Keeping Claims Honest: A Deterministic Toolkit for the Gap Between Proxy and Truth

Abstract. Across domains that look unrelated — optimized business metrics, model evaluations, multi-agent systems, forecasting, consciousness reports, computational geometry, fractals, and even electromagnetism and energy accounting — the same failure recurs: a proxy that was supposed to stand in for a truth comes apart from it, and the gap is not noticed because nothing independent was checking. This paper presents a family of small, deterministic, self-testing tools built on one discipline for that gap. The discipline has four moving parts: separate the proxy from the truth and watch for decoupling; locate the truth on a reachability spectrum that dictates whether to solve, detect, or withhold; require every recursion to bottom out at a base case (well-foundedness); and refuse to certify beyond the evidence. Each tool is one instantiation of that discipline in one domain. We describe the method, organize the family, report worked results with real numbers, and — as a first-class part of the contribution — state plainly what the toolkit deliberately does not do.

---

1. The through-line: proxy is not truth

Goodhart's law is usually quoted as an aphorism ("when a measure becomes a target, it ceases to be a good measure") and then set aside. The claim of this work is that it is not an aphorism but a structural fact with a structural remedy, and that the same structure appears far outside economics. A proxy is any measurable stand-in for something we actually care about but cannot directly see: a KPI for real value delivered, a benchmark score for real capability, a forecast for a future outcome, a behavioral report for an inner state, a model's prediction for physical reality. In each case the proxy and the truth are two different things that usually move together — and the characteristic failure is that they stop moving together while the proxy keeps looking fine.

Once stated this way, the remedy is forced: you cannot detect the gap from the proxy alone. You need a second, independent measurement of the truth, and you need to watch the two over time. That single requirement — an independent check — is the seed from which everything else in the toolkit grows.

2. The method: four invariants

The tools share four disciplines. They are not domain assumptions; they are constraints on what counts as a legitimate claim.

(1) Decoupling is the failure mode. A proxy is trustworthy exactly while it tracks an independent ground truth. The operational signature of gaming is not a bad proxy value — it is a rising proxy with a falling truth and broken co-movement. This is checkable over time given two aligned series, and it is the pattern behind a peg drifting from its backing, a benchmark inflating while real capability stalls, and a model idealizing away reality outside its regime.

(2) The reachability-of-truth spectrum. Not all truths are equally accessible, and the honest action depends on which kind you face. Some truths are exactly computable (a geometric predicate, a mixture that is well-separated) — there, you solve. Some are partially observable against an independent reference (a metric, an eval, a physical measurement) — there, you detect decoupling. And some are not third-person accessible at all (whether a system has subjective experience) — there, the only honest move is to withhold, recording the claim without certifying it. A great deal of dishonesty comes from applying the wrong regime: treating a withhold-case as if it were solvable, or a detect-case as if it were already proven.

(3) Well-foundedness: recursions must bottom out. A justification that depends on a justification that depends on a justification, with no base case, never grounds anything. Legitimate structures terminate: a dependency graph has roots that depend on nothing; a meta-level tower reaches a fixed point where applying it again changes nothing; a self-similar structure is bounded by real cutoffs; a process has a beginning and an end. The refusal of infinite regress — including the seductive "infrastructure of infrastructure of infrastructure…" and "holds at every scale, forever" — is a recurring, load-bearing move, not a stylistic preference.

(4) Refuse to certify beyond the evidence. No tool in the family issues a verdict of PROVEN. A universal claim is at most corroborated and is refuted by a single counterexample (the white raven). A model is validated in the regime you measured and unverified outside it. A future is a forecast, never a fact. A quale is recorded, never machine-certified. This is the discipline that most often separates the toolkit's output from the confident overclaim it is auditing.

A fifth idea, conservation, is really invariant (1) in a different coordinate system: a flow through stages must balance, and unaccounted loss (a leak) or unaccounted gain (fabrication) is decoupling between what entered and what left.

3. The family of governors

The tools instantiate the four invariants across domains. They are deterministic and self-testing (each runs its own assertions and a demonstration), and stdlib-only except where a numerical demo needs numpy.

Definition-time and operation-time integrity. goodhart_auditor catches a metric that overclaims by its name before it is ever run; decoupling_monitor catches a metric that was honest at definition but is being gamed in operation, by watching proxy against an independent truth over time; knowledge_maturity grades how well-established a claim's backing is; ground_truth_auditor checks whether a claimed ground truth is actually independent; eval_gaming_detector looks for the signatures of a benchmark being optimized rather than measured.

Decision and containment. governed_decision turns an assessment into an action verdict through five gates (trust, maturity, timing, safety, authority), with outcomes from WITHHOLD through AUTHORIZED_ACT; option_space audits a set of choices for Pareto-dominated decoys and completeness; containment_guard, agent_mesh_cage, and the reference architectures enforce fail-closed admission, non-self-approval, and human-grounded authority for multi-agent systems.

Meta-governors. determinism_governor, its system-of-systems and dimensional variants, and fixed_point_governor govern self-application: a meta-construction is admitted only if it reaches a fixed point, and an ungrounded regress is refused fail-closed.

Reachability instances. temporal_governor (the future is a forecast, not a fact) and the "Forecasts Are Not Facts" paper; qualia_report_governor (recorded, not verified) and the "Recorded, Not Verified" paper; the geometry work (exactly-solvable robustness predicates); and em_estimation, which runs Expectation–Maximization and reports the recovered latent structure only when it is reachable (well-separated, restarts agree), withholding it as UNIDENTIFIED otherwise.

Structure and relation. dependency_graph (well-founded roots; math as the base case); sciences_layers (physics as the interface, not a proxy, between math and biology); math_to_reality (a model is a proxy for reality — validated in regime, decoupling outside it, never "reality is mathematical"); words_vs_numbers (Stevens' levels; metric vs semantic governance); taxonomy_builder and raven_taxonomy (a general classification engine and the confirm/refute/ unverified taxonomy with red and blue as the two acting roles).

Scale, recursion, and process. fractal_recursion (self-similarity across scale; grounded as a set, ungrounded as a descent); fractal_prerequisite (self-similarity is the bounded prerequisite for scale-invariance; an unbounded demand is refused); bounded_process (a beginning and an end are the two cutoffs that ground a process).

Physics and structure as instances of the same discipline. duality_governor (a claim needs an independent second side; a check derived from the claim is circular); flow_conservation (leaks and fabrication in a pipeline); water_infra (formless content is ungovernable until a container gives it shape); em_field (a valid free electromagnetic wave is E ⟂ B, transverse, |E| = c|B| — a coupled duality whose energy is conserved); energy_matter (a first-law auditor that refuses over-unity and shows the same nuclear event balancing only when E = mc² is included); emergence_infra (genuine emergence vs mere aggregation vs the over-claim).

4. Worked results

The tools produce concrete, reproducible numbers, not just verdicts.

• A real decoupling. On US GDP-per-capita against median household income, 2000–2019, the decoupling monitor flags DRIFTING and then DECOUPLED around 2012, with a peak gap near 19 indexed points by 2014 — a genuine, sourced instance of a headline proxy separating from the median lived reality it is often taken to represent.
• A model decoupling at a known boundary. math_to_reality on Newtonian momentum against relativistic reality reports 0.5% error at v/c = 0.1, 4.6% at 0.3, then decouples — 13% at 0.5, 69% at 0.95 — and returns the untested v/c = 0.99 as UNVERIFIED. The break lands exactly where physics says the idealization fails.
• Why the matter term is not optional. energy_matter classifies the same nuclear event as VIOLATION_CREATION with the mass term off and CONSERVED with it on: a 1 mg deficit supplies ≈ 9×10¹³ J.
• An exact fractal fact. fractal_recursion computes the Cantor dimension in closed form as log2/log3 = 0.630930 and recovers the same value to six figures by box-counting a generated point set.
• Inference governed by reachability. em_estimation recovers a μ = ±5 mixture (components 9.9 standard deviations apart) and withholds a μ = ±0.3 mixture (0.05 sd apart) as UNIDENTIFIED, because the data does not determine the latent labels.

None of these required trusting the tool's own output as its check; each was measured against an independent reference, which is the whole point.

5. What the toolkit deliberately does not do

The exclusions are part of the design, not gaps in it.

It is not fit for safety-critical control. Nothing here is validated to aviation DAL A (DO-178C/DO-254), functional-safety SIL (IEC 61508, where SIL 4 demands ~10⁻⁴–10⁻⁵ probability of failure on demand), or nuclear Class 1E (IEC 61513/60880, IEEE 7-4.3.2), and it must not be placed in a loop that flies, doses, arms, or trips a reactor. It is an assurance and integrity aid, not a certified safety function.

It does not resolve consciousness. The qualia work is explicit that it offers no theory of experience; it records first-person reports as testimony and refuses machine-certification of a quale, because that truth is not third-person reachable.

It does not explain everything, and its own tools say why — which is the subject of the companion paper.

6. Honest positioning

Every classification the toolkit makes is only as good as the declarations it is given: the measurement semantics you state, the ground truth you supply, the cutoffs you name. Validation of a taxonomy confirms the categories are complete and exclusive on the items you provided, not for all conceivable items. The relations it formalizes (math as root, physics as interface) are stated, contestable positions, not proven facts. The tools are deterministic and self-testing so that their behavior is reproducible and auditable; that is a claim about the tools, not a guarantee about the world they are pointed at.

7. Conclusion

The unifying result is not a grand theory. It is that one modest discipline — check a claim against something it does not control, know whether its truth is solvable, detectable, or unreachable, make your recursions bottom out, and never certify past your evidence — generalizes across an unreasonable range of domains, from business metrics to Maxwell's equations. The breadth is evidence that the discipline travels, not that any single theory does. Keeping claims honest turns out to be the same job everywhere; the tools here are that job, done small and done twice-over-checkable, one domain at a time.

Gergely Vámossy (2026). Keeping Claims Honest: A Deterministic Toolkit for the Gap Between Proxy and Truth. https://vamossy.com/research/keeping-claims-honest