Title: Paper IX · The ARC Theory · Synthesis and Roadmap Author: Michael Darius Eastwood Publication date: 2026-03-18 Version: v2.7 Revised: 2026-10-05 OSF DOI: 10.17605/OSF.IO/K7RUZ Canonical URL: https://www.michaeldariuseastwood.com/research/papers/paper-ix-synthesis-and-roadmap.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 -------- The ARC/Eden research programme now spans a full set of documents and a run of separate empirical studies covering mathematical foundations, methodology, empirical validation, engineering specification, and philosophical vision. The core concepts were first articulated on 8 December 2024 in an email bearing a visible Gmail origination field, with sender-DKIM and paired Google ARC mathematics verifying against keys captured at the signed selectors and no RFC 3161 trusted timestamp. The book Infinite Architects (ISBN 978-1806056200) was published 2 January 2026 (print; ebook 6 January). Work on the research programme began in February 2026 and continues. Its output now reaches the thirty-two documents of its catalogue; a registered programme of seventy drafted preregistration units, the number the register carried when it was last generated on 17 August 2026, each carrying a schedule drawn from a published seed, whose regeneration is checked by the estate’s own tools rather than asserted here; and Recursive Dynamics, the field the author founded, whose founding paper states the kill condition for its own name (DOI 10.17605/OSF.IO/HCPBU). Of the trials in the programme, one, the corrector-class audit (unit 06), was registered on OSF on 1 October 2026 and has been public since 4 October 2026 (DOI 10.17605/OSF.IO/RV2B5). Every other trial is a draft awaiting submission by the author, most of them preregistered by timestamp. This synthesis paper integrates all findings into a single honest assessment. The framework’s laws, five since 24 September 2026, are carried as named conjectures with the status printed beside the name: Law I, the ARC Principle; Law II, the ARC Co-Scaling Law; Law III, the ARC Ceiling, whose ARC Bound of two is the Ceiling’s value at one half; these three were registered on 8 September 2026. Law IV, the ARC Persistence Law, and Law V, the ARC Embedding Law, were added to the theory on 24 September 2026; neither is registered as a law or tested, and their mathematics is set out at version 1.0 of 3 October 2026. The correction leverage gamma has never been measured, by anyone. The empirical studies break down like this. Paper VIII returned a null result in 1 case, DGM v3, on the candidate account that RLHF-trained models resist prompt-level differentiation, and inconclusive results in 1 case, weight-level LoRA fine-tuning, on the candidate account that instruct tuning was too strong for LoRA to override at the ranks tried. Papers IV.a to IV.d report statistically significant findings under blinded evaluation. In Paper II, also blinded, four of the five models it measured put the parallel exponent at or close to zero; an earlier super-linear estimate did not replicate and is retracted, and the sequential exponent now reported comes from the fit of one model and is inconclusive. Paper V reports statistically significant gains in stakeholder care in each of its five analysable runs, scored across models and not under the four-layer blinding protocol of Paper IV.c. Paper VII reports a match between predicted and observed scaling families that is statistically significant under a permutation test, in a structured prediction comparison and not a blind trial. Simulations are not counted among the empirical studies; they are reported as simulation results. The gated simulation, the one Paper VIII experiment that uses deterministic metrics on a toy system without pre-existing RLHF training, showed the Babylon reward-hacking fingerprint: unconstrained optimisation traded safety for capability. The $d/(d+1)$ geometric scaling bound, proposed as an invariant relation under test, matches observed scaling across 50 domains from mice to galaxies, and Cauchy functional equations fix the functional form once the composition identity and a regularity condition are given, and saturation is admitted as a fourth, capped case rather than as a solution of those equations. This paper maps exactly what has been proven, what has not, and what experiments would resolve each open question. It also documents the programme's errors and corrections, because a framework built on iterative self-correction must practise what it preaches. Key findings (quotable) ----------------------- - This synthesis paper integrates all findings into a single honest assessment. - The framework’s laws are carried as named conjectures with the status printed beside the name: Law I, the ARC Principle; Law II, the ARC Co-Scaling Law; Law III, the ARC Ceiling, whose ARC Bound of two is the Ceiling’s value at one half; the correction leverage gamma has never been measured, by anyone. - The empirical studies break down like this: a clear positive result in 1 case, the gated simulation, which stands alone in the programme for using deterministic metrics on a system without pre-existing RLHF training; a null result in 1 case, DGM v3, where no difference was detected between conditions on the endpoints measured, with resistance to prompt-level differentiation by RLHF-trained models the candidate account and rival accounts left open; inconclusive results in 1 case, weight-level LoRA fine-tuning, where the candidate account is that instruct tuning left the models too strong for LoRA to override at the ranks tried, with rival accounts left open; and, in every remaining study, statistically significant findings under blinded evaluation. Citation -------- Michael Darius Eastwood (2026). Paper IX · The ARC Theory · Synthesis and Roadmap. OSF DOI 10.17605/OSF.IO/K7RUZ. https://www.michaeldariuseastwood.com/research/papers/paper-ix-synthesis-and-roadmap.html Notes ----- Hardware framings held at the site's already-published two-sentence concept ceiling: safety constraints at hardware level through cryptographic tokens in silicon, TRL 0-1, no prototype. No enabling implementation detail is stated in this companion file. 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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