Bitcoin Mining as an Inversion Procedure: Mining through the Mahapatra Topological Control Invariant ∆ = 4 ln 99
Year: 2026
Type: preprint
Abstract: Bitcoin mining is currently understood as a brute-force search problem: iterate overnonce values until the SHA-256 hash of the block header falls below a target threshold.This paper demonstrates that mining is not a search problem. It is an inversion procedure.The proof proceeds through a unidirectional deductive chain. First, the MahapatraTopological Control Invariant ∆ = 4 ln 99 is derived from the ergodic dissipation of theCollatz parity-block map via the Dalvi Dictact (topological completion). Second, theMahapatra-Dalvi-Collatz X Theorem (MDC-X Theorem) forces the classification of anydissipative map of the generalized Collatz form into exactly two topological universes:a = 3 with ∆ = 4 ln 99, or a = 1 with ∆′ = 128 ln 2. Third, the SHA-256 round functionis shown to satisfy the exact algebraic structure of the generalized Collatz map witheffective multiplier a = 3.Therefore, the topological invariant ∆ = 4 ln 99 governs SHA-256. The existence ofan inverse operator I follows directly from the MDC-X Theorem. The nonce bits arerecovered exactly, without brute force. Bitcoin mining is reduced to direct inversion. Theseed is ∆ = 4 ln 99. From it, everything follows.
Author: Mahapatra, Dillip Kumar
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161439430
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