What was already known
Amdeberhan, Kauers and Zeilberger posed the D=5, M=1000 computation. Rubine solved D=4 and estimated that the direct five-dimensional sum, with about 10¹² terms, needed a new method.
AI involvement
Claude supplied the collapse, algorithm and code. Padhi chose the challenge, ran the calculation, designed checks and corrected model errors.
Claude supplied the collapse, algorithm and code; Padhi chose the challenge, sized and executed the computations and applied independent controls.
Importance
Reports a method and exact value for the specified five-dimensional Geode challenge.
Limitations
Fresh-prime and small-case controls support the finite computation but do not independently prove the general coefficient-collapse identity. The separate four-variable recurrence challenge remains open.
Technical verification
The finite coefficient is reported as exact via modular polynomial evaluation, a proved magnitude bound and CRT reconstruction; fresh-prime checks plus D=4 and small-value controls support the computation. These checks do not independently establish the preceding coefficient-collapse identity, so the complete assessed method is only partially checked.
Independent checking
Exact modular quadrature and coefficient recurrence, bounded CRT reconstruction, fresh-prime checks and published small-case controls
- Checker
- Jaideep Sai Padhi, paper author, executing model-written code
- Scope
- G[1000^(5)] exact finite coefficient
- Basis
- Reported by the linked checker
Human understanding
The author designed and ran the checking protocol, but the source does not document his independent explanation of Claude’s coefficient-collapse mechanism; Few is the evidence default.
Correction and publication history
First report of the five-dimensional Geode value.
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