diff --git a/paper/paper_a_conclusion_v3.md b/paper/paper_a_conclusion_v3.md index 54feb29..3371aa0 100644 --- a/paper/paper_a_conclusion_v3.md +++ b/paper/paper_a_conclusion_v3.md @@ -5,7 +5,7 @@ We have presented an end-to-end AI pipeline for detecting non-hand-signed auditor signatures in financial audit reports at scale. Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity verification, with threshold selection placed on a statistically principled footing through two methodologically distinct threshold estimators and a density-smoothness diagnostic applied at two analysis levels. -Our contributions are fourfold. +The seven numbered contributions listed in Section I can be grouped into four broader methodological themes, summarized below. First, we argued that non-hand-signing detection is a distinct problem from signature forgery detection, requiring analytical tools focused on the upper tail of intra-signer similarity rather than inter-signer discriminability. diff --git a/paper/paper_a_discussion_v3.md b/paper/paper_a_discussion_v3.md index f9382d8..555f3ab 100644 --- a/paper/paper_a_discussion_v3.md +++ b/paper/paper_a_discussion_v3.md @@ -41,7 +41,7 @@ Three convergent strands of evidence support the replication-dominated framing. First, the visual-inspection evidence: randomly sampled Firm A reports exhibit pixel-identical signature images across different audit engagements and fiscal years for the majority of partners---a physical impossibility under independent hand-signing events. Second, the signature-level statistical evidence: Firm A's per-signature cosine distribution is unimodal long-tail rather than a tight single peak; 92.5% of Firm A signatures exceed cosine 0.95, with the remaining 7.5% forming the left tail. Third, the accountant-level evidence: of the 171 Firm A CPAs with enough signatures ($\geq 10$) to enter the accountant-level GMM, 32 (19%) fall into the middle-band C2 cluster rather than the high-replication C1 cluster---consistent with within-firm heterogeneity in signing practice (spanning a minority of hand-signers, CPAs undergoing mid-sample mechanism transitions, and CPAs whose pooled coordinates reflect mixed-quality replication) rather than a pure replication population. -Nine additional Firm A CPAs are excluded from the GMM for having fewer than 10 signatures, so we cannot place them in a cluster from the cross-sectional analysis alone. +Of the 178 valid Firm A CPAs (the 180 registered CPAs minus two excluded for disambiguation ties in the registry; Section IV-G.2), seven are outside the GMM for having fewer than 10 signatures, so we cannot place them in a cluster from the cross-sectional analysis alone. The held-out Firm A 70/30 validation (Section IV-G.2) gives capture rates on a non-calibration Firm A subset that sit in the same replication-dominated regime as the calibration fold across the full range of operating rules (extreme rules are statistically indistinguishable; operational rules in the 85–95% band differ between folds by 1–5 percentage points, reflecting within-Firm-A heterogeneity in replication intensity rather than a generalization failure). The accountant-level GMM (Section IV-E) and the threshold-independent partner-ranking analysis (Section IV-H.2) are the cross-checks that are robust to fold-level sampling variance. diff --git a/paper/paper_a_methodology_v3.md b/paper/paper_a_methodology_v3.md index 6c78571..d16fae6 100644 --- a/paper/paper_a_methodology_v3.md +++ b/paper/paper_a_methodology_v3.md @@ -287,7 +287,7 @@ High feature-level similarity without structural corroboration---consistent with 5. **Likely hand-signed:** Cosine below the all-pairs KDE crossover threshold. We note three conventions about the thresholds. -First, the cosine cutoff $0.95$ is the whole-sample Firm A P95 of the per-signature best-match cosine distribution (chosen for its transparent percentile interpretation in the whole-sample reference distribution), and the cosine crossover $0.837$ is the all-pairs intra/inter KDE crossover; both are derived from whole-sample distributions rather than from the 70% calibration fold, so the classifier inherits its operational cosine cuts from the whole-sample Firm A and all-pairs distributions. +First, the cosine cutoff $0.95$ corresponds to approximately the whole-sample Firm A P7.5 of the per-signature best-match cosine distribution---that is, 92.5% of whole-sample Firm A signatures exceed this cutoff and 7.5% fall at or below it (Section III-H)---chosen as a round-number lower-tail boundary whose complement (92.5% above) has a transparent interpretation in the whole-sample reference distribution; the cosine crossover $0.837$ is the all-pairs intra/inter KDE crossover; both are derived from whole-sample distributions rather than from the 70% calibration fold, so the classifier inherits its operational cosine cuts from the whole-sample Firm A and all-pairs distributions. Section IV-G.2 reports both calibration-fold and held-out-fold capture rates for this classifier so that fold-level sampling variance is visible. Second, the dHash cutoffs $\leq 5$ and $> 15$ are chosen from the whole-sample Firm A $\text{dHash}_\text{indep}$ distribution: $\leq 5$ captures the upper tail of the high-similarity mode (whole-sample Firm A median $\text{dHash}_\text{indep} = 2$, P75 $\approx 4$, so $\leq 5$ is the band immediately above median), while $> 15$ marks the regime in which independent-minimum structural similarity is no longer indicative of image reproduction. Third, the three accountant-level 1D estimators (KDE antimode $0.973$, Beta-2 crossing $0.979$, logit-GMM-2 crossing $0.976$) and the accountant-level 2D GMM marginal ($0.945$) are *not* the operational thresholds of this classifier: they are the *convergent external reference* that supports the choice of signature-level operational cut. diff --git a/paper/paper_a_results_v3.md b/paper/paper_a_results_v3.md index 99804e6..5e52e61 100644 --- a/paper/paper_a_results_v3.md +++ b/paper/paper_a_results_v3.md @@ -352,8 +352,8 @@ Taiwanese statutory audit reports are co-signed by two engagement partners (a pr Under firm-wide stamping practice at a given firm, both signers on the same report should receive the same signature-level classification. Disagreement between the two signers on a report is informative about whether the stamping practice is firm-wide or partner-specific. -For each report with exactly two signatures and complete per-signature data (83,970 reports assigned to a single firm, plus 384 reports with one signer per firm in the mixed-firm buckets for 84,354 total), we classify each signature using the dual-descriptor rules of Section III-L and record whether the two classifications agree. -Table XVI reports per-firm intra-report agreement (firm-assignment defined by the firm identity of both signers; mixed-firm reports are reported separately). +For each report with exactly two signatures and complete per-signature data (84,354 reports total: 83,970 single-firm reports, in which both signers are at the same firm, and 384 mixed-firm reports, in which the two signers are at different firms), we classify each signature using the dual-descriptor rules of Section III-L and record whether the two classifications agree. +Table XVI reports per-firm intra-report agreement for the 83,970 single-firm reports only (firm-assignment defined by the common firm identity of both signers); the 384 mixed-firm reports (0.46% of the 2-signature corpus) are excluded from the intra-report analysis because firm-level agreement is not well defined when the two signers are at different firms.