ARC Principle equation U = I x R^alpha formally published as a conjecture

The claim - verbatim

Michael Darius Eastwood first published the ARC Principle equation - expressed in the book Infinite Architects as U = I x R squared and in the research papers as U = I x R^alpha with the exponent open to measurement - as a conjecture in the paperback edition of Infinite Architects (ISBN 978-1806056200) on 2 January 2026 and formally in Paper I on 17 January 2026. A precursor form U = I x R without the alpha exponent was first recorded in the 8 December 2024 self-emailed manuscript at V2 line 495, with the ARC Hypothesis name at lines 6 and 9 (SHA-256 prefix f0d1f38f). The equation is framed throughout as a conjecture, not proven physics.

Anchored evidence

• ISBN 978-1806056200 (paperback, 2 Jan 2026)
• ISBN 979-8302196163 (ebook, 6 Jan 2026)
• research/papers/paper-i-arc-principle.html (JSON-LD datePublished 2026-01-17; explicit U = I x R^alpha)
• OSF DOI 10.17605/OSF.IO/6C5XB
• research/priority.json priorityChain position 1 (precursor U = I x R at V2 line 9, the first of thirteen occurrences, none carrying an exponent, named at lines 6 and 9, in the 8 Dec 2024 manuscript)
• CANONICAL_CLAIMS_REGISTER.md (Facts of record: U = I x R squared as the book's featured conjecture; papers use U = I x R^alpha; ALWAYS conjecture framing)

Limits and citation guidance - what this claim does not support, and how to cite it

Limits. The early sequential alpha of approximately 2.24 was retracted; the robust v13 estimate is approximately 0.49 by regression (sub-linear; SE 0.20), with an endpoint estimate of 0.59 (bootstrap interval [-1.3, 2.9]); alpha > 1 remains an open dated prediction. Do not present as 'validated to R squared = 1.0' (algebraic identity check only). The retired retail label must not be used on non-book-marketing surfaces; on research and priority surfaces the name is the ARC Principle. Bare exponential form alpha = d/(d+1) is prior work.