Statistical Reporting Standards — Statistical Reporting Standards & APA 7.0 Format Quick Reference

This document defines the complete review standards for statistical reporting in quantitative research. methodology_reviewer_agent uses this document as the primary reference in Step 4a (Statistical Reporting Adequacy).

1. Universal Statistical Reporting Checklist

All quantitative research papers must report the following items. Check each item during review:

1.1 Descriptive Statistics

Item	Standard	Common Omission
Mean (M)	Must be reported for all continuous variables	Only overall reported, not by group
Standard deviation (SD)	Must appear paired with the mean	Standard error (SE) used incorrectly in place of SD
Sample size (N / n)	Both total and group sample sizes must be reported	Sample attrition during analysis unexplained
Range	Report Min-Max or interquartile range	Completely absent, unable to judge distribution characteristics
Categorical variable distribution	Report frequency (f) and percentage (%)	Only percentage reported, missing raw frequency

1.2 Effect Size

Item	Standard	Common Omission
Reporting obligation	All statistical tests must be accompanied by effect sizes — APA 7.0 mandatory requirement	Only p-value reported, no effect size
Select appropriate metric	Choose effect size metric corresponding to the analysis method (see Section 2)	Inappropriate effect size metric used
Interpretation	Must provide Cohen's conventional benchmarks or field-specific benchmarks	Numbers reported but magnitude not interpreted

Common Effect Size Metrics Quick Reference:

Analysis Method	Effect Size Metric	Small/Medium/Large (Cohen's Convention)
t-test	Cohen's d	0.2 / 0.5 / 0.8
ANOVA	eta-squared	.01 / .06 / .14
ANOVA (partial)	partial eta-squared	.01 / .06 / .14
Correlation	r	.10 / .30 / .50
Regression	R-squared, f-squared	f-squared: .02 / .15 / .35
Chi-square	Cramer's V, phi	V: .10 / .30 / .50 (df=1)
Odds Ratio	OR	1.5 / 2.5 / 4.3 (Rosenthal)

1.3 Confidence Intervals

Item	Standard	Common Omission
CI reporting	All effect sizes and key estimates should report 95% CI	CI completely absent
Format	95% CI [lower bound, upper bound]	Inconsistent format or using parentheses instead of brackets
Interpretation	Describe the substantive meaning of the CI, not just statistical meaning	Only checking whether CI includes zero, not interpreting width

1.4 Statistical Significance

Item	Standard	Common Omission
p-value format	Report exact p value (e.g., p = .032)	Only reporting p < .05 or p > .05
p < .001	Can report p < .001 when p is very small	Reporting p = .000 (raw statistical software output)
Alpha level	Declare alpha level a priori	Failure to state whether alpha = .05 or another value
Multiple comparisons	Use Bonferroni, Holm, FDR correction	Multiple comparisons without any correction
Non-significant results	Must be fully reported; cannot be hidden	Selectively reporting only significant results

1.5 Statistical Power

Item	Standard	Common Omission
A priori power analysis	State target power (typically >= .80), assumed effect size, alpha, required sample size	Power analysis completely absent
Effect size source	Based on prior research, pilot study, or theoretical expectation	Using Cohen's convention without explanation
Tool	Use G*Power, pwr package, etc.	Tool not specified
Post-hoc power	Report observed power for non-significant results	Type II error risk not discussed for non-significant results
Sensitivity analysis	Report the minimum detectable effect size given N	Sensitivity analysis not conducted

1.6 Missing Data Handling

Item	Standard	Common Omission
Missing data reporting	Report missing data amount and proportion for each variable	Missing data situation not reported
Missing mechanism	Discuss MCAR / MAR / MNAR	MCAR assumed without testing
Handling method	State the method used: listwise deletion / pairwise deletion / MI / FIML	Not stated or only using listwise deletion
Sensitivity analysis	Compare result robustness across different missing data handling methods	Only one method used, sensitivity not tested

1.7 Assumption Testing

Assumption	Applicable Analysis	Testing Method	Common Omission
Normality	t-test, ANOVA, regression	Shapiro-Wilk / K-S / Q-Q plot / skewness & kurtosis	Completely untested or only invoking CLT
Homogeneity of variance	Independent t-test, ANOVA	Levene's test	Not reported or alternative method not used when violated
Linearity	Regression, correlation	Residual plot / scatter plot	Linearity assumed without testing
Independence	Most parametric tests	Durbin-Watson / research design explanation	Nested data not handled
Multicollinearity	Multiple regression	VIF, tolerance, correlation matrix	VIF not reported or reported but not addressed
Residual normality / homoscedasticity	Regression	Residual plot, Breusch-Pagan	Residuals not checked after model fitting

2. Method-Specific Checklists

2.1 t-test (Independent / Paired Samples)

Check Item	Description
Report t statistic	t(df) = X.XX, p = .XXX
Independent vs paired	Correct selection? Paired designs need to report pairing logic
Effect size	Cohen's d (independent) or d_z (paired)
Assumption testing	Normality (important for small samples), homogeneity of variance (independent t-test)
Welch's t-test	Is Welch correction used when variances are unequal?
Directionality	Is one-tailed vs two-tailed supported by a priori theoretical basis?

2.2 ANOVA (One-Way / Factorial / Repeated Measures)

Check Item	Description
Report F statistic	F(df1, df2) = X.XX, p = .XXX
Effect size	eta-squared, partial eta-squared, or omega-squared
Post-hoc comparisons	When main effect is significant, are post-hoc tests done (Tukey / Bonferroni / Games-Howell)?
Interaction effects	In factorial designs, are interactions interpreted? Are simple effects tested?
Sphericity assumption	For repeated measures, is Mauchly's test reported + Greenhouse-Geisser / Huynh-Feldt correction?
Assumption testing	Normality, homogeneity of variance (Levene's), independence of between-group observations
Unequal group sizes	When group sizes differ substantially, is Type III SS used?

2.3 Regression Analysis (Linear / Logistic)

Linear Regression

Check Item	Description
Model summary	R-squared, adjusted R-squared, F test for model
Coefficient table	B, SE, beta, t, p, 95% CI for B
Multicollinearity	VIF (< 5 or < 10 depending on field convention), tolerance
Residual diagnostics	Normality, homoscedasticity, linearity, outliers (Cook's D)
Variable selection	Rationale for enter vs stepwise method
Effect size	R-squared, f-squared, Cohen's f-squared

Logistic Regression

Check Item	Description
Model fit	Hosmer-Lemeshow / chi-squared / -2LL / Nagelkerke R-squared
Coefficient reporting	B, SE, Wald, OR, 95% CI for OR
Classification accuracy	Classification table, sensitivity, specificity, AUC/ROC
Assumptions	Independence of observations, linearity in the logit (linear relationship between continuous predictors and logit)
Sample size	At least 10-20 events per predictor variable (EPV rule)

2.4 Structural Equation Modeling (SEM)

Check Item	Standard
Sample size	Typically >= 200; or 5-10 times the number of estimated parameters
Model fit indices	Must report multiple indices simultaneously (at least 4)
CFI / TLI	>= .95 (good); >= .90 (acceptable)
RMSEA	<= .06 (good); <= .08 (acceptable); must report 90% CI
SRMR	<= .08
chi-squared/df	<= 3 (some scholars suggest <= 2)
Factor loadings	Standardized >= .50 (ideal >= .70)
Measurement model	CFA before SEM (two-step approach) — Anderson & Gerbing (1988)
Reliability and validity	CR >= .70, AVE >= .50, discriminant validity (Fornell-Larcker / HTMT)
Modification indices	When using modification indices, must have theoretical support
Normality	Multivariate normality (Mardia's coefficient); when violated, use robust ML or bootstrapping

2.5 Hierarchical Linear Modeling (HLM / MLM)

Check Item	Standard
Nested structure	Clearly explain each level (e.g., students -> classes -> schools)
ICC	Report Intraclass Correlation Coefficient; ICC > .05 supports using MLM
Random effects	Report random intercept and (if applicable) random slope variances
Fixed effects	Report coefficients, SE, t / z, p, CI
Between-group sample size	Level-2 unit count (typically recommended >= 30)
Centering	Explain whether grand-mean centering or group-mean centering is used and why
Model comparison	Use deviance (-2LL), AIC, BIC to compare nested models
Effect size	Pseudo R-squared (e.g., Snijders & Bosker's R-squared)

2.6 Chi-Square Test

Check Item	Description
Reporting format	chi-squared(df, N = XX) = X.XX, p = .XXX
Effect size	Cramer's V (larger than 2x2) or phi (2x2)
Expected frequencies	All cells expected frequency >= 5; if any cell < 5, use Fisher's exact test
Independence	Are observations truly independent? (Repeated measures are not suitable for ordinary chi-square)
Residual analysis	When significant, check standardized residuals to determine which cells contribute to significance

2.7 Non-Parametric Tests

Check Item	Description
Justification for use	Clearly explain why parametric tests are not used (e.g., normality violation, ordinal scale)
Method selection	Mann-Whitney U / Wilcoxon / Kruskal-Wallis / Friedman — is the correct test matched
Effect size	r = Z / sqrt(N) (Mann-Whitney); W (Kendall's)
Reporting format	Report test statistic, p-value, effect size
Post-hoc comparisons	After significant Kruskal-Wallis, pairwise comparisons + correction needed

3. APA 7th Edition Statistical Format Quick Reference

3.1 Number Formatting

Rule	Correct	Incorrect
p-value no leading zero	p = .032	p = 0.032
Statistics that can exceed 1.0 have leading zero	M = 0.75	M = .75
Statistics that cannot exceed 1.0 have no leading zero	r = .45	r = 0.45
Generally 2 decimal places	M = 3.45	M = 3.4
p-value 2-3 decimal places	p = .03 or p = .032	p = .0321
Percentages 0-1 decimal places	45.2%	45.2381%

Statistics that cannot exceed 1.0 (no leading zero): correlation coefficients (r, R), proportions (p-value), Cramer's V, phi, eta-squared, R-squared, beta (standardized regression coefficient)

Statistics that can exceed 1.0 (leading zero): M, SD, B (unstandardized regression coefficient), Cohen's d, t, F, chi-squared

3.2 Statistical Symbol Italicization Rules

Italic	Non-italic
M, SD, SE	df
N (total sample), n (subsample)	SS, MS
t, F, p, r, R, z	OR, CI, VIF
d, f-squared, eta-squared, omega-squared	AIC, BIC, CFI, TLI
B, beta	RMSEA, SRMR
chi-squared	ICC
U, W (non-parametric statistics)	ANOVA, SEM, HLM

3.3 Statistical Results Reporting Format Examples

Analysis Method	APA Format Example
Independent samples t-test	t(58) = 2.45, p = .017, d = 0.63, 95% CI [0.12, 1.14]
Paired samples t-test	t(29) = -3.12, p = .004, d_z = 0.57
One-way ANOVA	F(2, 87) = 4.56, p = .013, partial eta-squared = .09
Linear regression	B = 0.34, SE = 0.12, beta = .28, t(95) = 2.83, p = .006, 95% CI [0.10, 0.58]
Logistic regression	B = 1.24, SE = 0.45, Wald = 7.59, p = .006, OR = 3.46, 95% CI [1.43, 8.37]
Chi-square	chi-squared(2, N = 150) = 8.34, p = .015, V = .24
Mann-Whitney	U = 245.00, z = -2.31, p = .021, r = .29
SEM fit	chi-squared(52) = 78.34, p = .011, CFI = .97, TLI = .96, RMSEA = .045 [.018, .068], SRMR = .038
HLM fixed effects	gamma_10 = 0.45, SE = 0.15, t(28) = 3.00, p = .006

3.4 Table Format Standards

Rule	Description
Three-line table	APA tables have only three horizontal lines (above header, below header, bottom of table), no vertical lines
Table numbering	Table 1, Table 2... (bold), title on the line below the number (italic)
Note levels	General note (Note.) -> Specific note (superscript a, b) -> Significance (p < .05, *p < .01)
Asterisks	p < .05. p < .01. **p < .001.
Alignment	Numbers right-aligned, decimal points aligned

4. Statistical Red Flags

The following patterns during review should raise red flags, requiring further investigation or author clarification:

Triage levels, not finding severities (#574 A3). The HIGH/MEDIUM/LOW labels in the tables below rank how urgently a red flag deserves scrutiny — they are detection triage, never a severity vocabulary. When a red flag becomes a reported weakness, its severity is the Schema 6 enum (Critical / Major / Minor), assigned by decision impact per the Finding Contract — never copied from the triage label.

4.1 P-hacking Indicators

Red Flag	Description	Severity
Many p near .05	Multiple results with p concentrated in the .04-.05 range	HIGH
Selective reporting	Only significant results reported, non-significant ones disappeared	HIGH
Vague analysis strategy	Analysis strategy not stated a priori, appears exploratory in hindsight	MEDIUM
Unexpected subgroups	Post-hoc subgroup decomposition to find significant results	MEDIUM
Flexible sample size	No pre-defined stopping rule (sequential testing without correction)	HIGH
"Excluding outliers"	Large number of outliers excluded with unclear criteria	MEDIUM

4.2 HARKing (Hypothesizing After Results are Known)

Red Flag	Description	Severity
Perfect hypothesis-result match	All hypotheses supported without exception	MEDIUM
Exploratory analysis packaged as confirmatory	Literature review clearly constructed post-hoc	HIGH
Hypothesis directionality change	Originally predicted positive but result was negative, yet claimed "as expected"	HIGH
No pre-registration	No OSF / AsPredicted pre-registration link provided (not mandatory but recommended)	LOW

4.3 Missing Effect Sizes and Confidence Intervals

Red Flag	Description	Severity
No effect sizes reported at all	Conclusions based solely on p-values	HIGH
CI completely absent	Cannot judge estimation precision	MEDIUM
Extremely wide CI	CI spans from small to large effect sizes, imprecise estimation	MEDIUM
Inconsistent effect sizes	Reported effect sizes inconsistent with calculations from raw data	HIGH

4.4 Sample Size Issues

Red Flag	Description	Severity
No power analysis	Sample size lacks a priori calculation basis	MEDIUM
Sample too small	In regression analysis, N < 10 x number of predictors	HIGH
Unexplained sample attrition	Large gap between starting N and final N without explanation	MEDIUM
SEM small sample	N < 200 without small sample correction	MEDIUM
HLM Level-2 insufficient	Level-2 units < 30	MEDIUM

4.5 Uncorrected Multiple Comparisons

Red Flag	Description	Severity
Multiple t-tests instead of ANOVA	3+ group comparisons using multiple t-tests	HIGH
No post-hoc after ANOVA	Main effect significant but claiming group differences without post-hoc tests	MEDIUM
Multiple DVs uncorrected	Multiple dependent variables tested separately on the same dataset without Bonferroni or FDR	MEDIUM
Multiple model comparisons	Trying multiple models but only reporting "the best one"	HIGH

4.6 Assumption Violation

Red Flag	Description	Severity
Assumption testing completely absent	Skipping normality/homogeneity/linearity tests	MEDIUM
Violations not addressed	Violations reported but original analysis still used	HIGH
CLT as excuse	"Because N > 30, normality can be ignored" without actual testing	LOW
Excessive VIF	VIF > 10 but no action taken	HIGH

4.7 Other Red Flags

Red Flag	Description	Severity
p = .000	Raw statistical software output, should be p < .001	LOW
df inconsistent with N	N derived from degrees of freedom doesn't match reported N	HIGH
Inconsistent table numbers	Text narrative contradicts table values	HIGH
Statistical software not stated	Not reporting SPSS / R / Stata / Mplus and version	LOW
Causal language	Non-experimental designs (correlational/survey) using causal inference language	MEDIUM
Unreachable mean (GRIM)	A reported mean of discrete-scale data cannot be produced by any integer sum at the reported N and precision	HIGH
Unreachable SD (GRIMMER)	A reported SD of discrete-scale data is not attainable by any response distribution consistent with the reported mean and N	HIGH
p incompatible with statistic and df	The reported p matches neither tail reading of the reported test statistic at the reported df	HIGH

5. Common Statistical Methods in Higher Education Research

Higher education research papers frequently involve the following topics and corresponding analysis methods. This table can be referenced during review to judge whether method selection is appropriate.

5.1 Recommended Methods by Research Question Type

Research Question Type	Recommended Method	Description
Two-group comparison (e.g., experimental vs control)	Independent samples t-test / Mann-Whitney	Depending on data normality
Multi-group comparison (e.g., different institution types)	ANOVA / Kruskal-Wallis	Mean comparison for 3+ groups
Pre-post comparison	Paired t-test / Wilcoxon	Change within the same group
Predictive analysis (continuous DV)	Multiple regression	Multiple predictors' effects on continuous outcome
Predictive analysis (binary DV)	Logistic regression	E.g., graduation/dropout, pass/fail
Nested data (students -> schools)	HLM / MLM	Higher education data naturally has nested structure
Latent constructs and path analysis	SEM / CFA	Measuring unobservable constructs (e.g., teaching quality)
Scale reliability and validity	EFA -> CFA	Scale development or validation
Categorical variable association	Chi-square / Fisher's exact	Cross-tabulation analysis
Longitudinal data	Growth curve models / Latent growth models	Tracking student trajectories over multiple years
Large-scale datasets	Weighted analysis / sampling design correction	Accounting for sampling design when using national survey data

5.2 Special Considerations for Higher Education Research

Consideration	Description
Nested structure	Higher education data almost always has nesting (students -> departments -> institutions); ignoring it underestimates standard errors and inflates Type I error
Sampling design	When using national databases (e.g., MOE statistics, public higher education data), must account for sampling weights and clustering
Selection bias	Students self-select into departments/institutions, not randomly assigned; consider propensity score matching or Heckman correction
Ceiling effects	Satisfaction surveys often show extreme skewness; need to check and consider Tobit model or non-parametric methods
Small population	Taiwan has a limited number of universities (~150); census surveys are not appropriate for inferential statistics (census, not sample)
Time series	Analyzing multi-year enrollment trends requires considering autocorrelation
Multiple roles	Same faculty completing multiple surveys (e.g., teaching evaluations) -> observations not independent

6. Statistical Reporting Completeness Judgement

methodology_reviewer_agent assesses each applicable item against the study design, analysis, reporting standard, and target venue. There is no weighted completeness score: a missing decision-bearing item cannot be offset by complete presentation items.

Item	Criterion-bound judgement
Descriptive statistics	`COMPLETE` / `PARTLY_COMPLETE` / `MISSING` / `NOT_APPLICABLE`, with the applicable reporting requirement
Effect sizes	same states, with the analyses to which the requirement applies
Confidence intervals or other uncertainty	same states, with the estimates to which the requirement applies
Assumption checks	same states, naming only assumptions required by the methods used
Power or precision justification	same states, when required by design or inference
Missing-data handling	same states, with the observed omission or method anchored
Format and table requirements	same states, separated from substantive statistical validity
Red-flag follow-up	each triggered item investigated and resolved, left unresolved, or marked not applicable

For every PARTLY_COMPLETE or MISSING item, identify the manuscript location, the criterion source, why the omission matters, and whether it affects a substantive conclusion or only reporting clarity. Synthesize the result narratively; do not convert item states or counts into points, percentages, or a decision category.

7. Quick Reference: Recommended Review Sequence

Methodology reviewer should follow this sequence when reviewing statistical reporting:

Step 1: Confirm research question -> analysis method correspondence is reasonable (Section 5)
Step 2: Check whether assumption testing is reported (Section 1.7)
Step 3: Check universal checklist item by item (Sections 1.1-1.6)
Step 4: Consult method-specific checklist (Section 2)
Step 5: Scan red flag list (Section 4)
Step 6: Verify APA formatting (Section 3)
Step 7: Produce the criterion-bound completeness judgement and narrative synthesis (Section 6)

8. Bounded Arithmetic Recompute Procedures (#610)

Epistemic status — read this before anything below. This layer does not replace the human reviewer, and it does not make the reviewer's arithmetic trustworthy. What the engineering can force is narrow and should be named honestly: the receipt grammar (methodology seat, sprint Phase 2) forces every recomputation attempt to be declared, structured, and auditable — required fields present, closed enums respected, each mismatch linked to exactly one weakness. Triggering likewise rests on a mandatory declaration with adjudicated honesty, never machine-checked triggering: when nothing is recomputable the seat must say so (no_recomputable_statistics:), and the checker verifies only that the declaration exists — never that it is true; a false attestation over recomputable statistics surfaces at adjudication as MISSED verdicts. It cannot force the arithmetic inside a receipt to be correct; model arithmetic is not deterministic, and a fully conforming receipt built on wrong arithmetic is still wrong. Correctness is decided by human adjudication against the four-verdict scale (VERIFIED / CLAIM_ONLY / MISCOMPUTED / MISSED) defined in docs/design/2026-08-02-610-statistical-recompute-baseline-spec.md §7.1. Everything in this section is a bounded aid to that human judgment, never a substitute for it.

Four bounded procedures cover the recomputable slice of the red flags in Section 4. Normative worked cases and undecidable boundaries live in the #610 spec §5; this section is the reviewer-facing operating summary. Outside a procedure's boundary the honest status is not_computable with its closed reason — never an extended or improvised calculation.

8.1 `p_from_test_statistic`

Recompute a reported p from a named test family, statistic, and df. Prerequisites: test family, statistic value, required df, reported p, and the tail rule where it matters. F and chi-square are upper-tail by family; t/z results must never silently become two-tailed. When the paper states no tail, the receipt must show BOTH labeled values (two-tailed and one-tailed) — a single-tail comparison alone supports no verdict. If the tail choice flips the verdict, the status is not_computable (tail_ambiguous). Adjusted, bootstrap, permutation, or exact p values without their procedure are not_computable (nonstandard_p_procedure).

8.2 `grim`

Test whether a reported mean of discrete-scale data is reachable. Apply only to an unweighted mean with known discrete granularity, known item-specific analytic N, and a stated precision/rounding rule. The completed procedure requires the rounding interval implied by the reported precision AND the nearest attainable values straddling the reported mean — an integer-product observation without the rounding-interval reachability check is not a completed GRIM procedure. Continuous, weighted, imputed, transformed, composite, or item-averaged values with unknown granularity are not_computable.

8.3 `grimmer`

Inherits every GRIM prerequisite and additionally requires the SD convention (sample vs population), reported precision, and finite discrete support. A mismatch needs a completed reachability proof over the bounded response space; intuition that an SD "looks too small" is not a procedure. If the mean itself is GRIM-inconsistent, the status is not_computable (mean_grim_inconsistent).

8.4 `n_from_df`

Invert a reported df to a required sample size under a NAMED test-specific identity (df=N-1 one-sample/paired t; df=N1+N2-2 equal-variance independent t; the identity is not universal and the receipt must name it). Welch–Satterthwaite, Kenward–Roger, corrected repeated-measures, multiple-imputation, and mixed/clustered/robust/survey-weighted analyses are not_computable unless their required inputs are present. Chi-square df usually encode table dimensions and cannot be inverted to N.

8.5 Red-flag classification (arithmetic rows)

Every arithmetic-flavored red-flag row in Section 4 is classified below so that no row is silently claimed "solved" by the four procedures (#610 spec §8). Inclusion criterion: a Section 4 row appears here exactly when its red flag concerns reported numeric values or quantities derivable from them — whether by recomputation or by direct comparison against a stated numeric threshold; rows about narrative, design, or process conduct (causal language, HARKing, selective reporting, software not stated) stay outside this classification. Classes: covered (a bounded procedure recomputes it — emit a receipt when attempted), reporting-only (noticing and citing suffices; there is nothing to recompute), direct-threshold (a read-off comparison against a stated numeric threshold; report as a finding, no receipt), and not_computable (arithmetic in nature, but no bounded procedure exists yet — must NOT be presented as verified).

Red-flag row (Section 4)	Classification	Handling
df inconsistent with N (4.7)	covered	`n_from_df` receipt
Unreachable mean — GRIM (4.7)	covered	`grim` receipt
Unreachable SD — GRIMMER (4.7)	covered	`grimmer` receipt
p incompatible with statistic and df (4.7)	covered	`p_from_test_statistic` receipt
Inconsistent effect sizes (4.3)	not_computable	No bounded effect-size consistency procedure exists yet (a future separate addition per the #610 spec); flag the inconsistency as a finding, never as a verified recomputation
Many p near .05 (4.1)	reporting-only	Distributional suspicion; cite the values, no recompute
Sample too small, N < 10 × predictors (4.4)	direct-threshold	Read-off comparison; finding only
SEM small sample, N < 200 (4.4)	direct-threshold	Read-off comparison; finding only
HLM Level-2 units < 30 (4.4)	direct-threshold	Read-off comparison; finding only
Excessive VIF > 10 (4.6)	direct-threshold	Read-off comparison; finding only
p = .000 (4.7)	reporting-only	Format defect; no recompute
Inconsistent table numbers (4.7)	reporting-only	Internal-consistency contradiction; cite both surfaces, no bounded recompute

8.6 Receipt grammar pointer

Under a sprint contract, every attempted recomputation is recorded as an AR<n> Arithmetic Receipt in the methodology Phase 2 card — grammar, conditional fields, and mismatch-to-weakness linkage are normative in the agent's Phase 2 section (canonical source: references/reviewer_sprint_prompt_source.md, methodology-receipt fragment) and machine-checked by scripts/check_phase_conformance.py. Method references: Brown & Heathers (2017) GRIM, https://doi.org/10.1177/1948550616673876; Anaya (2016) GRIMMER, https://doi.org/10.7287/peerj.preprints.2400v1.

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