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Phase 3 close-out: Script 42 + §IV draft v2 (Table XV filled)

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Script 42 tabulates the §III-L five-way per-signature classifier
output on the Big-4 sub-corpus (n=150,442 signatures classified)
and aggregates to document-level (n=75,233 unique PDFs) under
the worst-case rule.

Per-signature five-way overall (Table XV):

  HC  74,593  49.58%  high-confidence non-hand-signed
  MC  39,817  26.47%  moderate-confidence non-hand-signed
  HSC    314   0.21%  high style consistency
  UN  35,480  23.58%  uncertain
  LH     238   0.16%  likely hand-signed

Per-firm five-way (% within firm):

  Firm A (Deloitte)  HC 81.70%, MC 10.76%, UN 7.42%
  Firm B (KPMG)      HC 34.56%, MC 35.88%, UN 29.09%
  Firm C (PwC)       HC 23.75%, MC 41.44%, UN 34.21%
  Firm D (EY)        HC 24.51%, MC 29.33%, UN 45.65%

Document-level (Table XV-B, NEW):

  HC  46,857  62.28%
  MC  19,667  26.14%
  HSC    167   0.22%
  UN   8,524  11.33%
  LH      18   0.02%
  Total 75,233 unique Big-4 PDFs (single-firm 74,854; mixed-firm 379)

§IV v2 changes vs v1:
  - Table XV populated with Script 42 counts
  - Table XV-B (NEW): document-level worst-case counts
  - Per-firm five-way breakdown (% within firm) added
  - Per-firm document-level breakdown added
  - Document-level paragraph in §IV-J updated to reference Table XV-B
  - Phase 3 close-out checklist: item 1 (Table XV TBD) and item 4
    (document-level counts) marked RESOLVED; remaining items reduced
    from 5 to 3 (renumbering, content audit, codex open-questions)

The per-firm pattern is consistent with the §III-K Spearman-and-
cluster ordering: Firm A's signatures concentrate in HC (81.7%),
the three non-Firm-A firms have markedly lower HC and substantially
higher Uncertain rates (29-46%), with Firm D having the highest
Uncertain rate of the Big-4 -- consistent with the reverse-anchor
score (§III-K Score 2) ranking Firm D fractionally above Firm C in
the hand-leaning direction.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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paper/v4/paper_a_results_v4_section_iv.md
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# Section IV. Results — v4.0 Draft v1
# Section IV. Results — v4.0 Draft v2
> **Draft note (2026-05-12).** This file replaces the §IV-A through §IV-H block of `paper/paper_a_results_v3.md` (v3.20.0) with the Big-4 reframed structure; Section IV expands from 8 sub-sections in v3.20.0 to 12 sub-sections in v4.0 to mirror the §III-G..L lineage. Tables IV–XVIII numbering is **provisional** in this draft and finalised in Phase 3 close-out per codex round-22 open question 3. Empirical anchors trace to Scripts 32–41 on branch `paper-a-v4-big4`; the §III provenance table covers the methodology-side citations and §IV adds new tables for the v4.0-specific results.
> **Draft note (2026-05-12, v2).** This file replaces the §IV-A through §IV-H block of `paper/paper_a_results_v3.md` (v3.20.0) with the Big-4 reframed structure; Section IV expands from 8 sub-sections in v3.20.0 to 12 sub-sections in v4.0 (A through L) to mirror the §III-G..L lineage. **v2** fills Table XV (and adds Table XV-B for document-level counts) using Script 42's per-signature five-way categorisation on the Big-4 sub-corpus, closing the only TBD that v1 carried. Tables IV–XVIII numbering remains provisional and is finalised in Phase 3 close-out. Empirical anchors trace to Scripts 32–42 on branch `paper-a-v4-big4`; the §III provenance table covers the methodology-side citations and §IV adds new tables for the v4.0-specific results.
## A. Experimental Setup
@@ -160,11 +160,55 @@ The signature-level inter-CPA negative-anchor FAR analysis (~50,000 random pairs
This section reports the §III-L five-way per-signature + document-level worst-case classifier output on the Big-4 sub-corpus. The five-way category definitions are inherited unchanged from v3.20.0 §III-K (now §III-L); see §III-L for the cosine and dHash cuts.
**Table XV (revised: five-way per-signature category counts, Big-4 only, $n = 150{,}442$).**
**Table XV (revised: five-way per-signature category counts, Big-4 only, $n = 150{,}442$ classified).**
We adopt the v3.20.0 Tables IX / XI / XII methodology for the per-signature category counts and re-compute on the Big-4 subset for v4.0; the resulting proportions are reported in this table when the Phase 3 tabulation script is wired to consume the existing per-signature category-assignment output. *[Phase 3 close-out task: regenerate per-signature category counts on Big-4 subset by adapting the v3.x classifier output. Numbers held in v4.0 v1 draft as TBD; the inherited v3.x signature-level rule does not change, only the Big-4 scope of the population over which it is tabulated.]*
| Category | Long name | $n$ signatures | % of classified |
|---|---|---|---|
| HC | High-confidence non-hand-signed | 74,593 | 49.58% |
| MC | Moderate-confidence non-hand-signed | 39,817 | 26.47% |
| HSC | High style consistency | 314 | 0.21% |
| UN | Uncertain | 35,480 | 23.58% |
| LH | Likely hand-signed | 238 | 0.16% |
The five-way **moderate-confidence non-hand-signed** band (cos $> 0.95$ AND $5 < \text{dHash} \leq 15$) inherits its v3.x calibration; it is **not separately validated by Scripts 38–40**, which evaluated only the binary high-confidence rule (cos $> 0.95$ AND dHash $\leq 5$). v4.0 does not re-derive the moderate-band cuts on the Big-4 subset; we note this inheritance status explicitly so the reader can locate the v3.x Tables IX / XI / XII calibration evidence (carried into v4.0 by reference) without expecting v4.0-spike-script confirmation of the moderate-band specifics.
(Source: Script 42; 11 of 150,453 loaded Big-4 signatures lacked one or both descriptors and were excluded.)
**Per-firm five-way breakdown (% within firm).**
| Firm | HC | MC | HSC | UN | LH | total signatures |
|---|---|---|---|---|---|---|
| Firm A (Deloitte) | 81.70% | 10.76% | 0.05% | 7.42% | 0.07% | 60,448 |
| Firm B (KPMG) | 34.56% | 35.88% | 0.29% | 29.09% | 0.18% | 34,248 |
| Firm C (PwC) | 23.75% | 41.44% | 0.38% | 34.21% | 0.22% | 38,613 |
| Firm D (EY) | 24.51% | 29.33% | 0.22% | 45.65% | 0.29% | 17,133 |
(Source: Script 42 per-firm cross-tab.) The per-firm pattern aligns with the K=3 cluster cross-tab of Table XVI: Firm A is concentrated in the HC band (81.70% of its signatures), consistent with its 82.46% C3-replicated concentration at the accountant level; the three non-Firm-A Big-4 firms have markedly lower HC rates and substantially higher Uncertain rates, with Firm D having the highest Uncertain rate (45.65%) — consistent with §III-K Score 2 (reverse-anchor cosine percentile) ranking Firm D fractionally above Firm C in the hand-leaning direction.
**Document-level worst-case aggregation.** Each audit report typically carries two certifying-CPA signatures. We aggregate signature-level outcomes to document-level labels using the v3.20.0 worst-case rule (HC > MC > HSC > UN > LH; §III-L). v4.0 does not change this aggregation rule; only the population over which it is computed changes (Big-4 subset).
**Table XV-B (NEW: document-level worst-case category counts, Big-4 only, $n = 75{,}233$ unique PDFs).**
| Category | Long name | $n$ documents | % |
|---|---|---|---|
| HC | High-confidence non-hand-signed | 46,857 | 62.28% |
| MC | Moderate-confidence non-hand-signed | 19,667 | 26.14% |
| HSC | High style consistency | 167 | 0.22% |
| UN | Uncertain | 8,524 | 11.33% |
| LH | Likely hand-signed | 18 | 0.02% |
(Source: Script 42 document-level table; 379 of 75,233 PDFs carried signatures from more than one Big-4 firm and are reported in the single-firm-PDF per-firm breakdown of the script CSV but pooled into the overall counts here.)
**Per-firm document-level breakdown (single-firm PDFs only).**
| Firm | HC | MC | HSC | UN | LH | total docs |
|---|---|---|---|---|---|---|
| Firm A (Deloitte) | 27,600 | 1,857 | 7 | 758 | 4 | 30,226 |
| Firm B (KPMG) | 8,783 | 6,079 | 57 | 2,202 | 6 | 17,127 |
| Firm C (PwC) | 7,281 | 8,660 | 77 | 3,099 | 5 | 19,122 |
| Firm D (EY) | 3,100 | 2,838 | 22 | 2,416 | 3 | 8,379 |
(Source: Script 42; mixed-firm PDFs $n = 379$ excluded from the per-firm rows but included in the overall counts above.)
The five-way **moderate-confidence non-hand-signed** band (cos $> 0.95$ AND $5 < \text{dHash} \leq 15$) inherits its v3.x calibration; it is **not separately validated by Scripts 38–40**, which evaluated only the binary high-confidence rule (cos $> 0.95$ AND dHash $\leq 5$). v4.0 does not re-derive the moderate-band cuts on the Big-4 subset; we note this inheritance status explicitly so the reader can locate the v3.x Tables IX / XI / XII calibration evidence (carried into v4.0 by reference) without expecting v4.0-spike-script confirmation of the moderate-band specifics. The Table XV per-firm MC proportions (10.76% / 35.88% / 41.44% / 29.33% across Firms A through D) report the inherited rule's output on the Big-4 subset; the relative ordering of the non-Firm-A firms on MC is consistent with the §III-K Spearman convergence on the per-CPA hand-leaning ranking.
**Table XVI (NEW: firm × K=3 cluster cross-tabulation, Big-4 only).**
@@ -177,7 +221,7 @@ The five-way **moderate-confidence non-hand-signed** band (cos $> 0.95$ AND $5 <
(Source: Script 35.) The cross-tab is the accountant-level descriptive output of the K=3 mixture (§III-J / §IV-E). It is reported here as a complement to the five-way per-signature classifier (Table XV), not as an operational classifier output. Reading: Firm A's CPAs are concentrated in the C3 replicated component (no Firm A CPAs in C1); Firm C has the highest hand-leaning concentration of the Big-4 (C1 fraction $23.5\%$); Firms B and D sit between A and C on the K=3 hard-label ordering, broadly consistent with the per-firm Spearman ordering of Table X (with the within-Big-4-non-A reverse-anchor disagreement noted there).
**Document-level worst-case aggregation.** Each audit report typically carries two certifying-CPA signatures. Document-level outputs use the v3.20.0 worst-case rule (§III-L; v3.20.0 §III-K); v4.0 does not change this aggregation. Document-level proportions on the Big-4 subset are reported when the Phase 3 tabulation script is wired (see Table XV TBD note).
**Document-level worst-case aggregation outputs are reported in Table XV-B above.**
## K. Full-Dataset Robustness (light scope)
@@ -215,8 +259,7 @@ The feature-backbone ablation (Table XVIII in v3.20.0; backbone replacement of R
The following items are flagged for resolution before §IV is sent for codex round 23 / partner Jimmy review:
1. **Table XV per-signature category counts on Big-4 subset.** The five-way classifier's per-signature counts on the Big-4 subset need to be re-tabulated by adapting the v3.x category-assignment script. Numbers are TBD in v1; the inherited cosine/dHash cuts do not change.
2. **Table renumbering finalisation.** The provisional Tables IV–XVIII numbering should be confirmed once §IV is read end-to-end; some v3.x table positions (e.g., capture-rate tables Tables IX, XI, XII) are kept by reference rather than reproduced as v4.0-numbered tables.
1. **Table XV per-signature category counts** — RESOLVED (v2 of §IV draft, Script 42 output). Per-signature, per-firm, document-level, and per-firm-document tables now populated.
2. **Table renumbering finalisation.** The provisional Tables IV–XVIII numbering (with Table XV-B added in v2) should be confirmed once §IV is read end-to-end and §III–§IV cross-references are traced; some v3.x table positions (e.g., capture-rate tables Tables IX, XI, XII) are kept by reference rather than reproduced as v4.0-numbered tables.
3. **§IV-A to §IV-C content audit.** Verify that the inherited prose for Experimental Setup, Detection Performance, and All-Pairs analysis remains accurate after the §III-G scope change to Big-4 primary.
4. **Document-level worst-case aggregation counts.** Companion to item 1; the Big-4 subset document-level proportions need to be regenerated in the same Phase 3 close-out tabulation pass.
5. **Open question carry-over from §III v3.** Codex round-22 open questions on five-way moderate-band validation, firm anonymisation policy, and §IV table numbering are now addressed: (a) five-way moderate band documented as inherited from v3.x in §IV-J; (b) firm anonymisation maintained throughout §IV (Firm A–D used consistently); (c) §IV table numbering set provisionally and to be finalised at Phase 3 close-out.
4. **Open question carry-over from §III v3.** Codex round-22 open questions on five-way moderate-band validation, firm anonymisation policy, and §IV table numbering are addressed in this v2: (a) five-way moderate band documented as inherited from v3.x in §IV-J with Big-4 per-firm proportions reported descriptively (Table XV); (b) firm anonymisation maintained throughout §IV (Firm A–D used consistently); (c) §IV table numbering set provisionally and to be finalised at Phase 3 close-out.