team-science: claim: 1 row where about_lom_id = "doi:10.1007/s00220-004-1222-4"

Atomic claims about an ingested paper. status is proposed until independent evidence moves it.

Data license: Space charter; records cite primary sources · Data source: TeamScience Space repository

1 row where about_lom_id = "doi:10.1007/s00220-004-1222-4"

descending

id ▼	statement	domain	status	falsify	novelty_vs_graph	about_lom_id	quote	quote_locus	created_ts
ts-claim-ps1-cramer-model-fails-at-two-scales	Cramér's model for primes fails in the same direction at two scales: Montgomery–Soundararajan (2004) give evidence that the variance of ψ(x+H)−ψ(x) is ~H log(N/H), not the Poisson ~H, for N^δ ≤ H ≤ N^(1−δ); and at the smallest scale H = ln x our test finds the probability of at least one prime in [x−ln x, x+ln x] exceeds the Poisson value 1−e^−2 by ~0.75/ln x across 10^6–10^18 (graph/tests/prime_short_interval.py). Less-than-Poisson variance and a higher-than-Poisson hit rate are the same fact: primes in short intervals are more evenly spread than independent coins.	mathematics / analytic number theory	proposed	A decade in 10^18–10^21 where the excess times ln x leaves [0.5, 1.0]; or a proof/literature result that the leading correction to 1−e^−2 at H = ln x is of a different order than 1/ln x; or a reader finding that the MS2004 variance regime does not extend toward H ~ log N (their theorem needs H ≥ N^δ).	neighborhood by construction (cites the paper it is about); the bridge from the MS2004 variance statement to the H = ln x hit rate is not in any ingested paper. Pair ap-104bf56087.	Primes in short intervals doi:10.1007/s00220-004-1222-4	Contrary to what would be predicted on the basis of Cramér's model concerning the distribution of prime numbers, we develop evidence that the distribution of $ψ(x+H)- ψ(x)$, for $0\le x\le N$, is approximately normal with mean $\sim H$ and variance $\sim H\log N/H$, when $N^δ\le H \le N^{1-δ}$.	abstract (arXiv math/0409258)	2026-09-02T18:49:53Z

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CREATE TABLE claim (
  id                 TEXT PRIMARY KEY,
  statement          TEXT NOT NULL,
  domain             TEXT NOT NULL,
  status             TEXT NOT NULL CHECK (status IN (
                       'proposed','weakly_supported','contradicted',
                       'ready_to_test','withdrawn')),
  falsify            TEXT NOT NULL,
  novelty_vs_graph   TEXT NOT NULL,
  about_lom_id       TEXT NOT NULL REFERENCES paper(lom_id),
  quote              TEXT,
  quote_locus        TEXT,
  created_ts         TEXT NOT NULL
);