI2a2204Avk5bUIBYdtgsr00QDAywlrZcYJVD36yASliDlGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:06.069075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:765324e6c0bc55598c91a00c36942f086bd2b33bb68614ee82cc44d1087472f2","sha256:169b72eb73371573f78d0dc5fe4d3f9f76dfa9b18fc57734d88aa1191d27f08c"],"state_sha256":"4491d91d6db94af1a41ce282b4dc6de5dbfc61e96660baef27e3d6c489224380"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qxr4kzwN6djg9Z5rzBNzhAKW4Szv5oQol4HdXwhRMq2xiSynxdIPlVeQMdETnd3H8Kfl76rJ5BiS7GfnDPgxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:12:35.079592Z","bundle_sha256":"9f39a3ec7c34178067185ed6302a664dcddebbad994df9fd420f22667580b2a1"}}