Published constants that agree with simple closed forms for 16 to 62 significant digits — and exact proofs that every one of them is lying. Digit agreement to any depth is not evidence, and this page is the demonstration: each of these impersonations would pass any decimal screen ever used to announce a discovery.
Published, not peer-reviewed, not independently rerun. Verdicts are conditional on the OEIS published digit streams being correct — a refutation here reads "not equal, given those digits".
The engine's double-precision screen tests each constant against ~14,000 closed-form spellings at 17 significant digits. For 5 constants, at least one rational value survived that screen — the constant and the form genuinely share 17 leading digits. Those survivors are re-decided at the FULL published precision, exactly:
where D is the published digit stream read as a k-digit integer and P/Q is the form's mantissa scaled to [1, 10). Everything in that line is a BigInt; the verdict is an integer comparison. No float participates, so there is no precision to argue about: the form either fits inside the digit interval or it provably does not.
The instrument is calibrated in the other direction on every build: constants whose closed form IS the truth (sqrt 2, pi, e, phi, ln 2 …) must keep their forms — zero false refutations is a gate in tools/test-engine.js, and it once caught this engine refuting sqrt(2) as the closed form of the decimal expansion of sqrt(2).
| entry | what OEIS says it is | impersonates | as spelled by the vocabulary | digits agree / published | verdict |
|---|---|---|---|---|---|
| A271880 | Decimal expansion of the probability that a random real n… | 2 | 2/1 sqrt(4/1) cbrt(8/1) sqrt2^(2/1) | 62 / 105 | refuted exactly |
| A271880 | Decimal expansion of the probability that a random real n… | 20 | 20/1 | 62 / 105 | refuted exactly |
| A271880 | Decimal expansion of the probability that a random real n… | 1/5 | 1/5 | 62 / 105 | refuted exactly |
| A181284 | Decimal expansion of sqrt(9/121 * 100^m + (112 - 44*m)/12… | 3/11 | 3/11 | 58 / 105 | refuted exactly |
| A181284 | Decimal expansion of sqrt(9/121 * 100^m + (112 - 44*m)/12… | 30/11 | 30/11 | 58 / 105 | refuted exactly |
| A359187 | Decimal expansion of the real part of (-sqrt(2))^^9, wher… | 1 | 1/1 sqrt(1/1) cbrt(1/1) | 44 / 87 | refuted exactly |
| A359187 | Decimal expansion of the real part of (-sqrt(2))^^9, wher… | 10 | 10/1 | 44 / 87 | refuted exactly |
| A359187 | Decimal expansion of the real part of (-sqrt(2))^^9, wher… | 1/10 | 1/10 | 44 / 87 | refuted exactly |
| A226120 | Decimal expansion of Sum_{n>=1} n^3/(exp(2*Pi*n/7)-1). | 1 | 1/1 sqrt(1/1) cbrt(1/1) | 16 / 100 | refuted exactly |
| A226120 | Decimal expansion of Sum_{n>=1} n^3/(exp(2*Pi*n/7)-1). | 10 | 10/1 | 16 / 100 | refuted exactly |
| A226120 | Decimal expansion of Sum_{n>=1} n^3/(exp(2*Pi*n/7)-1). | 1/10 | 1/10 | 16 / 100 | refuted exactly |
| A266296 | Decimal expansion of a number close to 24, related to the… | 24 | 24/1 | 16 / 105 | refuted exactly |
| A266296 | Decimal expansion of a number close to 24, related to the… | 12/5 | 12/5 | 16 / 105 | refuted exactly |
| A266296 | Decimal expansion of a number close to 24, related to the… | 6/25 | 6/25 | 16 / 105 | refuted exactly |
Multiple spellings of one value (sqrt(4/1), cbrt(8/1), sqrt2^(2/1) are all 2) are listed together and counted separately — the vocabulary generates forms, and every generated form that fit at 17 digits was individually put to the exact test.
Digit-matching pipelines — the Ramanujan Machine's published methodology among them — declare a hit when a computed value agrees with a closed form to some tens of digits, and argue from collision probability that the match is almost certainly an identity. This catalog is the reverse experiment on the same kind of data: here are constants that sustain the match to 62 digits and are provably NOT the number they resemble.
A271880 — the probability that a random real is "evil" — agrees with 1/5 for 62 digits before diverging; OEIS records the difference separately (A271881, about 2.17e-64). Any screen shallower than 64 digits calls this 1/5.
A266296 is literally named "a number close to 24, related to the Ramanujan constant" — the near-integer phenomenon that made e^(pi sqrt 163) famous, caught here impersonating 24 for 16 digits and refuted at 105.
The point is not that these five are surprising — OEIS contributors know them. The point is that a probability argument cannot tell these five from a real identity, and an exact decision can. A pipeline whose screening step can mint false positives is indistinguishable from one that cannot; the cure is a certificate, and each row of this catalog carries one: a single integer inequality anyone can recheck.