schema_version: 1
contribution_id: con_e76145b1d71d44b588b72dad990e5892
revision_id: rev_865087fcd1ab400c8b32a27cb809ddfa
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type: attempt
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title: A globally certified borrowing-constrained bond economy, sharp limits to moment compression, and the cost of distribution-state validation
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claim:
  type: partial_result
  scope_statement: |-
    This contribution proves a uniform residual certificate and a residual-to-equilibrium error bound for an explicitly specified two-date heterogeneous-household economy. The primitive class is a numerical parameter box, the initial distribution ranges over every probability law on a fixed wealth interval, the bond price is endogenous, and the borrowing constraint can switch. With exact bin probabilities supplied, a histogram algorithm uses O(1/epsilon) arithmetic operations per state evaluation and has an analytically certified uniform residual. For one fixed economy in this class, the exact mean-only price uncertainty is calculated, and the optimal information error from the first m exact polynomial moments is proved to have order 1/m, even on a fixed-mean distribution domain. A separate theorem gives exponential point-query complexity for certifying arbitrary Lipschitz residuals over a distribution state space. An explicit counterexample shows that the declared residual does not control the fraction exactly at the borrowing limit. Conditional moment, Gaussian likelihood, and counterfactual error bounds are also supplied.

    Assumptions and limitations: The economic theorem has two dates, logarithmic utility, one risk-free government bond, no aggregate uncertainty, and a strictly inactive upper asset cap. It does not establish the requested programme for rich recursive models. Distribution-access costs are explicit: exact bin masses, or a separately charged mechanism for obtaining them, are required. Arithmetic-operation counts are distinguished from bit complexity and elapsed time. Polynomial moments are exact information in the information bounds. The oracle lower bound concerns arbitrary Lipschitz scalar functions, whose realisability as economic residuals is not proved. No general mathematical novelty, proof-assistant verification, empirical calibration, or matched hardware benchmark is claimed.
  assumptions: []
  limitations: []
attribution:
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    login_at_event: kendonB
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    login_at_event: kendonB
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  organisations: []
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model_uses:
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- provider: OpenAI
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lineage: []
artifacts:
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  path: files/attempt.md
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- role: supplementary
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  path: files/disclosures.md
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rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - kendonB
declarations:
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    actor: per_35802f56649c44d7a168a7b6d018e269
    recorded_at: '2026-10-18T18:54:17Z'
    evidence_url: https://github.com/We-Solve/research/issues/2
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    actor: per_35802f56649c44d7a168a7b6d018e269
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