Title: Paper XIII · The ARC Theory · Laws I and II, the ARC Principle and the ARC Co-Scaling Law · The Self-Acceleration Exponent: a Measurable Threshold Joining Growth to Stability | Michael Darius Eastwood Research
Author: Michael Darius Eastwood
Publication date: 2026-08-16
Version: v1.10
Revised: 2026-10-05
OSF DOI: 10.17605/OSF.IO/HT8WU
Canonical URL: https://www.michaeldariuseastwood.com/research/papers/paper-xiii-self-acceleration-exponent.html

Registration
------------
Theory-level predictions preregistered on OSF: DOI 10.17605/OSF.IO/P8CKQ,
registered 8 September 2026 (version 1.100), updated 13 September 2026 (version
1.102), twenty-two propositions. Companion: Register · The ARC Theory ·
Operational Definitions, version 1.9.1, 5 October 2026.

Abstract
--------
Two frameworks in this programme describe recursive self-improvement and have
never been related. One derives how capability compounds with recursive depth
and yields the scaling exponent α = 1/(1 − β_L). The other derives when a
self-improving system remains correctable and yields the criterion β_X > k. They
use the same two letters for different quantities, which has prevented the
comparison rather than merely obscuring it.

This paper resolves the notation, derives the relation between the frameworks,
and finds that the quantity deciding the outcome is neither capability nor speed
but how fast a system compresses its own iteration time. Writing cycle duration
as Δt ∝ C^{−δ} defines the self-acceleration exponent δ, and the growth exponent
of the corrective framework follows exactly: k = δ − 1/α

Key findings (quotable)
-----------------------
- The self-acceleration exponent is the quantity that decides how fast a system's own improvement compounds.
- It is stated as a measurable rather than a posited value, with the measurement described before any result.
- The unit is drafted, dated and prepared as a draft registration awaiting human submission; nothing has been submitted.

Priority claims relevant to this paper
--------------------------------------
- PC-XIII-001 (2026-08-16): The self-acceleration exponent stated as a
measurable quantity with its measurement fixed in advance, first published 16
August 2026.

Citation
--------
Michael Darius Eastwood (2026). Paper XIII · The ARC Theory · Laws I and II, the
ARC Principle and the ARC Co-Scaling Law · The Self-Acceleration Exponent: a
Measurable Threshold Joining Growth to Stability | Michael Darius Eastwood
Research. OSF DOI 10.17605/OSF.IO/HT8WU.
https://www.michaeldariuseastwood.com/research/papers/paper-xiii-self-acceleration-exponent.html

Notes
-----
DOI 10.17605/OSF.IO/HT8WU. Sidecar authored 20 August 2026; the paper had none.

Provenance note
---------------
Michael Darius Eastwood conceived and directs this research programme and is the
author of this work. Across the programme, he has used more than six AI systems
in parallel, under his own instructions, to stress-test his arguments, identify
possible errors, and assist in preparing draft text from his own outlines. He
determines what is adopted, revised or rejected and takes responsibility for the
published content. These systems are tools, not authors.

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