GPT-5.5 Pro
The sparse-polynomial framework was developed with GPT-5.5 Pro and validated empirically by the authors.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Minimum Sparsity of S-Decoding Polynomials
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Can an $S$-decoding polynomial modulo a suitable product of $k$ primes attain the lower-bound minimum of $k + 1$ nonzero coefficients? A construction matches the bound for special products of $k$ primes, yielding exponentially fewer-server PIR.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
Author-checked ePrint with empirical validation of the construction. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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ePrint 2026/1515 - Exponentially fewer-server PIR from sparser S-decoding polynomials
conditional on a plausible number-theoretic conjecture; unconditional through s = 15
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.