gbanyan
d3b63fc0b7
The within-auditor-year uniformity assumption (A2) introduced in v3.11
Section III-G was empirically tested via a new within-year uniformity
check (signature_analysis/27_within_year_uniformity.py; output in
reports/within_year_uniformity/). The check found that within-year
pairwise cosine distributions even at the calibration firm show
substantial heterogeneity inconsistent with strict single-mechanism
uniformity (Firm A 2023 CPAs typically have median pairwise cosine
around 0.85 with 20-70% of pairs below the all-pairs KDE crossover
0.837). A2 as stated ("a CPA who replicates any signature image in
that year is treated as doing so for every report") is therefore
falsified empirically.
Three explanations are compatible with the data and cannot be
disambiguated without manual inspection: (i) true within-year
mechanism mixing, (ii) multi-template replication workflows at the
same firm within a year, (iii) feature-extraction noise on repeatedly
scanned stamped images. Since A2 is falsified and its implications
cannot be restored under any of the three explanations, we remove
A2 entirely rather than downgrading it to an "approximation" or
"interpretive convention."
Changes applied:
1. Methodology Section III-G: A2 block deleted. Section now has only
A1 (pair-detectability, cross-year pair-existence). Replaced A2
with an explicit statement that we make no within-year or
across-year uniformity assumption, that per-signature labels are
signature-level quantities throughout, and that we abstain from
partner-level frequency inferences. Three candidate explanations
for within-year signature heterogeneity are listed (single-template
replication, multi-template replication in parallel, within-year
mixing, or combinations) without attempting disaggregation.
2. Methodology III-H strand 2 (L154) softened: "7.5% form a long left
tail consistent with a minority of hand-signers" rewritten as
reflecting "within-firm heterogeneity in signing output (we do not
disaggregate partner-level mechanism here; see Section III-G)."
3. Methodology III-H visual-inspection strand (L152) and the
corresponding Discussion V-C first strand (L41) and Conclusion L21
softened: "for the majority of partners" changed to "for many of
the sampled partners" (Codex round-14 MAJOR: "majority of partners"
is itself a partner-level frequency claim under the new scope-of-
claims regime).
4. Methodology III-K.3 Firm A anchor (L247): dropped "(consistent
with a minority of hand-signers)" parenthetical.
5. Results IV-D cosine distribution narrative (L72): softened to
"within-firm heterogeneity in signing outputs (see Section IV-E
and Section III-G for the scope of partner-level claims)."
6. Results IV-E cluster split framing (L128): "minority-hand-signers
framing of Section III-H" renamed to "within-firm heterogeneity
framing of Section III-H" (matches the new III-H text).
7. Results IV-H.1 partner-level reading (L286): removed entirely.
The v3.13 text "Under the within-year label-uniformity convention
A2, this left-tail share is read as a partner-level minority of
hand-signing CPAs" is replaced by a signature-level statement
that explicitly lists hand-signing partners, multi-template
replication, or a combination as possibilities without attempting
attribution.
8. Results IV-H.1 stability argument (L308): softened from "persistent
minority of hand-signing Firm A partners" to "persistent within-
firm heterogeneity component," preserving the substantive argument
that stability across production technologies is inconsistent with
a noise-only explanation.
9. Results IV-I Firm A Capture Profile (L407): rewrote the "Firm A's
minority hand-signers have not been captured" phrasing as a
signature-level framing about the 7.5% left tail not projecting
into the lowest-cosine document-level category under the dual-
descriptor rules.
10. Abstract (L5): softened "alongside within-firm heterogeneity
consistent with a minority of hand-signers" to "alongside residual
within-firm heterogeneity." Abstract at 244/250 words.
11. Discussion V-C third strand (L43): added "multi-template
replication workflows" to the list of possibilities and added
a local "we do not disaggregate these mechanisms; see Section
III-G for the scope of claims" disclaimer (Codex round-14 MINOR 5).
12. Discussion Limitations: added an Eighth limitation explicitly
stating that partner-level frequency inferences are not made and
why (no within-year uniformity assumption is adopted).
13. Methodology L124 opening: "We make one stipulation about within-
auditor-year structure" fixed to "same-CPA pair detectability,"
since A1 is a cross-year pair-existence property, not a within-
year claim (Codex round-14 MINOR 3).
14. Two broken cross-references fixed (Codex round-14 MINOR 6):
methodology L86 Section V-D -> V-G (Limitations is G, not D which
is Style-Replication Gap); methodology L167 Section III-I ->
Section IV-D (the empirical cosine distribution is in IV-D, not
III-I).
Script 27 and its output (reports/within_year_uniformity/*) remain
in the repository as internal due-diligence evidence but are not
cited from the paper. The paper's substantive claims at signature-
level and accountant (cross-year pooled) level are unchanged; only
the partner-level interpretive overlay is removed. All tables
(IV-XVIII), Appendix A (BD/McCrary sensitivity), and all reported
numbers are unchanged.
Codex round-14 (gpt-5.5 xhigh) verification: Major Revision caused
by one BLOCKER (stale DOCX artifact, not part of this commit) plus
one MAJOR ("majority of partners" partner-frequency claim) plus
four MINOR findings. All five markdown findings addressed in this
commit. DOCX regeneration deferred to pre-submission packaging.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2.0 KiB
Abstract
Regulations require Certified Public Accountants (CPAs) to attest to each audit report by affixing a signature. Digitization makes reusing a stored signature image across reports trivial---through administrative stamping or firm-level electronic signing---potentially undermining individualized attestation. Unlike forgery, non-hand-signed reproduction reuses the legitimate signer's own stored image, making it visually invisible to report users and infeasible to audit at scale manually. We present a pipeline integrating a Vision-Language Model for signature-page identification, YOLOv11 for signature detection, and ResNet-50 for feature extraction, followed by dual-descriptor verification combining cosine similarity and difference hashing. For threshold determination we apply two estimators---kernel-density antimode with a Hartigan unimodality test and an EM-fitted Beta mixture with a logit-Gaussian robustness check---plus a Burgstahler-Dichev/McCrary density-smoothness diagnostic, at the signature and accountant levels. Applied to 90,282 audit reports filed in Taiwan over 2013-2023 (182,328 signatures from 758 CPAs), the methods reveal a level asymmetry: signature-level similarity is a continuous quality spectrum that no two-component mixture separates, while accountant-level aggregates cluster into three smoothly-mixed groups with the antimode and two mixture estimators converging within $\sim$0.006 at cosine \approx 0.975. A major Big-4 firm is used as a replication-dominated (not pure) calibration anchor, with visual inspection and accountant-level mixture evidence supporting majority non-hand-signing alongside residual within-firm heterogeneity; capture rates on both 70/30 calibration and held-out folds are reported with Wilson 95% intervals to make fold-level variance visible. Validation against 310 byte-identical positives and a $\sim$50,000-pair inter-CPA negative anchor yields FAR \leq 0.001 at all accountant-level thresholds.