Datasets:

seancollins
/

formal-refutations

Error code:   StreamingRowsError
Exception:    CastError
Message:      Couldn't cast
claim: string
verdict: string
reason: string
prover: string
to
{'claim': Value('string'), 'verdict': Value('string'), 'prover': Value('string')}
because column names don't match
Traceback:    Traceback (most recent call last):
                File "/src/services/worker/src/worker/utils.py", line 147, in get_rows_or_raise
                  return get_rows(
                      dataset=dataset,
                  ...<4 lines>...
                      column_names=column_names,
                  )
                File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
                  return func(*args, **kwargs)
                File "/src/services/worker/src/worker/utils.py", line 127, in get_rows
                  rows_plus_one = list(itertools.islice(safe_iter(ds, dataset=dataset), rows_max_number + 1))
                File "/src/services/worker/src/worker/utils.py", line 478, in safe_iter
                  yield from ds.decode(False) if ds.features else ds
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2818, in __iter__
                  for key, example in ex_iterable:
                                      ^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2355, in __iter__
                  for key, pa_table in self._iter_arrow():
                                       ~~~~~~~~~~~~~~~~^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2380, in _iter_arrow
                  for key, pa_table in self.ex_iterable._iter_arrow():
                                       ~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 536, in _iter_arrow
                  for key, pa_table in iterator:
                                       ^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 419, in _iter_arrow
                  for key, pa_table in self.generate_tables_fn(**gen_kwags):
                                       ~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
                  self._cast_table(pa_table, json_field_paths=json_field_paths),
                  ~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
                  pa_table = table_cast(pa_table, self.info.features.arrow_schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2369, in table_cast
                  return cast_table_to_schema(table, schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2297, in cast_table_to_schema
                  raise CastError(
                  ...<3 lines>...
                  )
              datasets.table.CastError: Couldn't cast
              claim: string
              verdict: string
              reason: string
              prover: string
              to
              {'claim': Value('string'), 'verdict': Value('string'), 'prover': Value('string')}
              because column names don't match

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Formally Verified Financial-Engineering Claims

A small, machine-checked database of quantitative-finance claims that were either refuted by a formal counterexample or confirmed by a formal proof in Lean 4 / Mathlib. The point is discipline over folklore: each entry is settled by a kernel-checked artifact, not an appeal to authority.

refutations.jsonl — 7 widely-repeated claims that are false as usually stated, each with the counterexample that breaks it (e.g. naive tail-integral CVaR is not coherent; Kelly maximizes E[log W], not E[W]; a symmetric random walk is an unbounded martingale).
confirmations.jsonl — 40 standard results confirmed by formal proof (ES/Rockafellar–Uryasev coherence, put–call parity, Cramér–Rao, Gale–Shapley stability, VCG strategy-proofness, …).

Each row: { "claim", "verdict", "reason"?, "prover" }.

Why

Practitioner intuition is often almost right in a way that fails at the edge — the sign flip, the negative-c scaling, the unbounded tail. Publishing the refutations, not just the confirmations, is the honest half of the ledger. All verdicts are reproducible against the Lean 4 / Mathlib sources.

Scope and limitations

This is a curated slice of standard, publicly-known results — a demonstration of the formal-verification method applied to quant finance, not an exhaustive library. Claims are settled relative to their stated hypotheses; a "REFUTED" verdict means the claim is false as commonly stated, and the reason names the missing condition.

Citation

Formally Verified Financial-Engineering Claims. Lean 4 / Mathlib. 2026. https://sunlitmoon.online

Companion CLI: SMC17/formal-counterex-zig.

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Formally Verified Financial-Engineering Claims

Contents

Why

Scope and limitations

Citation