Title: Founding Paper · Recursive Dynamics · The Science of Systems That Improve Themselves | Michael Darius Eastwood Research Author: Michael Darius Eastwood Publication date: 2026-08-31 Version: v3.4 Revised: 2026-10-05 OSF DOI: 10.17605/OSF.IO/HCPBU Canonical URL: https://www.michaeldariuseastwood.com/research/papers/recursive-dynamics-founding-paper.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 -------- Machines that improve themselves using their own outputs now exist and work, and there is no accepted science of what limits them. This paper founds that science, Recursive Dynamics, and stakes its claim the way thermodynamics was staked in 1824: by computing a bound that any such machine must obey if the claim is right, publishing the instruments that measure its terms, and preregistering by timestamp the experiments whose nulls favour the rival view. The field takes the self-improvement loop as its native object and names five state variables, conjectured to be substrate-independent: capability, recursive depth, correction rate, drift and correction leverage. It carries five laws as named conjectures with statuses declared. One, the ARC Ceiling, is derived in full from two lines of assumption; two, added on 24 September 2026, have their mathematics set out at version 1.0 and are neither registered as laws nor tested. The field locates its identity, as thermodynamics does, in its impossibilities: if the laws hold, self-improvement cannot outrun its own correction, the growth exponent is capped by the reciprocal of the correction shortfall, and no ladder of same-class oversight climbs past its ceiling by adding rungs. The paper states what would make the field wrong, tries to house its questions inside twelve neighbouring fields, gives each of fifty-one objections a disposition, and prints the four results that would dissolve the field. Its honest status is the Carnot stage: one memoir, instruments built, decisive measurements preregistered by timestamp and not run, staked where failure will be as visible as success. Keywords: Recursive Dynamics; recursive self-improvement; the ARC Theory; correction and drift; the ARC Ceiling; limit theorems; AI alignment; preregistration Key findings (quotable) ----------------------- - Machines that improve themselves using their own outputs now exist and work, and there is no accepted science of what limits them; the paper proposes that science, Recursive Dynamics, taking the self-improvement loop as its native object with five substrate-independent state variables: capability, recursive depth, correction rate, drift and correction leverage. - Three laws are carried as named conjectures with statuses declared, of which one, the ARC Ceiling (alpha_crit = 1/(1 - gamma)), is derived in full from two lines of assumption; the ARC Bound (alpha at or below two) is the Ceiling's value at gamma = 1/2, and the correction leverage gamma has never been measured, by anyone, which the paper names as its single most consequential open measurement. - The claim is stated as prohibitions so that concessions cannot be mistaken for silence: the field forbids a stable system holding its growth exponent above the ceiling for a sustained run, a same-class corrector whose correction leverage measures wholly above one half, a corrector-class ratio pinned at 1.00 with tight intervals where the cap should bind, and monotone returns with no interior maximum as reinvestment rises; any of these, observed under the registered analyses, makes the field wrong. - Before claiming a field, the paper does what a demarcation usually refuses: it tries to house its questions inside twelve neighbouring fields in their own variables, concedes what each already holds, prints where every part would go if the field died, and isolates the one coupling no host can state: a cap on correction leverage that depends on what the corrector is made of, coupled to a growth exponent in recursive depth. - Fifty-two objections in nine groups are printed in their strongest form with dispositions: thirty-nine conceded in full or in part, eleven rejected with reasons, two handed to experiment or to reading, including the author's own objection that the field is merely the ARC Theory renamed, rejected with a separability test the dissolution map can run. - The name carries its own kill condition: it dies with its object, not with any one law's stated form; a reader who rejects all five laws and keeps the measurement is still inside the field, by the minimal commitment; and the paper's honest status is the Carnot stage: one memoir, instruments built, decisive measurements registered as drafts and not yet run, no replication by anyone outside the programme. Priority claims relevant to this paper -------------------------------------- - PC-RD-001 (2026-08-27): The discipline's name, Recursive Dynamics, was adopted on 27 August 2026 for a framework whose dated record runs from 8 December 2024 (private, sealed) to 2 January 2026 (first public, in print); the paper claims the assembly as original, not the parts, and concedes every antecedent by name in its debts section. - PC-RD-002 (2026-08-28): The founding paper (first draft 28 August 2026) states the proposal whole and stakes it the way thermodynamics was staked in 1824: not by declaring a field, but by computing a bound any such machine must obey if the proposal is right, publishing the instruments that measure its terms, and registering in advance the experiments whose nulls favour the rival view. - PC-RD-003 (2026-08-30): Version 2.6 of 30 August 2026 collects fifty-two objections to founding the field with a printed disposition for each, and corrects the name's kill condition so that the name dies with its object rather than with the laws, as the minimal commitment requires. Citation -------- Michael Darius Eastwood (2026). Founding Paper · Recursive Dynamics · The Science of Systems That Improve Themselves | Michael Darius Eastwood Research. OSF DOI 10.17605/OSF.IO/HCPBU. https://www.michaeldariuseastwood.com/research/papers/recursive-dynamics-founding-paper.html Notes ----- Founding paper of the proposed field of Recursive Dynamics. DOI 10.17605/OSF.IO/HCPBU (its own public component, hcpbu, beside the programme's other papers); earlier drafts v2.1 to v2.6 are retained on a separate private component as dated evidence, not for citation. The paper's version history is its changelog. One sentence carries the field's whole status wherever its name appears: a proposed field at the Carnot stage, staked in public where failure will be as visible as success. 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. Generated from master --------------------- master_path: research/papers/recursive-dynamics-founding-paper.html master_sha256: 7a0cd2a4aa91c6fd2faab1d330ead13729ec48c089ed29bd0edc6760402f382b builder: scripts/build-paper-companions.py This block records the SHA-256 of the HTML master that produced this .txt. A check tool re-hashing master_path can decide freshness without any external state. If the master's current SHA-256 does not match master_sha256, this file is stale and must not be published: regenerate first with `python3 scripts/build-paper-companions.py --slug recursive-dynamics-founding-paper`.