{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:F227ZSJCAI6U46LDRYX3ICFT7F","short_pith_number":"pith:F227ZSJC","canonical_record":{"source":{"id":"1607.03862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-11T11:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"d3dd3f0c13595783b99e0e6aa27977020aac6aadfb46e7b2c7793fc5f343f2a8","abstract_canon_sha256":"825730713e8f2c313592d9a4a3cf100af02af28e446c0aaf24ce209e2ecbbfa5"},"schema_version":"1.0"},"canonical_sha256":"2eb5fcc922023d4e79638e2fb408b3f9548680a5786fc350ed07881c5335a35b","source":{"kind":"arxiv","id":"1607.03862","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03862","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03862v1","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03862","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"pith_short_12","alias_value":"F227ZSJCAI6U","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F227ZSJCAI6U46LD","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F227ZSJC","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:F227ZSJCAI6U46LDRYX3ICFT7F","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-11T11:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"d3dd3f0c13595783b99e0e6aa27977020aac6aadfb46e7b2c7793fc5f343f2a8","abstract_canon_sha256":"825730713e8f2c313592d9a4a3cf100af02af28e446c0aaf24ce209e2ecbbfa5"},"schema_version":"1.0"},"canonical_sha256":"2eb5fcc922023d4e79638e2fb408b3f9548680a5786fc350ed07881c5335a35b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:05.538390Z","signature_b64":"aS1zgHxgRpRTkngKIXzOf9lRhYQ5McpTAYvmszFiu6/dcSoLCBmaqOr0EabeRhS9hEl7V6dXz82YKOuHpd+XCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eb5fcc922023d4e79638e2fb408b3f9548680a5786fc350ed07881c5335a35b","last_reissued_at":"2026-05-18T01:11:05.537856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:05.537856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03862","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bmj/LuldWfyTy5bH3zAi2cbQ4VU/ueH25Oxm4hrdQlcRf8IAARTFP7yTPToZ+ISzR33Kybuk2ir8NixvokYxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:13:22.442425Z"},"content_sha256":"d8412e41d36aecda408aa2b6ed80e915fed2ca5168487751362b289e2a9e8075","schema_version":"1.0","event_id":"sha256:d8412e41d36aecda408aa2b6ed80e915fed2ca5168487751362b289e2a9e8075"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:F227ZSJCAI6U46LDRYX3ICFT7F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of aggregation functions with given super-additive and sub-additive transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexandra \\v{S}ipo\\v{s}ov\\'a, Jozef \\v{S}ir\\'a\\v{n}, Ladislav \\v{S}ipeky","submitted_at":"2016-07-11T11:34:44Z","abstract_excerpt":"In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, $A\\mapsto A^*$ and $A\\mapsto A_*$, of an aggregation function $A$. We prove that if $A^*$ has a slightly stronger property of being strictly directionally convex, then $A=A^*$ and $A_*$ is linear; dually, if $A_*$ is strictly directionally concave, then $A=A_*$ and $A^*$ is linear. This implies, for example, the existence of pairs of functions $f\\le g$ sub-additive and super-additive on $[0,\\infty[^n$, respectively, with zero value at the origin and satisfying relatively mild extra co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03862","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmtqzYQPbnmhVcJ1RWFJVGNWq6xIzdLBOSvJ+qEQ/DlCaNRhRIm0N++Y36XNFesoLJplDAVZjbMqMrnhSDaxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:13:22.442774Z"},"content_sha256":"1d670982a7c1259c8ba232d4077d1a3bc27496c2c0b6ca3a2ac21427ee78e8a2","schema_version":"1.0","event_id":"sha256:1d670982a7c1259c8ba232d4077d1a3bc27496c2c0b6ca3a2ac21427ee78e8a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F227ZSJCAI6U46LDRYX3ICFT7F/bundle.json","state_url":"https://pith.science/pith/F227ZSJCAI6U46LDRYX3ICFT7F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F227ZSJCAI6U46LDRYX3ICFT7F/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":"2026-05-30T08:13:22Z","links":{"resolver":"https://pith.science/pith/F227ZSJCAI6U46LDRYX3ICFT7F","bundle":"https://pith.science/pith/F227ZSJCAI6U46LDRYX3ICFT7F/bundle.json","state":"https://pith.science/pith/F227ZSJCAI6U46LDRYX3ICFT7F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F227ZSJCAI6U46LDRYX3ICFT7F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F227ZSJCAI6U46LDRYX3ICFT7F","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":"825730713e8f2c313592d9a4a3cf100af02af28e446c0aaf24ce209e2ecbbfa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-11T11:34:44Z","title_canon_sha256":"d3dd3f0c13595783b99e0e6aa27977020aac6aadfb46e7b2c7793fc5f343f2a8"},"schema_version":"1.0","source":{"id":"1607.03862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03862","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03862v1","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03862","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"pith_short_12","alias_value":"F227ZSJCAI6U","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F227ZSJCAI6U46LD","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F227ZSJC","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:1d670982a7c1259c8ba232d4077d1a3bc27496c2c0b6ca3a2ac21427ee78e8a2","target":"graph","created_at":"2026-05-18T01:11:05Z","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":"In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, $A\\mapsto A^*$ and $A\\mapsto A_*$, of an aggregation function $A$. We prove that if $A^*$ has a slightly stronger property of being strictly directionally convex, then $A=A^*$ and $A_*$ is linear; dually, if $A_*$ is strictly directionally concave, then $A=A_*$ and $A^*$ is linear. This implies, for example, the existence of pairs of functions $f\\le g$ sub-additive and super-additive on $[0,\\infty[^n$, respectively, with zero value at the origin and satisfying relatively mild extra co","authors_text":"Alexandra \\v{S}ipo\\v{s}ov\\'a, Jozef \\v{S}ir\\'a\\v{n}, Ladislav \\v{S}ipeky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-11T11:34:44Z","title":"On the existence of aggregation functions with given super-additive and sub-additive transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03862","kind":"arxiv","version":1},"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:d8412e41d36aecda408aa2b6ed80e915fed2ca5168487751362b289e2a9e8075","target":"record","created_at":"2026-05-18T01:11:05Z","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":"825730713e8f2c313592d9a4a3cf100af02af28e446c0aaf24ce209e2ecbbfa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-11T11:34:44Z","title_canon_sha256":"d3dd3f0c13595783b99e0e6aa27977020aac6aadfb46e7b2c7793fc5f343f2a8"},"schema_version":"1.0","source":{"id":"1607.03862","kind":"arxiv","version":1}},"canonical_sha256":"2eb5fcc922023d4e79638e2fb408b3f9548680a5786fc350ed07881c5335a35b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2eb5fcc922023d4e79638e2fb408b3f9548680a5786fc350ed07881c5335a35b","first_computed_at":"2026-05-18T01:11:05.537856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:05.537856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aS1zgHxgRpRTkngKIXzOf9lRhYQ5McpTAYvmszFiu6/dcSoLCBmaqOr0EabeRhS9hEl7V6dXz82YKOuHpd+XCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:05.538390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8412e41d36aecda408aa2b6ed80e915fed2ca5168487751362b289e2a9e8075","sha256:1d670982a7c1259c8ba232d4077d1a3bc27496c2c0b6ca3a2ac21427ee78e8a2"],"state_sha256":"4e24b351a4a78e4893e25474b4ec00b08505eb41f95d706426753dde1134a7b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OGzYKulgCSggttoVo6jv3LYXJdcKx6DoekMysXZwigsl1hhSn2YMCugiR4AB+eV3f4Exih/1KHWc3FPNcM+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:13:22.444709Z","bundle_sha256":"49be13b7eb065034c5ff70a396227dd08b22ba81aaa168699b81fa07a8e1d58a"}}