What was already known
Euclid needs about 1.44 log₂(a) remainder calls on worst-case Fibonacci inputs. Moschovakis’s 2012 Conjecture 3.4 and the precise 2019 book formulation (4F-5) propose logarithmic intrinsic lower bounds. A derivation is weaker than an executable algorithm because it does not pay to choose its next operands.
AI involvement
The disclosure says GPT-6 Astra identified the principal result during a human-initiated investigation and produced its mathematics, Lean development and manuscript. Jason Davies directed the project and publication but wrote none of the text or code; Claude handled review and packaging.
Importance
Shows that uniformity and the homomorphism-test framework alone cannot prove a logarithmic remainder-call lower bound.
Limitations
No single algorithm with this sublogarithmic cost is supplied; the deterministic and nondeterministic algorithm Main Conjectures remain open. The passage from intrinsic complexity to one optimal uniform process cites the book’s Theorem 4F.1, outside the formalization. The coefficient 6 is not claimed optimal, and no expert review is reported.
Technical verification
The pinned standalone challenge and successful Palomar report match the sublogarithmic derivation bound and the two intrinsic-complexity refutations. Protected comparison and Lean, NanoDa and con-ron checks allow only standard axioms. The cited best-uniform-process theorem is outside these checked claims.
Formal checking
Protected statement comparison and successful kernel checks of the selected sublogarithmic bounds and refutations under standard axioms
- Checker
- Palomar: Lean, NanoDa and con-ron
- Scope
- For every positive integer pair a≥b, gcd(a,b) has a remainder-only derivation using at most (6+o(1)) log₂(a)/log₂log₂(a) remainder calls, uniformly in b. Previously computed values may be reused and the choice of operands is free. This refutes Moschovakis’s stated uniform-process lower-bound conjectures, not the Main Conjecture for algorithms.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. The source reports no expert review. Its proof exposition is model-written; a human explanation of the central residue-contraction mechanism is not documented.
Correction and publication history
Added a reviewed, scoped central-AI contribution with checking and attribution limits.
Read this published revision