Theorem Laboratory

For a declared input q and welfare coordinate W, there exists a function g with W = g composed with q exactly when W is constant on every q-fiber.

Assumptions

• The complete declared input q is specified.
• The welfare coordinate W and its domain are specified.
• The claim concerns exact functional recovery on that domain.

Proof status

complete in released source

Locator

Section 4.1, Proposition 4.1

Note

The result is the elementary factorization-through-fibers criterion; the paper's contribution is its institutional use and audit protocol.

Evidence

• The released paper supplies exact constructed witness pairs.
• Historical benchmark material motivates the application but does not establish every formal premise.

Boundaries

• The result does not say the target is unknowable.
• The result does not establish that an intervention improves outcomes.

Objections

• A richer input may separate a pair that payoffs alone do not.
• Finite-resolution field data may support only approximate or partial identification.

Reform implications

• Declare the complete input before evaluating a rule.
• Add an independently verified separating signal when an existing fiber crosses the decision threshold.

Related claims

w-independence · declared-input-blindness · target-recovery · transformation-recoverability

Under the payoff-level bridge premise, no function of the parties' payoff vector equals W at every profile in the domain.

Assumptions

• A verified pair has equal total payoffs for every modeled party.
• The same pair has different values of W.
• The payoff vector is the complete input being tested.

Proof status

complete in released source

Locator

Section 4.3, Corollary 4.3

Note

Direct application of the fiber characterization to the witness pair.

Evidence

• The paper provides constructed exact witnesses.
• No domain-level SAPM measurement is admitted for public propagation.

Boundaries

• The claim concerns exact recovery from payoffs.
• It does not exclude independent measurement of W.

Objections

• Interest non-inclusion does not by itself imply the payoff-level witness.
• A decomposed or enriched input requires its own fiber test.

Reform implications

• Keep measurement, authority, and incentive design as separate steps.

Related claims

fiber-characterization · path-theorem · outcome-taxonomy

Under private dominance, strict pathwise system tension, regularity, and frontier reachability, W at every privately Pareto-efficient endpoint is strictly below W at disagreement.

Assumptions

• Private dominance at the disagreement point.
• Strict welfare decline almost everywhere on every admissible private-improvement path.
• Absolute continuity of welfare along each path.
• Reachability of each private frontier point by an admissible path.

Proof status

complete in released source

Locator

Section 6.1, Theorem 6.1

Note

Integrates the signed welfare derivative along each admissible path.

Evidence

• A constructed full-hypothesis example is provided.
• The released review states that the historical material does not establish the full theorem premises.

Boundaries

• The result is conditional on the defined path class.
• It does not prohibit a transformed game from containing a system-preserving frontier.

Objections

• The pathwise tension premise carries much of the endpoint conclusion.
• Empirical reachability and universal path signs are difficult to verify.

Reform implications

• Change information, payoffs, or feasible actions when a fixed game's verified path conditions are adverse.
• Re-test the transformed game rather than inheriting the original conclusion.

Related claims

finite-path-theorem · two-implementations · ratchet-threshold

For a rule S on declared input q, equality of q on a pair forces equality of S(q) on that pair; a target difference then proves blindness to that distinction.

Assumptions

• The complete declared input is enumerated.
• The two situations agree on that complete input.
• The target differs on the pair.

Proof status

complete in released source

Locator

Section 6.4, Corollary 6.8

Note

A function-evaluation consequence stated in profile and cross-game forms.

Evidence

• Application requires a rule-specific input audit.

Boundaries

• No named bargaining or mechanism procedure is covered until its complete input and output class are verified.

Objections

• A same-payoff witness does not establish equality of a richer solution concept's input.

Reform implications

• Write the input contract for a decision procedure before claiming it can see a welfare distinction.

Related claims

fiber-characterization · price-input-variation · transformation-recoverability

Under private dominance, discrete pathwise tension, and finite reachability, every privately Pareto-efficient endpoint has welfare below the disagreement baseline.

Assumptions

• A finite transition relation is specified.
• Each permitted private-improvement step strictly lowers W.
• A permitted improvement chain reaches every relevant frontier point.

Proof status

complete in released source

Locator

Section 7.1, Theorem 7.1

Note

Uses a finite telescoping sum; no limiting argument is required.

Evidence

• The transition relation is an empirical or institutional input to every application.

Boundaries

• The discrete and continuous results are separate statements.

Objections

• A different protocol can remove a chain or add a system-preserving transition.

Reform implications

• Protocol design can change the transition relation and therefore the theorem's applicability.

Related claims

path-theorem · two-implementations

Under the maintained price-input architecture, equal complete inputs imply equal realized prices.

Assumptions

• The complete price-forming input is declared.
• The realized price is a function of that input on the stated domain.

Proof status

complete in released source

Locator

Section 4, Proposition 1

Note

A direct consequence of the maintained functional architecture.

Evidence

• Institutional audits illustrate input and governance changes without claiming a cross-domain empirical result.

Boundaries

• Price variation is weaker than target recovery.
• Target recovery is weaker than outcome validity.

Objections

• A price can respond without recovering the analyst's target.
• An omitted public coordination signal means the declared input was incomplete.

Reform implications

• Enumerate measurement, valuation, rule-consequence, and anticipation routes separately.

Related claims

target-recovery · fiber-characterization

Target recovery is a factorization condition through q or P; decision recovery composes the recovered target with the maintained decision rule.

Assumptions

• The decision target and domain are declared.
• The complete input and realized price maps are declared.
• The maintained decision rule is a function of the target.

Proof status

complete in released source

Locator

Section 4, Proposition 2 and Corollary 3

Note

Applies the fiber criterion separately to input, price, target, and decision.

Evidence

• The paper gives falsification tests for equal-input and equal-price witness pairs.

Boundaries

• The result is domain-specific.
• It supplies no public domain magnitude.

Objections

• A recovered target can still be misspecified.
• An implementable decision can still perform poorly.

Reform implications

• Validate the target and outcomes after establishing information recovery.

Related claims

price-input-variation · disclosure-selection · fiber-characterization

In the stated finite Bayesian setting, payoff-orthogonal public disclosure can alter equilibrium selection while leaving the inherited payoff and feasibility structure unchanged.

Assumptions

• The disclosed coordinate is payoff-orthogonal in the formal sense.
• The game and continuation equilibria satisfy the proposition's finite Bayesian assumptions.
• The claim concerns selection among inherited continuation equilibria.

Proof status

complete in released source

Locator

Section 5, Proposition 4

Note

The paper distinguishes information from a current payoff, rule, or anticipated consequence route.

Evidence

• The proposition is formal; application-specific disclosure effects require separate evidence.

Boundaries

• The result does not claim that disclosure creates new incentives.
• Richer dynamic trading or endogenous information acquisition lies outside the proposition.

Objections

• Many real disclosures correlate with private costs or beliefs and fail payoff-orthogonality.
• Selection among inherited equilibria need not improve welfare.

Reform implications

• Identify whether a disclosure changes measurement, payoffs, enforceability, anticipation, or equilibrium selection.

Related claims

target-recovery · transformation-recoverability

Exact criterion classification factors through the declared input before and after an information transformation.

Assumptions

• The institutional criterion and rule input are declared.
• The induced welfare measure is fixed for the application.
• Any added measurement channel is separately grounded.

Proof status

complete in released source

Locator

Section 4.1, Proposition 1

Note

Applies the factorization criterion to an institutional welfare classifier.

Evidence

• The released paper exhibits an exact witness inside its solved extraction game.

Boundaries

• The proposition does not establish a universal four-channel necessity theorem.

Objections

• Information recovery does not supply enforcement authority.
• A richer inherited input may already separate the pair.

Reform implications

• Audit information, payoff, feasible-action, and authority channels separately.

Related claims

fiber-characterization · two-implementations · disclosure-selection

The specified payoff transformation and feasible-action transformation implement the unique optimum in the solved model.

Assumptions

• The quadratic extraction game and damage function are correctly specified.
• The charge is observable and enforceable.
• The caps are feasible and enforceable.
• The equilibrium concept and timing match the solved game.

Proof status

complete in released source

Locator

Section 5.6, Proposition 2

Note

Solves both transformed games and compares their equilibrium with the welfare optimum.

Evidence

• This is a solved model result.
• The six-case pilot reported a null for the diagnostic worksheet and is not evidence that these instruments work in a new domain.

Boundaries

• The result belongs to the stated model.
• It is not a universal implementation theorem.

Objections

• Application fails when observation, authority, or enforcement assumptions do not hold.
• The solved model does not identify the cheapest real institution.

Reform implications

• Choose the cheapest adequate channel only after measuring implementation cost, error, and enforcement response.

Related claims

transformation-recoverability · adoption-region · path-theorem

Adoption and instrument choice follow the net-welfare comparison in the stated decision model, with enforcement handled as a separate threshold.

Assumptions

• Implementation cost and measurement error are specified.
• The enforcement response is estimated separately.
• The domain analysis recomputes the decision region.

Proof status

complete in released source

Locator

Section 6, Proposition 3

Note

A decision-model result rather than a universal institutional theorem.

Evidence

• The paper supplies a computational pilot and preserves its null result.

Boundaries

• No domain may inherit the paper's illustration without recomputation.

Objections

• Misspecified costs, error, or enforcement response invalidate the inherited region.

Reform implications

• Keep diagnostic accuracy, instrument adoption, and enforcement feasibility as separate decisions.

Related claims

two-implementations · fiscal-boundary

Under strict concavity and differentiability, the optimum is determined by the endpoint comparisons or the unique interior equality of marginal benefit and government-wide marginal financing cost.

Assumptions

• The government's objective is continuously differentiable and strictly concave on the stated interval.
• All financing channels in the government-wide account are included.
• The marginal objects are measured in consistent units.

Proof status

complete in released source

Locator

Section 4.1, Proposition 1

Note

A concave optimization boundary result.

Evidence

• The released paper provides a worked treasury example and a prospective empirical protocol.
• It does not claim a completed causal study.

Boundaries

• The result does not place a jurisdiction relative to its latent cutoff without measurement.

Objections

• Omitted replacement channels make the financing cost incomplete.
• A later held derivative's broader empirical claims remain under review and do not change this released artifact.

Reform implications

• Build the government-wide financing account before diagnosing fiscal dependence.

Related claims

conditional-remittance · marginal-decoupling · asset-account-identity

The sign of the remittance comparative static is conditional on the declared financing rule and its cross-effects.

Assumptions

• The financing rule is declared.
• Cross-effects on implementation cost and welfare weight are included.
• The local comparative-static conditions hold.

Proof status

complete in released source

Locator

Section 4.2, Proposition 2

Note

Derives the sign condition and states the policy-contingent boundary.

Evidence

• The proposition is formal; the empirical program is prospective.

Boundaries

• The proposition applies to the declared financing rule and nothing broader.

Objections

• A remittance level alone does not identify the sign.
• Strategic and dynamic effects require additional modeling.

Reform implications

• Trace how the financing rule changes incentives, costs, and available replacement resources.

Related claims

fiscal-boundary · marginal-decoupling

At the stated reform point, the fiscal contribution to the marginal objective is zero exactly under the proposition's government-wide marginal condition.

Assumptions

• The reform point and all financing channels are specified.
• The relevant marginal contributions are measured.
• The condition is evaluated locally.

Proof status

complete in released source

Locator

Section 4.3, Proposition 3

Note

A local identity in the stated government-wide account.

Evidence

• Institutional routing can motivate the condition but does not measure it by itself.

Boundaries

• The claim is local and does not establish a durable dynamic exit.

Objections

• A statutory routing change is not equivalent to an estimated zero marginal fiscal contribution.

Reform implications

• Measure the marginal financing effect after institutional routing changes.

Related claims

asset-account-identity · fiscal-boundary

Under the proposition's timing assumptions, the current withdrawal term is fixed with respect to the current reform choice.

Assumptions

• The withdrawal rule is predetermined.
• The asset stock is fixed when current reform is chosen.
• The claim concerns the current decision, not future political dynamics.

Proof status

complete in released source

Locator

Section 4.4, Proposition 4

Note

A contemporaneous accounting identity with an explicit dynamic boundary.

Evidence

• The Norway section is an institutional illustration and explicitly does not prove a universal remedy.

Boundaries

• The identity does not establish causality or constitutional entrenchment.

Objections

• Future withdrawals, rule changes, and political expectations can create dynamic effects outside the identity.

Reform implications

• Separate current-account arithmetic from dynamic commitment and political effects.

Related claims

marginal-decoupling · fiscal-boundary