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Paper A v3.20.0: partner Jimmy 2026-04-27 review + DOCX rendering overhaul

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Substantive content (addresses partner Jimmy's 2026-04-27 review of v3.19.1):

Must-fix items (6/6):
- §III-F SSIM/pixel rejection rewritten from first principles (design-level
  argument from luminance/contrast/structure local-window product, not the
  prior empirical 0.70 result)
- Table VI restructured by population × method; added missing Firm A
  logit-Gaussian-2 0.999 row; KDE marked undefined (unimodal), BD/McCrary
  marked bin-unstable (Appendix A)
- Tables IX / XI / §IV-F.3 dHash 5/8/15 inconsistency resolved: ≤8 demoted
  from "operational dual" to "calibration-fold-adjacent reference"; the
  actual classifier rule cos>0.95 AND dH≤15 = 92.46% added throughout
- New Fig. 4 (yearly per-firm best-match cosine, 5 lines, 2013-2023, Firm A
  on top); script 30_yearly_big4_comparison.py
- Tables XIV / XV extended with top-20% (94.8%) and top-30% (81.3%) brackets
- §III-K reframed P7.5 from "round-number lower-tail boundary" to operating
  point; new Table XII-B (cosine-FAR-capture tradeoff at 5 thresholds:
  0.9407 / 0.945 / 0.95 / 0.977 / 0.985)

Nice-to-have items (3/3):
- Table XII expanded to 6-cut classifier sensitivity grid (0.940-0.985)
- Defensive parentheticals (84,386 vs 85,042; 30,226 vs 30,222) moved to
  table notes; cut "invite reviewer skepticism" and "non-load-bearing"

Codex 3-pass verification cleanup:
- Stale 0.973/0.977/0.979 references unified on canonical 0.977 (Firm A
  Beta-2 forced-fit crossing from beta_mixture_results.json)
- dHash≤8 wording corrected to P95-adjacent (P95 = 9, ≤8 is the integer
  immediately below) instead of misleading "rounded down"
- Table XII-B prose corrected: per-segment qualification of "non-Firm-A
  capture falls faster" (true on 0.95→0.977 segment but contracts on
  0.977→0.985 segment); arithmetic now from exact counts

Within-year analyses removed:
- Within-year ranking robustness check (Class A) was added in nice-to-have
  pass but contradicts v3.14 A2-removal stance; removed from §IV-G.2 + the
  Appendix B provenance row
- Within-CPA future-work disclosures (Class B) removed from Discussion
  limitation #5 and Conclusion future-work paragraph; subsequent limitations
  renumbered Sixth → Fifth, Seventh → Sixth

DOCX rendering pipeline overhaul (paper/export_v3.py):

Critical fix - every v3 DOCX since v3.0 was shipping WITHOUT TABLES:
strip_comments() was wholesale-deleting HTML comments, but every numerical
table is wrapped in <!-- TABLE X: ... -->, so the table body was deleted
alongside the wrapper. Now unwraps TABLE comments (emit synthetic
__TABLE_CAPTION__: marker + table body) while still stripping non-TABLE
editorial comments. Result: 19 tables now render in the DOCX.

Other rendering fixes:
- LaTeX → Unicode conversion (50+ token replacements: Greek alphabet, ≤≥,
  ×·≈, →↔⇒, etc.); \frac/\sqrt linearisation; TeX brace tricks ({=}, {,})
- Math-context-scoped sub/superscript via PUA sentinels (/):
  no more underscore-eating in identifiers like signature_analysis
- Display equations rendered via matplotlib mathtext to PNG (3 equations:
  cosine sim, mixture crossing, BD/McCrary Z statistic), embedded as
  numbered equation blocks (1), (2), (3); content-addressed cache at
  paper/equations/ (gitignored, regenerable)
- Manual numbered/bulleted list rendering with hanging indent (replaces
  python-docx style="List Number" which silently drops the number prefix
  when no numbering definition is bound)
- Markdown blockquote (> ...) defensively stripped
- Pandoc footnote ([^name]) markers no longer leak (inlined at source)
- Heading text cleaned of LaTeX residue + PUA sentinels
- File paths in body text (signature_analysis/X.py, reports/Y.json)
  trimmed to "(reproduction artifact in Appendix B)" pointers

New leak linter: paper/lint_paper_v3.py - two-pass markdown source +
rendered DOCX leak detector; auto-runs at end of export_v3.py.

Script changes:
- 21_expanded_validation.py: added 0.9407, 0.977, 0.985 to canonical FAR
  threshold list so Table XII-B is reproducible from persisted JSON
- 30_yearly_big4_comparison.py: NEW; generates Fig. 4 + per-firm yearly
  data (writes to reports/figures/ and reports/firm_yearly_comparison/)
- 31_within_year_ranking_robustness.py: NEW; supports the within-year
  robustness check (no longer cited in paper but kept as repo-internal
  due-diligence artifact)

Partner handoff DOCX shipped to
~/Downloads/Paper_A_IEEE_Access_Draft_v3.20.0_20260505.docx (536 KB:
19 tables + 4 figures + 3 equation images).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This commit is contained in:
gbanyan
2026-05-06 13:44:49 +08:00
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commit 53125d11d9
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paper/paper_a_methodology_v3.md
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@@ -109,8 +109,22 @@ Non-hand-signing yields extreme similarity under *both* descriptors, since the u
Hand-signing, by contrast, yields high dHash similarity (the overall layout of a signature is preserved across writing occasions) but measurably lower cosine similarity (fine execution varies).
Convergence of the two descriptors is therefore a natural robustness check; when they disagree, the case is flagged as borderline.
We specifically excluded SSIM (Structural Similarity Index) [30] after empirical testing showed it to be unreliable for scanned documents: the calibration firm (Section III-H) exhibited a mean SSIM of only 0.70 due to scan-induced pixel-level variations, despite near-identical visual content.
Cosine similarity and dHash are both robust to the noise introduced by the print-scan cycle.
We did not use SSIM (Structural Similarity Index) [30] or pixel-level comparison as primary descriptors, and the reasons are specific to what each of those measures was designed to do rather than to how either happened to perform on our corpus.
SSIM was developed by Wang et al. [30] as a perceptual quality index for *natural images*, and it factorises local-window image statistics into three components---luminance, contrast, and structural correlation---combined multiplicatively over a sliding window.
Each of these components is computed at the pixel level on the original-resolution image and is *designed to be sensitive* to small fluctuations in local luminance and local contrast, because that is what makes SSIM track human perception of natural-image quality.
Applied to a binarised auditor's signature crop, exactly those design choices become liabilities: the JPEG block artifacts, scan-noise speckle, and faint scanner-rule ghosts that are routine in a print-scan cycle perturb local luminance and local contrast in every window they touch, and SSIM amplifies those perturbations in the structural-correlation product.
A signature reproduced twice from the same stored image---the very case that defines our positive class---is therefore one in which SSIM is structurally guaranteed to penalise the easily perturbed margins around the strokes, even though the strokes themselves are identical up to rendering noise.
This is a property of how SSIM is constructed, not a finding about how it scored on our data; the empirical observation that the calibration firm exhibits a mean SSIM of only $0.70$ in our corpus is a confirmation of the design-level prediction rather than the basis for the rejection.
Pixel-level comparison---whether $L_1$, $L_2$, or pixel-identity counting---fails on a stricter design ground.
Pixel-level distances are defined on geometrically aligned images at a common resolution, and they treat any sub-pixel translation, rotation, or rescale as a large perturbation by construction (a one-pixel uniform translation flips a fraction of foreground pixels on a thin-stroke signature crop and inflates pixel L1 distance to the same magnitude as for a different signer's signature).
Two scans of the same physical document, however, do not share a common pixel grid: scanner DPI, paper-handling alignment, and PDF-page rasterisation each contribute random sub-pixel offsets, and the print-scan cycle that intervenes between the stored stamp image and the audit-report PDF additionally introduces resolution mismatch and small geometric drift.
A pixel-level descriptor cannot therefore satisfy the basic stability requirement for our task: two presentations of the same stored image must score nearly identically.
We retain pixel-identity counting only as a *threshold-free anchor* (Section III-J), because byte-identical pairs in our corpus are necessarily produced by literal file reuse rather than by repeated scanning, and so they do not interact with the alignment-fragility argument; they are not used as a primary similarity descriptor.
Cosine similarity on deep embeddings and dHash, in contrast, both remain stable across the print-scan-rasterise cycle by design: cosine on L2-normalised pooled features is invariant to overall scale and bias and degrades gracefully under local-pixel noise that the convolutional backbone has been trained to absorb [14], [21], while dHash compresses the image to a $9 \times 8$ grayscale grid before computing horizontal-gradient signs, which removes the resolution and sub-pixel-alignment sensitivity that breaks pixel-level comparison [19], [27].
Together they constitute the dual descriptor used throughout the rest of this paper.
## G. Unit of Analysis and Summary Statistics
@@ -144,11 +158,11 @@ A distinctive aspect of our methodology is the use of Firm A---a major Big-4 acc
Rather than treating Firm A as a synthetic or laboratory positive control, we treat it as a naturally occurring *replication-dominated population*: a CPA population whose aggregate signing behavior is dominated by non-hand-signing but is not a pure positive class.
Practitioner knowledge motivated treating Firm A as a candidate calibration reference: the firm is understood within the audit profession to reproduce a stored signature image for the majority of certifying partners---originally via administrative stamping workflows and later via firm-level electronic signing systems---while not ruling out that a minority of partners may continue to hand-sign some or all of their reports.
This practitioner background is *non-load-bearing* in our analysis: the evidentiary basis used in this paper is the observable image evidence reported below---byte-identical same-CPA pairs, the Firm A per-signature similarity distribution, partner-ranking concentration, and intra-report consistency---which does not depend on any claim about signing practice beyond what the audit-report images themselves show.
This practitioner background motivates Firm A's selection but is not used as evidence: the evidentiary basis in the analyses below---byte-identical same-CPA pairs, the Firm A per-signature similarity distribution, partner-ranking concentration, and intra-report consistency---is derived entirely from the audit-report images themselves and does not depend on any claim about firm-level signing practice.
We establish Firm A's replication-dominated status through two primary independent quantitative analyses plus a third strand comprising three complementary checks, each of which can be reproduced from the public audit-report corpus alone:
First, *automated byte-level pair analysis* (Section IV-F.1; reproduced by `signature_analysis/28_byte_identity_decomposition.py` with output in `reports/byte_identity_decomp/byte_identity_decomposition.json`) identifies 145 Firm A signatures that are byte-identical to at least one other same-CPA signature from a different audit report, distributed across 50 distinct Firm A partners (of 180 registered); 35 of these byte-identical matches span different fiscal years.
First, *automated byte-level pair analysis* (Section IV-F.1; reproduction artifact listed in Appendix B) identifies 145 Firm A signatures that are byte-identical to at least one other same-CPA signature from a different audit report, distributed across 50 distinct Firm A partners (of 180 registered); 35 of these byte-identical matches span different fiscal years.
Byte-identity implies pixel-identity by construction, and independent hand-signing cannot produce pixel-identical images across distinct reports---these pairs therefore establish image reuse as a concrete, threshold-free phenomenon within Firm A and confirm that replication is widespread (50 of 180 registered partners) rather than confined to a handful of CPAs.
Second, *signature-level distributional evidence*: Firm A's per-signature best-match cosine distribution fails to reject unimodality (Hartigan dip test $p = 0.17$, $N = 60{,}448$ Firm A signatures; Section IV-D) and exhibits a long left tail, consistent with a dominant high-similarity regime plus residual within-firm heterogeneity rather than two cleanly separated mechanisms.
@@ -160,10 +174,8 @@ Third, we additionally validate the Firm A benchmark through three complementary
(b) *Partner-level similarity ranking (Section IV-G.2).* When every auditor-year is ranked globally by its per-auditor-year mean best-match cosine (across all firms: Big-4 and Non-Big-4), Firm A auditor-years account for 95.9% of the top decile against a baseline share of 27.8% (a 3.5$\times$ concentration ratio), and this over-representation is stable across 2013-2023. This analysis uses only the ordinal ranking and is independent of any absolute cutoff.
(c) *Intra-report consistency (Section IV-G.3).* Because each Taiwanese statutory audit report is co-signed by two engagement partners, firm-wide stamping practice predicts that both signers on a given Firm A report should receive the same signature-level label under the classifier. Firm A exhibits 89.9% intra-report agreement against 62-67% at the other Big-4 firms. This test uses the operational classifier and is therefore a *consistency* check on the classifier's firm-level output rather than a threshold-free test; the cross-firm gap (not the absolute rate) is the substantive finding.
We emphasize that the 92.5% figure is a within-sample consistency check rather than an independent validation of Firm A's status; the validation role is played by the byte-level pixel-identity evidence, the unimodal-long-tail dip-test result, the three complementary analyses above, and the held-out Firm A fold (described in Section III-J; fold-level rate differences are disclosed in Section IV-F.2).
We emphasize that Firm A's replication-dominated status was *not* derived from the thresholds we calibrate against it.
Its identification rests on the byte-level pair evidence and the dip-test-confirmed unimodal-long-tail shape, both of which are independent of any threshold choice.
The 92.5% figure is a within-sample consistency check rather than an independent validation of Firm A's status; the validation role is played by the byte-level pixel-identity evidence, the unimodal-long-tail dip-test result, the three complementary analyses above, and the held-out Firm A fold (described in Section III-J; fold-level rate differences are disclosed in Section IV-F.2).
Firm A's replication-dominated status itself was *not* derived from the thresholds we calibrate against it; it rests on the byte-level pair evidence and the dip-test-confirmed unimodal-long-tail shape, both of which are independent of any threshold choice.
The "replication-dominated, not pure" framing is important both for internal consistency---it predicts and explains the long left tail observed in Firm A's cosine distribution (Section IV-D)---and for avoiding overclaim in downstream inference.
## I. Signature-Level Threshold Characterisation
@@ -171,9 +183,9 @@ The "replication-dominated, not pure" framing is important both for internal con
This section describes how we set the operational classifier's similarity threshold and how we characterise the per-signature similarity distribution that supports it.
The two roles are kept separate by design.
> **Operational threshold (used by the classifier).** The cosine cut is anchored on the whole-sample Firm A P7.5 percentile (cos $> 0.95$; Section III-K).
>
> **Statistical characterisation (used to motivate the choice of anchor and to describe the distributional structure).** A Hartigan dip test, an EM-fitted Beta mixture (with logit-Gaussian robustness check), and a Burgstahler-Dichev / McCrary density-smoothness procedure---all applied at the per-signature level (Section IV-D).
**Operational threshold (used by the classifier).** The cosine cut is anchored on the whole-sample Firm A P7.5 percentile (cos $> 0.95$; Section III-K).
**Statistical characterisation (used to motivate the choice of anchor and to describe the distributional structure).** A Hartigan dip test, an EM-fitted Beta mixture (with logit-Gaussian robustness check), and a Burgstahler-Dichev / McCrary density-smoothness procedure---all applied at the per-signature level (Section IV-D).
The reason for the split is empirical.
The three statistical diagnostics jointly find that per-signature similarity forms a continuous quality spectrum (Section IV-D, summarised below): the dip test fails to reject unimodality for Firm A; BIC strongly prefers a 3-component over a 2-component Beta fit, so the 2-component crossing is a forced fit; and the BD/McCrary candidate transition lies inside the non-hand-signed mode rather than between modes (and is not bin-width-stable; Appendix A).
@@ -279,9 +291,14 @@ 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 $0.95$ 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-F.3 reports a sensitivity check confirming that replacing $0.95$ with the nearby rounded sensitivity cut $0.945$ (motivated by the calibration-fold P5 = 0.9407, see Section IV-F.2) shifts whole-Firm-A dual-rule capture by 1.19 percentage points, so the round-number heuristic is robust to nearby percentile-based alternatives.
Section IV-F.2 reports both calibration-fold and held-out-fold capture rates for this classifier so that fold-level sampling variance is visible.
First, the cosine cutoff $0.95$ is the *operating point* chosen for the five-way classifier from a small grid of candidate cuts, on the basis of an explicit capture-vs-FAR tradeoff against the inter-CPA negative anchor of Section III-J---*not* a discovered natural boundary in the per-signature distribution.
The candidate grid spans the calibration-fold P5 (0.9407), its rounded value (0.945), the operational anchor (0.95), and two reference points drawn from the signature-level threshold-estimator outputs of Section IV-D (the Firm A Beta-2 forced-fit crossing 0.977 and the BD/McCrary candidate transition 0.985); for each grid point Section IV-F.3 reports the Firm A capture rate, the non-Firm-A capture rate, and the inter-CPA FAR with Wilson 95% CI (Table XII-B).
Three considerations motivate the operating point at 0.95.
(i) *Inter-CPA specificity.* At cosine $> 0.95$ the inter-CPA FAR against the 50,000-pair anchor of Section IV-F.1 is $0.0005$ (Wilson 95% CI $[0.0003, 0.0007]$): one in two thousand random cross-CPA pairs exceeds the cut, an order-of-magnitude margin against the working assumption that random cross-CPA pairs do not arise from image reuse.
(ii) *Capture stability under nearby alternatives.* Moving the cut to $0.945$ raises Firm A capture by 1.51 percentage points (operational dual rule cos $> t$ AND $\text{dHash}_\text{indep} \leq 15$; Section IV-F.3) and inter-CPA FAR by $0.00032$, while moving it to the calibration-fold P5 of $0.9407$ raises Firm A capture by 2.63 percentage points and inter-CPA FAR by $0.00076$; in either direction the qualitative finding---Firm A is replication-dominated, non-Firm-A capture is much lower at the same cut, and the inter-CPA noise floor is small---is preserved.
(iii) *Interpretive transparency.* The complement $7.5\%$ corresponds to 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)---which gives the operational cut a transparent reading in the replication-dominated reference population without requiring a parametric mixture fit that the data of Section IV-D do not support.
The cosine crossover $0.837$ is the all-pairs intra/inter KDE crossover; both $0.95$ and $0.837$ 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-F.2 reports both calibration-fold and held-out-fold capture rates for this classifier so that fold-level sampling variance is visible; Section IV-F.3 (Table XII-B) reports the full capture-vs-FAR tradeoff at the candidate grid above.
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 signature-level threshold-estimator outputs of Section IV-D (KDE antimode, Beta-mixture and logit-Gaussian crossings, BD/McCrary diagnostic) are *not* the operational thresholds of this classifier: they are descriptive characterisation of the per-signature similarity distribution, and Section IV-D shows they do not converge to a clean two-mechanism boundary at the per-signature level---which is why the operational cosine cut is anchored on the whole-sample Firm A percentile rather than on any mixture-fit crossing.