GTPA: Agency on a Noisy Base Motion, Without Physics. Core Edition with Part H, the Human Sector

GTPA v2.1 is a mathematical framework for modelling an agent that acts on a noisy base motion. The agent reads the base through a lens, estimates an error, chooses an action by one control law with one effort metric, and adds that action to the base with a dial; at dial zero the base is recovered exactly, and the efficacy of an action is measured against that copy without action. Each statement carries its hypotheses, a status and a check level; worked models are declared as models, and their results hold for those models only. It supersedes GTPA v2.0 (10.5281/zenodo.23172305). It keeps the core of v2.0 with no statement changed and adds Part H, the human sector, which v2.0 deferred. Part H re-derives UTHA v1.0 (10.5281/zenodo.17994554) statement by statement as a class of declared models of the core, with written mapping assumptions and zero evidence about any person. Each of UTHA's 68 statements gets a disposition; most do not enter Part H: the core of v2.0 already settles many of them, and the others are physics, claims about people with no evidence, or ill-posed as written. Result H.14 shows that in Model H.10, a declared model whose territory switches at random between two rates, some constitution that adjusts to the error beats the best fixed constitution at every switching rate; it holds in that declared model only and says nothing about people. It decides there the clash between GTPA v1.2 and UTHA over Class A; how much plasticity gains, and which law is best, stay open. Part H also answers the two questions that v2.0 left for it (EG-06.b and EG-07.c). The base motion is that of UFD v2.0 (10.5281/zenodo.23171454), unchanged. The proofs of the core cited by number are in BLOCK-B-ANSWERS.pdf, BLOCK-C-THEOREMS.pdf and BLOCK-C-OBJECTS.pdf; their texts are unchanged since v2.0, and their PDFs are rebuilt because the v2.0 PDFs dropped a few characters inside five quotations. All PDFs of this record are compiled with LaTeX, with the formulas set as mathematics; the v2.0 PDFs set them as code, which dropped or misplaced some bars, dots and tildes over Greek letters. The GTPA v2.0 PDF also carries an older header than its text: a placeholder publication date (2026-10-XX) and a sentence saying that the proof files are not part of the record, although they are deposited with it; v2.1 supersedes it. Part H's proofs are written in the text. The statement-by-statement audit of GTPA v1.2 is the errata annex, CROSSWALK-v1.2.pdf, with one sentence now pointing to Part H. Checks: the core of the control law (Result 2.5: the effort Hessian is never singular, the minimizer is unique, and it spends nothing in directions where the action has no effect) is now formally checked in Lean (GtpaControlLaw.lean, deposited with this record), in 18 theorems with no unproved step and only Lean's standard axioms; it is the only part checked at that level. The decisive calculations of the core and of Part H were recomputed by machine with no disagreement; for Result H.14 this includes an exact isolation of the best fixed gain and interval-certified signs, while three analytic arguments of its proof rest on an independent read. The text was read by independent AI contexts from the same provider as the drafting model (Claude, by Anthropic), and their findings are fixed; no AI system of another provider has checked it. It is not physics and it says nothing about any person.