Proof Systems & Succinct Arguments

Status	Statement	Tags
	dv-SNARG, One Group Element Numbered Conjecture 1.3 of the source. Its own theorems achieve one group element plus O(tau) bits, and (with a random oracle) one group element, one hash output and about 2 tau bits; the conjecture halves the additive term to tau + o(tau) and asks for no random oracle. 4 open	Generic Group Model Proof Size Lower Bounds Snarksggmcharacterization
	SZK Batch Verification Named by the source as the most pressing open question its work leaves. Its Theorem 1.1 gives the NISZK analogue: communication and CRS length poly(n, log k) for k up to 2⁽ⁿ0.01). A poly(n) dependence is unavoidable even at k = 1 under a sub-exponential hardness assumption, so log k is the aggressive part of the bound. The source also offers a weaker fallback target: any sub-linear dependence on k. 5 open	Batch Verification Direct Product Theorems Limited Independence Randomness Extractioncharacterization
	CSAT with Small Space and Preprocessing Conjecture 1.2 of the source, a parameterized family rather than a single claim. Corollary 1.3 turns each parameter setting into a limitation on succinct IOPs. The source attaches decreasing confidence as the class T grows, calling the largest setting only (arguably) unlikely to be false rather than confidently believed. 4 open	Interactive Oracle Proofs Proof Size Lower Bounds Space Bounded Computation Time Space Tradeoffslower-boundbarrier (ai)
	DPP Field Size The small-field regime is settled: soundness Theta(1/sqrt q) is achieved and proved optimal. In the large-field regime the source achieves soundness eps for every prime p at least Omega~(S^9/eps6) and states in as many words that it believes the S-dependence is not tight. 4 open	Linear Pcps Snarkstight-boundadaptation (ai)
	No 2-element split NILPs A submitted construction gives a two-element split NILP for Boolean circuit satisfiability in the plain generic Type-III bilinear-group model; proof review and formalization remain open. 2 open	Generic Group Model Proof Size Lower Bounds Snarksimpossibilityresearch-solved
	RS Proximity Gaps to Capacity Proved up to the Johnson/Guruswami-Sudan bound delta < 1 - sqrt(rho); conjectured up to capacity delta <= 1 - rho - eta. The source records that nothing known contradicts c1 = c2 = 2, and that in characteristic greater than the degree nothing known contradicts c1 = c2 = 1 – while those smaller exponents are provably ruled out in characteristic two. 5 open	Proximity Testing Reed Solomon Codes Snarkstight-boundbarrier (ai)
	RBR Soundness Amplification Known in the special case of r-round protocols whose standard and round-by-round soundness errors are maximally separated, eps_RBR about eps^{1/r}; open in general, including the eps^{2/r} regime the source’s own protocol occupies. 4 open	Fiat Shamir Parallel Repetitionlower-bound
	SSS Implies Fiat-Shamir Friendly Conjecture 1.3 of the source. It is explicit that it does not prove it – ‘only conjecture it’ – and asks for the proof or refutation as an important open problem. It does prove that SSS implies straight-line soundness, hence post-quantum soundness, and that its own instantiation of Kilian’s protocol is SSS. 4 open	Commitment Schemes Fiat Shamir Snarkscharacterization