{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BYQREYC4ZOS4TMNHWZ6MVK5RVH","short_pith_number":"pith:BYQREYC4","canonical_record":{"source":{"id":"1105.0292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-05-02T10:33:22Z","cross_cats_sorted":[],"title_canon_sha256":"03117064de814ef9f589eeae23b5c447fbfc83ac0d80d0131e14776453eddadf","abstract_canon_sha256":"ade4f0683e6138c4e243806467b0e452b2bd73b7f96653bd7335fe5ce29e421a"},"schema_version":"1.0"},"canonical_sha256":"0e2112605ccba5c9b1a7b67ccaabb1a9f45fd96e4ada05f921f09ef3f2c710e6","source":{"kind":"arxiv","id":"1105.0292","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0292","created_at":"2026-05-18T04:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0292v1","created_at":"2026-05-18T04:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0292","created_at":"2026-05-18T04:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"BYQREYC4ZOS4","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BYQREYC4ZOS4TMNH","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BYQREYC4","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BYQREYC4ZOS4TMNHWZ6MVK5RVH","target":"record","payload":{"canonical_record":{"source":{"id":"1105.0292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-05-02T10:33:22Z","cross_cats_sorted":[],"title_canon_sha256":"03117064de814ef9f589eeae23b5c447fbfc83ac0d80d0131e14776453eddadf","abstract_canon_sha256":"ade4f0683e6138c4e243806467b0e452b2bd73b7f96653bd7335fe5ce29e421a"},"schema_version":"1.0"},"canonical_sha256":"0e2112605ccba5c9b1a7b67ccaabb1a9f45fd96e4ada05f921f09ef3f2c710e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:12.098002Z","signature_b64":"louLh4bvjz6ycv1803tnXqdF9h6K9wjs4iEIn3Se1vHR1dld3MHaIooDDVG3g6R+Kt4pPM0YzRxwl3RCBP4sDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e2112605ccba5c9b1a7b67ccaabb1a9f45fd96e4ada05f921f09ef3f2c710e6","last_reissued_at":"2026-05-18T04:23:12.097382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:12.097382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.0292","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":"2026-05-18T04:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8s5CDj2TV70BSUFTte3zD1aifrxt/QDM7k0UO3TD9ArIEwi54XKEeTy/RG8CTiWQgfofgZQXrArbP4cYUDsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:49:50.997646Z"},"content_sha256":"f35a27a97fee6fe1c0c4004f2e57c6c8fc34241c82b29259ae7de607be466397","schema_version":"1.0","event_id":"sha256:f35a27a97fee6fe1c0c4004f2e57c6c8fc34241c82b29259ae7de607be466397"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BYQREYC4ZOS4TMNHWZ6MVK5RVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inequalities for multiplicative arithmetic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jozsef Sandor","submitted_at":"2011-05-02T10:33:22Z","abstract_excerpt":"We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0292","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":"2026-05-18T04:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUlTtNzcrr0skn5Iws1kYRbABmRFJXGzo+VG5Y0ASkARTDIxosH3Lvc0DVD5FqCXVxUA8miDtTa6so/yDkuzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:49:50.997992Z"},"content_sha256":"dc33d4234500d1e04894b5bca51733f07124354bb1931c4f9c38b04df1b89cc4","schema_version":"1.0","event_id":"sha256:dc33d4234500d1e04894b5bca51733f07124354bb1931c4f9c38b04df1b89cc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BYQREYC4ZOS4TMNHWZ6MVK5RVH/bundle.json","state_url":"https://pith.science/pith/BYQREYC4ZOS4TMNHWZ6MVK5RVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BYQREYC4ZOS4TMNHWZ6MVK5RVH/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":"2026-06-22T13:49:50Z","links":{"resolver":"https://pith.science/pith/BYQREYC4ZOS4TMNHWZ6MVK5RVH","bundle":"https://pith.science/pith/BYQREYC4ZOS4TMNHWZ6MVK5RVH/bundle.json","state":"https://pith.science/pith/BYQREYC4ZOS4TMNHWZ6MVK5RVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BYQREYC4ZOS4TMNHWZ6MVK5RVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BYQREYC4ZOS4TMNHWZ6MVK5RVH","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":"ade4f0683e6138c4e243806467b0e452b2bd73b7f96653bd7335fe5ce29e421a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-05-02T10:33:22Z","title_canon_sha256":"03117064de814ef9f589eeae23b5c447fbfc83ac0d80d0131e14776453eddadf"},"schema_version":"1.0","source":{"id":"1105.0292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0292","created_at":"2026-05-18T04:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0292v1","created_at":"2026-05-18T04:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0292","created_at":"2026-05-18T04:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"BYQREYC4ZOS4","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BYQREYC4ZOS4TMNH","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BYQREYC4","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:dc33d4234500d1e04894b5bca51733f07124354bb1931c4f9c38b04df1b89cc4","target":"graph","created_at":"2026-05-18T04:23:12Z","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 study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.","authors_text":"Jozsef Sandor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-05-02T10:33:22Z","title":"Inequalities for multiplicative arithmetic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0292","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:f35a27a97fee6fe1c0c4004f2e57c6c8fc34241c82b29259ae7de607be466397","target":"record","created_at":"2026-05-18T04:23:12Z","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":"ade4f0683e6138c4e243806467b0e452b2bd73b7f96653bd7335fe5ce29e421a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-05-02T10:33:22Z","title_canon_sha256":"03117064de814ef9f589eeae23b5c447fbfc83ac0d80d0131e14776453eddadf"},"schema_version":"1.0","source":{"id":"1105.0292","kind":"arxiv","version":1}},"canonical_sha256":"0e2112605ccba5c9b1a7b67ccaabb1a9f45fd96e4ada05f921f09ef3f2c710e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e2112605ccba5c9b1a7b67ccaabb1a9f45fd96e4ada05f921f09ef3f2c710e6","first_computed_at":"2026-05-18T04:23:12.097382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:12.097382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"louLh4bvjz6ycv1803tnXqdF9h6K9wjs4iEIn3Se1vHR1dld3MHaIooDDVG3g6R+Kt4pPM0YzRxwl3RCBP4sDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:12.098002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f35a27a97fee6fe1c0c4004f2e57c6c8fc34241c82b29259ae7de607be466397","sha256:dc33d4234500d1e04894b5bca51733f07124354bb1931c4f9c38b04df1b89cc4"],"state_sha256":"77cb824995295300df6f738ef6892b379dafe1d72ce952b7897f72ce5357bd4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AL4WdLjLx0idx+7WtcADvi36inipv1LQ7TLU8zcmFCYN8aR/5owxlguAVNmZ7+VjYBIoX2LSlpGsXu/92Nk3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:49:51.000072Z","bundle_sha256":"abaaab49b79af9ac027cc2c0cbc01e7cc43f3ae26636fb05c3dd4bc44985b64d"}}