Title: Recursive Dynamics: The Proposal of a Field | Michael Darius Eastwood Research Author: Michael Darius Eastwood Publication date: 2026-08-31 Version: v2.6 OSF DOI: 10.17605/OSF.IO/HCPBU Canonical URL: https://www.michaeldariuseastwood.com/research/papers/recursive-dynamics-founding-paper.html 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 proposes that science and stakes its claim the way thermodynamics was staked in 1824: not by declaring a field, but by computing a bound that 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. The field, Recursive Dynamics, takes the self-improvement loop as its native object; proposes five substrate-independent state variables written exactly as the programme's notation register defines them (capability, recursive depth, correction rate, drift, correction leverage); carries three laws as named conjectures with statuses declared, of which one, the ARC Ceiling, is derived in full from two lines of assumption; and 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, so the engineering lever is what the corrector is made of. Stated as prohibitions, so that no reader mistakes the paper's concessions 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 one where the cap binds; and monotone returns with no interior maximum as reinvestment rises. Any of these, observed under the registered analyses, makes the field wrong. Before any of that, the paper does the thing a demarcation usually refuses: it tries to house its questions inside twelve neighbouring fields in their own variables, concedes what each already holds (the first law to endogenous growth theory, the form of the ceiling to queueing theory, the shape of the second law to error-threshold theory), prints where every part would go if the field died, and isolates the one coupling no host can state. It then does the thing a founding proposal usually skips: it collects every objection to founding the field that its author and his adversarial readers could find, fifty-two of them, states each in its strongest form, and prints a disposition for each, conceding thirty-nine in full or in part, rejecting eleven with reasons, and handing two to experiment or to reading. The case for the field is scored against six licence conditions with the evidence for each; the precedent class of fields founded on a limit theorem in their own variables is named with its disanalogy; the founding conjunction, the set of results no neighbouring field could state in its own variables, is separated into what is registered today and what is only proposed; and the four results that would dissolve the field are printed with a commitment to publish them under this title. Its honest status is the Carnot stage: one memoir, instruments built, decisive measurements registered and not run, staked where failure will be as visible as success. 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 three 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). Recursive Dynamics: The Proposal of a Field | Michael Darius Eastwood Research. The ARC Theory ยท ARC/Eden experiments, 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. 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