{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZU2G3YCGNQ3XOR4KYS2VK4YHTE","short_pith_number":"pith:ZU2G3YCG","canonical_record":{"source":{"id":"1506.02536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-08T15:10:57Z","cross_cats_sorted":[],"title_canon_sha256":"a24af3aef6dd197e1d47c72b2acb5d0cee235639f549d14ee00588d80ddecdc1","abstract_canon_sha256":"d29aa4b1f03a7341c353fb2f5c7509beaa522c9d8882a0d2d0ad56bd7d898ed0"},"schema_version":"1.0"},"canonical_sha256":"cd346de0466c3777478ac4b55573079920b1c9bb2bcb2d33d2e5e7983d6bae47","source":{"kind":"arxiv","id":"1506.02536","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02536","created_at":"2026-05-18T01:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02536v1","created_at":"2026-05-18T01:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02536","created_at":"2026-05-18T01:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZU2G3YCGNQ3X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZU2G3YCGNQ3XOR4K","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZU2G3YCG","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZU2G3YCGNQ3XOR4KYS2VK4YHTE","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-08T15:10:57Z","cross_cats_sorted":[],"title_canon_sha256":"a24af3aef6dd197e1d47c72b2acb5d0cee235639f549d14ee00588d80ddecdc1","abstract_canon_sha256":"d29aa4b1f03a7341c353fb2f5c7509beaa522c9d8882a0d2d0ad56bd7d898ed0"},"schema_version":"1.0"},"canonical_sha256":"cd346de0466c3777478ac4b55573079920b1c9bb2bcb2d33d2e5e7983d6bae47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:50.810250Z","signature_b64":"BvA5adAdxz+oXdQufkGZk/bfq77ke+cdliajqb8NbboM7BPkriuMc1cms8yxqgPzr6FVrc3SIcBSCuIog0PkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd346de0466c3777478ac4b55573079920b1c9bb2bcb2d33d2e5e7983d6bae47","last_reissued_at":"2026-05-18T01:55:50.809569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:50.809569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02536","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":"2026-05-18T01:55:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBYJj8/sDWvHzj7QfisBw1VB/rqclxPJiGtE6tU2CFH+G1gLxFLc1+tBwb80QSVXUiTQkD3eszA+3dGky1bOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:28:33.607789Z"},"content_sha256":"5f07ee99591c414ac60d02e0d63c2adf38337400477fd682ee56d378eb784997","schema_version":"1.0","event_id":"sha256:5f07ee99591c414ac60d02e0d63c2adf38337400477fd682ee56d378eb784997"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZU2G3YCGNQ3XOR4KYS2VK4YHTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On approximate ternary m-derivations and $\\sigma$-homomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. G. Ghazanfari, Z. Alizadeh","submitted_at":"2015-06-08T15:10:57Z","abstract_excerpt":"In this paper we introduce ternary modules over ternary algebras and using fixed point methods, we prove the stability and super-stability of ternary additive, quadratic, cubic and quartic derivations and $\\sigma$-homomorphisms in such structures for the functional equation \\begin{equation*} \\begin{split} &\\quad f(ax+y)+f(ax-y)= a^{m-2}[f(x+y)+f(x-y)]\\\\&+2(a^2-1)[a^{m-2}f(x)+\\frac{(m-2)(1-(m-2)^2)}{6}f(y)]. \\end{split} \\end{equation*} for each $m=1,2,3,4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02536","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":"2026-05-18T01:55:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NF2EUjS4kgkGQUy/Oc8t6uenpsFNlECWyC0hymCUGO5NC38YQSZyxyhw7DOpMyYN6exrsVbHJ4QdRS40mXnzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:28:33.608472Z"},"content_sha256":"67d62f7cb3128eee40a7de8a9c056e7dadb7971124a15fa2a41be0dd8341c2dc","schema_version":"1.0","event_id":"sha256:67d62f7cb3128eee40a7de8a9c056e7dadb7971124a15fa2a41be0dd8341c2dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZU2G3YCGNQ3XOR4KYS2VK4YHTE/bundle.json","state_url":"https://pith.science/pith/ZU2G3YCGNQ3XOR4KYS2VK4YHTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZU2G3YCGNQ3XOR4KYS2VK4YHTE/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":"2026-06-08T19:28:33Z","links":{"resolver":"https://pith.science/pith/ZU2G3YCGNQ3XOR4KYS2VK4YHTE","bundle":"https://pith.science/pith/ZU2G3YCGNQ3XOR4KYS2VK4YHTE/bundle.json","state":"https://pith.science/pith/ZU2G3YCGNQ3XOR4KYS2VK4YHTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZU2G3YCGNQ3XOR4KYS2VK4YHTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZU2G3YCGNQ3XOR4KYS2VK4YHTE","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":"d29aa4b1f03a7341c353fb2f5c7509beaa522c9d8882a0d2d0ad56bd7d898ed0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-08T15:10:57Z","title_canon_sha256":"a24af3aef6dd197e1d47c72b2acb5d0cee235639f549d14ee00588d80ddecdc1"},"schema_version":"1.0","source":{"id":"1506.02536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02536","created_at":"2026-05-18T01:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02536v1","created_at":"2026-05-18T01:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02536","created_at":"2026-05-18T01:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZU2G3YCGNQ3X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZU2G3YCGNQ3XOR4K","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZU2G3YCG","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:67d62f7cb3128eee40a7de8a9c056e7dadb7971124a15fa2a41be0dd8341c2dc","target":"graph","created_at":"2026-05-18T01:55:50Z","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 paper we introduce ternary modules over ternary algebras and using fixed point methods, we prove the stability and super-stability of ternary additive, quadratic, cubic and quartic derivations and $\\sigma$-homomorphisms in such structures for the functional equation \\begin{equation*} \\begin{split} &\\quad f(ax+y)+f(ax-y)= a^{m-2}[f(x+y)+f(x-y)]\\\\&+2(a^2-1)[a^{m-2}f(x)+\\frac{(m-2)(1-(m-2)^2)}{6}f(y)]. \\end{split} \\end{equation*} for each $m=1,2,3,4$.","authors_text":"A. G. Ghazanfari, Z. Alizadeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-08T15:10:57Z","title":"On approximate ternary m-derivations and $\\sigma$-homomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02536","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":"sha256:5f07ee99591c414ac60d02e0d63c2adf38337400477fd682ee56d378eb784997","target":"record","created_at":"2026-05-18T01:55:50Z","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":"d29aa4b1f03a7341c353fb2f5c7509beaa522c9d8882a0d2d0ad56bd7d898ed0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-08T15:10:57Z","title_canon_sha256":"a24af3aef6dd197e1d47c72b2acb5d0cee235639f549d14ee00588d80ddecdc1"},"schema_version":"1.0","source":{"id":"1506.02536","kind":"arxiv","version":1}},"canonical_sha256":"cd346de0466c3777478ac4b55573079920b1c9bb2bcb2d33d2e5e7983d6bae47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd346de0466c3777478ac4b55573079920b1c9bb2bcb2d33d2e5e7983d6bae47","first_computed_at":"2026-05-18T01:55:50.809569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:50.809569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BvA5adAdxz+oXdQufkGZk/bfq77ke+cdliajqb8NbboM7BPkriuMc1cms8yxqgPzr6FVrc3SIcBSCuIog0PkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:50.810250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f07ee99591c414ac60d02e0d63c2adf38337400477fd682ee56d378eb784997","sha256:67d62f7cb3128eee40a7de8a9c056e7dadb7971124a15fa2a41be0dd8341c2dc"],"state_sha256":"882f68109eebb3fcf424477cf3ed48382e7a1a9ac711dd6961aeaead858e1f2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmTsJ3uYmS/U68yXfFY8tmmFescZjjPrxz27yriRnC1DNfNnlLoB9bjP8igiKdfk6VkyXmWB9y1ejLnWmi6nCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:28:33.612246Z","bundle_sha256":"921fafb76553fce0576c8f83aa26aa4204d76f176cd843b31131b9af661d5f2f"}}