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# --------------------------------
# Independent studies on the same topic will produce
# similar but never identical numbers.
# Random sampling variation guarantees this.
#
# When two papers report the exact same mean to four
# decimal places, the same standard deviation, the same
# sample size, and the same p-value β they are not
# independent. One copied from the other, or both
# copied from a shared fabricated source.
#
# This module extracts the numerical fingerprint of a
# single paper: every mean, SD, sample size, percentage,
# correlation, and p-value it reports.
#
# That fingerprint can then be compared against others.
# But even in isolation, the fingerprint reveals problems:
# numbers that are suspiciously round, values that are
# mathematically impossible given each other, and
# distributions of digits that do not look like real data.
#
# A paper's numbers should look like they came from
# the world. When they look like they came from a
# spreadsheet cell someone typed by hand β that is a signal.
import re
import math
from dataclasses import dataclass, field
from collections import Counter
# ββ data structures ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
@dataclass
class NumericFingerprint:
means: list
std_devs: list
sample_sizes: list
percentages: list
correlations: list
p_values: list
all_decimals: list
@dataclass
class DataFingerprintFlag:
flag_type: str
severity: str
description: str
evidence: str
suggestion: str
@dataclass
class DataFingerprintResult:
fingerprint: NumericFingerprint
total_numbers: int
round_number_ratio: float
terminal_digit_bias: float
impossible_pairs: list
suspicious_duplicates: list
fingerprint_score: float
risk_level: str
summary: str
flags: list
flags_count: int
# ββ main class ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
class DataFingerprintAnalyzer:
"""
Extracts the complete numerical fingerprint of a paper
and tests it for signs of fabrication or cloning.
Four detection layers:
1. Round number bias β fabricated data rounds too cleanly
2. Terminal digit bias β humans avoid certain ending digits
3. Impossible value pairs β SD larger than mean for positive scales
4. Suspicious internal duplicates β same value repeated too often
"""
# regex patterns for specific statistical values
_MEAN_PATTERN = re.compile(
r'(?:mean|average|M)\s*[=:]\s*(-?\d+\.?\d*)', re.IGNORECASE
)
_SD_PATTERN = re.compile(
r'(?:SD|S\.D\.|std|standard deviation)\s*[=:]\s*(\d+\.?\d*)',
re.IGNORECASE
)
_N_PATTERN = re.compile(
r'(?:N|n|sample size)\s*[=:]\s*(\d+)', re.IGNORECASE
)
_PCT_PATTERN = re.compile(
r'(\d+\.?\d*)\s*%'
)
_CORR_PATTERN = re.compile(
r'(?:r|correlation)\s*[=:]\s*(-?\d*\.?\d+)', re.IGNORECASE
)
_PVAL_PATTERN = re.compile(
r'p\s*[=<>]\s*(0?\.\d+|\d+\.\d+[eE][+-]?\d+)', re.IGNORECASE
)
def analyze(self, text: str) -> DataFingerprintResult:
fp = self._extract_fingerprint(text)
flags = []
round_ratio = self._check_round_number_bias(fp, flags)
terminal_bias = self._check_terminal_digit_bias(fp, flags)
impossible = self._check_impossible_pairs(fp, flags)
duplicates = self._check_suspicious_duplicates(fp, flags)
total = self._count_total(fp)
score = self._compute_score(
round_ratio, terminal_bias, impossible, duplicates, total
)
level = self._get_risk_level(score)
return DataFingerprintResult(
fingerprint = fp,
total_numbers = total,
round_number_ratio = round(round_ratio, 3),
terminal_digit_bias = round(terminal_bias, 3),
impossible_pairs = impossible,
suspicious_duplicates = duplicates,
fingerprint_score = round(score, 3),
risk_level = level,
summary = self._write_summary(flags, level, total),
flags = flags,
flags_count = len(flags),
)
# ββ extraction βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _extract_fingerprint(self, text: str) -> NumericFingerprint:
means = self._parse_floats(self._MEAN_PATTERN, text)
std_devs = self._parse_floats(self._SD_PATTERN, text)
sample_sizes = self._parse_ints( self._N_PATTERN, text)
percentages = self._parse_floats(self._PCT_PATTERN, text)
correlations = self._parse_floats(self._CORR_PATTERN, text)
p_values = self._parse_floats(self._PVAL_PATTERN, text)
# all decimal numbers in the paper for digit-level analysis
all_decimals = [
float(m.group())
for m in re.finditer(r'-?\d+\.\d+', text)
if self._safe_float(m.group()) is not None
]
return NumericFingerprint(
means = means,
std_devs = std_devs,
sample_sizes = sample_sizes,
percentages = percentages,
correlations = correlations,
p_values = p_values,
all_decimals = all_decimals,
)
def _parse_floats(self, pattern: re.Pattern, text: str) -> list:
results = []
for match in pattern.finditer(text):
val = self._safe_float(match.group(1))
if val is not None:
results.append(val)
return results
def _parse_ints(self, pattern: re.Pattern, text: str) -> list:
results = []
for match in pattern.finditer(text):
try:
val = int(match.group(1))
if 1 <= val <= 1_000_000:
results.append(val)
except (ValueError, IndexError):
pass
return results
def _safe_float(self, raw: str) -> float:
try:
return float(raw.strip())
except (ValueError, AttributeError):
return None
# ββ detection checks βββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _check_round_number_bias(
self, fp: NumericFingerprint, flags: list
) -> float:
"""
Real data does not round to whole numbers or .5 steps very often.
When more than 60% of reported values are suspiciously round,
someone likely typed them rather than computed them.
"""
all_vals = fp.means + fp.std_devs + fp.percentages
if len(all_vals) < 4:
return 0.0
round_count = sum(
1 for v in all_vals
if v == round(v, 0) or v == round(v, 1) and str(v).endswith(('0', '5'))
)
ratio = round_count / len(all_vals)
if ratio >= 0.60:
flags.append(DataFingerprintFlag(
flag_type = "round_number_bias",
severity = "medium",
description = (
f"{round_count}/{len(all_vals)} reported values "
f"({round(ratio * 100, 1)}%) are suspiciously round. "
f"Real measured data rarely rounds this cleanly."
),
evidence = (
f"Round values detected among means, SDs, and percentages. "
f"Round ratio: {round(ratio, 3)}."
),
suggestion = (
"Verify that reported values are directly from analysis "
"output, not manually entered approximations."
),
))
return ratio
def _check_terminal_digit_bias(
self, fp: NumericFingerprint, flags: list
) -> float:
"""
The last digit of a truly random number is uniformly distributed
across 0-9. Humans fabricating numbers unconsciously prefer
certain digits (0, 5) and avoid others (7, 9).
A chi-square test on terminal digits detects this.
"""
all_vals = fp.all_decimals + [float(n) for n in fp.sample_sizes]
if len(all_vals) < 10:
return 0.0
terminals = []
for v in all_vals:
parts = str(abs(v)).replace('.', '')
if parts:
terminals.append(int(parts[-1]))
if not terminals:
return 0.0
counter = Counter(terminals)
expected = len(terminals) / 10.0
chi_sq = sum(
((counter.get(d, 0) - expected) ** 2) / expected
for d in range(10)
)
# chi-square critical value at p=0.05 with 9 df is 16.92
bias_score = min(chi_sq / 50.0, 1.0)
if chi_sq >= 16.92:
dominant_digit = counter.most_common(1)[0]
flags.append(DataFingerprintFlag(
flag_type = "terminal_digit_bias",
severity = "medium",
description = (
f"Terminal digit distribution deviates significantly "
f"from uniform expectation. "
f"Chi-square statistic: {round(chi_sq, 2)} "
f"(critical value: 16.92). "
f"This pattern is consistent with human number fabrication."
),
evidence = (
f"Most frequent terminal digit: "
f"'{dominant_digit[0]}' appears {dominant_digit[1]} times. "
f"Expected uniform frequency: {round(expected, 1)} each."
),
suggestion = (
"Re-examine raw data files to confirm reported values "
"match analysis output. Terminal digit bias is a "
"well-established fabrication marker."
),
))
return round(bias_score, 3)
def _check_impossible_pairs(
self, fp: NumericFingerprint, flags: list
) -> list:
"""
Statistical relationships constrain what values can coexist.
SD > mean is impossible for strictly positive Likert-scale data.
Correlation outside [-1, 1] is mathematically impossible.
P-value outside [0, 1] cannot exist.
"""
impossible = []
# SD > mean for positive scales (Likert 1-7, reaction times, etc.)
for mean, sd in zip(fp.means, fp.std_devs):
if mean > 0 and sd > mean * 2:
pair = f"M={mean}, SD={sd}"
impossible.append(pair)
if impossible:
flags.append(DataFingerprintFlag(
flag_type = "impossible_sd_mean_pair",
severity = "high",
description = (
f"{len(impossible)} mean/SD pair(s) where the standard "
f"deviation is implausibly large relative to the mean. "
f"For bounded positive scales, SD > 2*mean is suspicious."
),
evidence = f"Impossible pairs: {impossible[:3]}.",
suggestion = (
"Verify these values against the original analysis output. "
"Large SDs relative to means may indicate data entry error "
"or scale confusion."
),
))
# correlation outside valid range
bad_corr = [r for r in fp.correlations if abs(r) > 1.0]
if bad_corr:
impossible.extend([f"r={r}" for r in bad_corr])
flags.append(DataFingerprintFlag(
flag_type = "impossible_correlation",
severity = "high",
description = (
f"{len(bad_corr)} correlation value(s) outside [-1, 1]. "
f"These values are mathematically impossible."
),
evidence = f"Invalid correlations: {bad_corr}.",
suggestion = "Correct these values before submission.",
))
# p-value outside [0, 1]
bad_p = [p for p in fp.p_values if p < 0 or p > 1]
if bad_p:
impossible.extend([f"p={p}" for p in bad_p])
flags.append(DataFingerprintFlag(
flag_type = "impossible_p_value",
severity = "high",
description = (
f"{len(bad_p)} p-value(s) outside [0, 1]. "
f"These values cannot exist."
),
evidence = f"Invalid p-values: {bad_p}.",
suggestion = "Check analysis code for unit or scale errors.",
))
return impossible
def _check_suspicious_duplicates(
self, fp: NumericFingerprint, flags: list
) -> list:
"""
The same specific decimal value appearing 3+ times in a paper
is unusual unless it is a threshold or constant.
In fabricated data, a single invented number gets reused.
"""
all_vals = fp.means + fp.std_devs + fp.percentages + fp.correlations
if len(all_vals) < 6:
return []
counter = Counter(all_vals)
duplicates = [
v for v, count in counter.items()
if count >= 3 and v not in (0.0, 1.0, 0.5, 100.0, 0.05)
]
if duplicates:
flags.append(DataFingerprintFlag(
flag_type = "suspicious_value_repetition",
severity = "medium",
description = (
f"{len(duplicates)} specific value(s) appear 3 or more "
f"times across different reported statistics. "
f"Genuine independent measurements rarely share "
f"exact decimal values."
),
evidence = (
f"Repeated values: "
f"{[round(v, 4) for v in duplicates[:5]]}."
),
suggestion = (
"Verify that repeated values reflect genuinely "
"identical measurements and are not copy-paste artifacts."
),
))
return duplicates
# ββ helpers ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _count_total(self, fp: NumericFingerprint) -> int:
return (
len(fp.means) + len(fp.std_devs) + len(fp.sample_sizes) +
len(fp.percentages) + len(fp.correlations) + len(fp.p_values)
)
# ββ scoring ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _compute_score(
self,
round_ratio: float,
terminal_bias: float,
impossible: list,
duplicates: list,
total: int,
) -> float:
if total == 0:
return 0.0
impossible_score = min(len(impossible) * 0.25, 1.0)
duplicate_score = min(len(duplicates) * 0.15, 1.0)
score = (
round_ratio * 0.25 +
terminal_bias * 0.25 +
impossible_score * 0.35 +
duplicate_score * 0.15
)
return min(score, 1.0)
def _get_risk_level(self, score: float) -> str:
if score >= 0.70: return "critical"
if score >= 0.45: return "high"
if score >= 0.25: return "medium"
return "low"
def _write_summary(
self, flags: list, risk_level: str, total: int
) -> str:
if total == 0:
return (
"Data Fingerprint Analysis: No statistical values extracted. "
"Include explicit M=, SD=, N=, r=, and p= reporting "
f"for full analysis. Risk level: {risk_level.upper()}."
)
if not flags:
return (
f"Data Fingerprint Analysis: {total} statistical value(s) "
f"analyzed. No fabrication signals detected. "
f"Numerical patterns appear consistent with genuine data. "
f"Risk level: {risk_level.upper()}."
)
high = sum(1 for f in flags if f.severity == "high")
medium = sum(1 for f in flags if f.severity == "medium")
parts = []
if high:
parts.append(
f"{high} impossible value{'s' if high > 1 else ''} detected"
)
if medium:
parts.append(
f"{medium} fabrication signal{'s' if medium > 1 else ''} found"
)
return (
f"Data Fingerprint Analysis: {total} value(s) analyzed. "
f"{'; '.join(parts)}. "
f"Risk level: {risk_level.upper()}."
) |