# Referee report: "The Bannai–Munemasa–Venkov lattice method for strongly regular graphs" (draft of 9 Oct 2026)

Referee: independent Fable 5.1 session, 2026-10-09 (fresh context; adversarial brief).  Manuscript:
`docs/paper/milgram_obstruction.tex` (784 lines, 15 pp).  My own scripts and outputs are in
`out/referee_milgram_fable/` (listed in §6).  Nothing was committed; the paper was not edited.

## 0. Verdict

**Accept with minor revision.**  The mathematics is correct.  I re-derived every lemma of Sections 2–4 by hand
(including the 2-adic case of Lemma 2.3(3) repaired after the Codex review), re-proved the three worked cases
(169_42, 96_35, 176_25) and the four short ones (616_205, 300_26, 430_39, 690_318) and the 75_32 reproduction
independently, wrote my own parity scanner and my own PARI determinant check on real graphs, and recomputed
every cell of Table 6.1 from the evidence logs.  No false exclusion was found; no existing parameter set is killed
by anything in the paper; all 47 table rows are "?" in both Brouwer snapshots held in the repository.  The
revisions needed are presentational (the odd-representation case must be written out as a lemma, one false sentence
in Remark 4.2, a stale table snapshot, incomplete bibliography).  **No row needs to be downgraded**: the
odd-representation sketch on which the "second implementation" of 105_40, 112_36, 133_32, 456_195 rests is
correct and I verified that the decider V3 implements exactly the (sound, necessary) conditions it states.

Grades of the findings: FATAL 0, MAJOR 1, MINOR 9, EDITORIAL 8.

## 1. The main theorem and its hypotheses (Sections 2–3)

Checked line by line; all correct.  Notes:

* **Lemma 2.1** (dual-vector identity): $VV^{\mathsf T}=eI+\kappa\Sigma\Sigma^{\mathsf T}$ is right (also when
  $T=e$, where $\kappa=0$); (3) and (4) are right.  The identities are real identities and hold for any admissible
  representation, which is what makes Proposition 3.3 and Remark 3.4 sound.
* **Lemma 2.2** ($H$ is a subgroup): correct; the prime-by-prime step $v_p(\mathrm{den}\,\kappa)\le 2v_p(h_1),2v_p(h_2)
  \Rightarrow \le v_p(h_1)+v_p(h_2)$ is right.  Note that because $T\in H$ (Lemma 2.3(1)), $H=\gamma\mathbb Z$ and
  $\gamma$ is simply the generator of $H$; the "gcd of divisors of $T$ in $H$" formulation is correct but roundabout
  (EDITORIAL E1).
* **Lemma 2.3(1),(2)**: correct (maximality is used exactly once, in the converse of (2)).
* **Lemma 2.3(3), the repaired step $r_y\mid C$**: I re-derived all cases.  $CY=T-e\in\mathbb Z$.  Odd $p$,
  $\pi=v_p(Y)<0$: $v_p(r_y)=\lceil-\pi/2\rceil\le-\pi\le v_p(C)$.  $p=2$, $\pi<0$: $v_2(r_y)=\lceil(1-\pi)/2\rceil
  \le-\pi$ iff $\pi\le-1$, fine.  $p=2$, $\pi=0$: $C$ odd $\Rightarrow\gamma$ odd $\Rightarrow v,T$ odd
  $\Rightarrow e$ even from $T-e=CY$; but $v\nu=T+ne$ even with $T$ odd forces $ne$ odd, so $e$ odd.  Contradiction.
  $p=2$, $\pi\ge1$: no 2-part in $r_y$.  **The repair is complete and correct.**  The last step
  ($e\bar x\in\langle\bar y\rangle$, $e r_y\bar x=0$) follows.
* **(F1)–(F5)**: (F2) I re-derived the list of anisotropic 2-modules (orders $\le8$; $\mathbb Z/8$,
  $(\mathbb Z/2)^4$, $\mathbb Z/4\oplus\mathbb Z/4$, $\mathbb Z/4\oplus(\mathbb Z/2)^2$ all isotropic) and the odd-$p$
  statement (exponent $p$, rank $\le2$).  (F3) phases are right, including: the anisotropic plane has phase 4 for
  every odd $p$ (used implicitly).  (F5) proof is right (each 2-adic plane with odd off-diagonal has determinant
  $\equiv-1\pmod4$; unit squares are $\equiv1\pmod8$).
* **Theorem 3.1**: necessary conditions (i)–(v) all follow; (v) is correctly existential in $t$ and independent of
  the representative $Q$.  **The hypothesis $b=\pm1$ is never used in the proof** (MINOR M7).
* **Remark 3.4 (odd vertex norm)** — the sketch on which the C2 grade of 105_40, 112_36, 133_32, 456_195 (and the
  V3 column of 96_35) depends.  I verified each claim: $L_0$ has index 2 (norm mod 2 is a homomorphism on an
  integral lattice); $v_i-v_j\in L_0$ and $2v_i\in L_0$, so for $x\in L_0^\#$ the $z_i$ are all integral or all in
  $\tfrac12+\mathbb Z$; in the second case $2\sigma\equiv v\pmod 2$, $\sum(2z_i)^2\equiv v\pmod 8$ (odd squares),
  and $Az-\theta z=B\sigma\mathbf 1$ gives $2B\sigma\in\mathbb Z$, i.e. $v\mid 2\sigma(k-\theta)$ (the sharper
  $2B\sigma\equiv k-\theta\pmod 2$ also holds; V3 uses the weaker one, which is still a valid necessary condition).
  I read `scripts/audit_milgram_fable_decider.py` `allowed_set(..., odd_half=True)` and confirmed it adds exactly
  the values $\tfrac{(v'j)^2(\ell-m)}{4mv\ell}+\tfrac{v}{4\ell}+\tfrac{2i}{\ell}$ over a full period with the parity
  filter $v'j\equiv v$, i.e. a superset of the true norm set — so a V3 "KILL" in an odd representation is a sound
  exclusion.  The rank used is that of $L_0$ (= rank $L$), correct.  **Conclusion: the four rows keep C2.**  But a
  published version cannot rest a grade on a remark that says "only sketched here" — see MAJOR A1.

## 2. The parity corollary (Section 4)

**Exact hypotheses, as I would state them.**  Integral eigenvalues; $\rho\in\{r,s\}$; the *vertex lattice $L$
itself* (no overlattice) of the centred representation $G=b(A-\rho I)+cJ$ with $b=\pm v/\gcd(v,k-\rho)$,
$c=-b(k-\rho)/v$; hypotheses $\nu=c-b\rho$ even (so $L$ is even) and $\ell=a|\theta-\rho|$ odd.  Then $\ell
L^\#\subseteq L$ (Lemma 2.1(2), since $VV^{\mathsf T}=eI$ when $T=0$), so $\det L=|L^\#/L|$ divides $\ell^n$ and is
odd, and (F5) applies to $L$ directly.  The relation $(A-rI)(A-sI)=\mu J$ introduces **no other primes**: the
support of $\det L$ is proved from $\ell L^\#\subseteq L$ alone, not from the minimal polynomial.  $\det L$ is a pure
prime power iff $\ell$ is; when $\ell$ has several primes all $\equiv1\pmod 4$ (65, 425, 377 in the table) the
conclusion $n\equiv0\pmod4$ still holds because every such $\Delta\equiv1\pmod 4$.  When $\ell$ has a prime
$\equiv3\pmod4$ the corollary gives only "$n$ even".  The corollary is **airtight**; it is the lattice-theoretic
content of "only primes dividing $r-s$ matter" plus the textbook congruence.

**Hand re-derivations.**
* $\mathrm{srg}(169,42,5,12)$: $r=3,s=-10$, $f=126$, $g=42$.  $\rho=s$: $k-\rho=52$, $\gcd(169,52)=13$, $a=13$,
  $G=13(A+10I)-4J$, $\nu=126$ even, $\ell=169$, rank $126$.  $\det L=13^j\equiv1\pmod4$ but (F5) needs
  $(-1)^{63}=-1$.  Correct.  ($\rho=r$: $G=-13(A-3I)+3J$, $\nu=42$, rank $42\equiv2$: same contradiction.)  For a
  non-existent graph there is no determinant to compute; what is determined is only $\det L\in\{13^j\}$, and no $j$
  works.  (Cf. the real NL$_6(13)=$ Paley(169): I computed $\det L=13^{119}$, rank $84\equiv0\pmod4$, consistent.)
* $\mathrm{srg}(391,140,39,56)$: $r=4,s=-21$, $f=322$, $g=68$.  $\rho=s$: $k-\rho=161$, $\gcd(391,161)=23$,
  $a=17$, $G=17(A+21I)-7J$, $\nu=350$ even, $\ell=17\cdot25=425=5^2\cdot17$, rank $322\equiv2\pmod4$, both primes
  $\equiv1\pmod4$: killed.  ($\rho=r$: $\ell=575=5^2\cdot23$, no conclusion.)  Correct.
* $\mathrm{srg}(625,182,45,56)$: $r=7,s=-18$, $f=442$, $g=182$.  $\rho=s$: $a=25$, $G=25(A+18I)-8J$, $\nu=442$,
  $\ell=625$, rank $442\equiv2$: killed; $\rho=r$: $G=-25(A-7I)+7J$, $\nu=182$, $\ell=625$, rank $182\equiv2$:
  killed.  Correct.
* $\mathrm{srg}(289,54,1,12)$ (Bondarenko–Radchenko): $a=17$, $G=17(A+14I)-4J$, $\nu=234$, $\ell=289$, rank
  $234\equiv2$: killed — a genuine three-line second proof.  Also re-checked 235_52 ($\ell=65$, $n=94$), 507_44
  ($\ell=169$, $n=198$), 871_348 ($\ell=377$, $n=402$), 375_154 ($\ell=125$, $n=66$), 875_184 ($\ell=125$, $n=322$).

**My own scanner** (`out/referee_milgram_fable/referee_parity.py`, own HTML parser and arithmetic, run on the
8 Oct snapshot `out/codex/supervisor_2026_10_08/brouwer_current` ($v\le1300$) and the 9 Oct snapshot
`out/audit_milgram_fable/brouwer` ($v\le750$); output `parity_scan_referee.txt`):
* 4538 rows parsed; 1096 existing rows ('+', '!', 'N!') with integral eigenvalues; 790 (row, $\rho$) pairs among
  them satisfy the hypotheses ($\nu$ even, $\ell$ odd) and are actually tested.  **Kills on existing rows: 0.**
* Killed complementary pairs: **21 = 20 open + 1 "−"**, exactly the paper's list (169_42, 169_70, 235_52, 289_54(−),
  289_90, 289_126, 375_154, 375_170, 391_140, 507_44, 625_130/182/234/286, 841_150/210/270/330/390, 871_348,
  875_184).  Statuses agree between the two snapshots.
* Observation worth stating in the paper: 14 of the 21 pairs are $\mathrm{NL}_m(q)$ with $q=p^e$, $p\equiv1\pmod4$
  prime, $m$ odd, $p\nmid m+1$: there $n=(q+1)(q-1-m)\equiv2\pmod4$ and $\ell=q^2$, so **no such NL$_m(q)$ exists**
  — a uniform generalisation of Bondarenko–Radchenko's $(289,54,1,12)=\mathrm{NL}_3(17)$, and consistent with
  $\mathrm{NL}_{(q-1)/2}(q)=$ Paley$(q^2)$ ($m$ even) and with $\mathrm{LS}_m(q)$ ($n=m(q-1)\equiv0$).  (MINOR M8)

**Real-lattice control** (`referee_detL.gp`, PARI; $\det L=$ product of the nonzero Smith invariants of the integer
matrix $G$, since $L\cong$ its $\mathbb Z$-row space and $L^\#\cong$ the saturation): own constructions Paley(9),
(25), (49), (81), (169), $L_2(5)$, $L_2(7)$, $L_2(13)$, $T(9)$, Shrikhande, Clebsch and complement
(`detL_own_constructions.txt`), plus the 189 audit graphs with $v\le130$ from `out/audit_milgram_fable/graphs/`
(`detL_audit_graphs_v130.txt`): **378 + 26 records, every prime of $\det L$ divides $\ell$ in all of them; in the
156 + 10 records where the hypotheses hold, (F5) is satisfied every time; 0 violations, 0 rank mismatches.**  E.g.
Paley(25): $\det L=5^{15}$, rank 12; Paley(49): $7^{32}$, rank 24; $L_2(13)$ ($\rho=r$): $13^{264}$, rank 144;
$T(9)$ ($\rho=s$): $3^{14}$, $\ell=63$, rank 8.

## 3. Hand-checked proofs (Section 5)

* **96_35** via $(96,60,38,36)$, $G=A+4I$: $e=10$, $T=64$, $d=33$, $\kappa=9/1024$, $B=9/16$; $H=64\mathbb Z$
  (16 | h from $B$, 32 | h from $\kappa h^2\in\mathbb Z$, then $9u^2\equiv 32u$ forces $u$ even); $\gamma=64$,
  $Y=3/2$, $r_y=2$, $C=36$; $10x=\sum z_iv_i-18(2t)y$ with $2y\in M$ gives $10D=0$; $b(\bar y,\bar y)=\tfrac12$ splits
  $\langle\bar y\rangle$ off $D_2$; on $\bar y^\perp\cap D_2$, $10Q\in2\mathbb Z$ and $Q\in\tfrac12\mathbb Z$ give
  $Q\in\mathbb Z$, phase $0/4$; $\langle 3/2\rangle$ phase 7; $D_5$ phase $0/4$; total $\{3,7\}\ne1$.  **Correct.**
* **176_25** via $(176,150,128,126)$: $\kappa=9/1694$, $B=9/11$, $H=154\mathbb Z$ ($154^2\cdot9/1694=126$ even),
  $Y=8/7$, $r_y=7$, $C=126$; $\exp D\mid70$; $10$ invertible on $D_7\Rightarrow D_7=\langle\bar y\rangle$,
  $q=2\cdot4/7$, $(4/7)=1$, phase 2; $D_2,D_5$ phase $0/4$; total $\{2,6\}\ne0$.  **Correct.**
* **169_42**: parity, see §2; the alternative constants $\gamma=130$, $Y=13/10$, $r_y=10$, $C=90$ for $A'+4I$ of
  the complement also check.  **Correct.**
* **616_205** ($\kappa=3/2299$, $\gamma=209$, $Y=56/19$, $r_y=19$, $C=57$, $D_{19}=\langle\bar y\rangle$ with
  $q\equiv18/19=2\cdot9/19$, phase 2, $D_{41}$ real: $\{2,6\}\ne0$), **300_26** ($\gamma=30$, $Y=10$, $r_y=1$, $C=2$,
  $10D=0$, phases $\{0,4\}\ne6$), **430_39** ($\gamma=43$, $Y=10$, $13D=0$, $\{0,4\}\ne2$), **690_318** via the
  complement ($\kappa=7/5625$, $\gamma=75$, $Y=46$, $53D=0$, $\{0,4\}\ne6$) and **75_32** ($\gamma=60$: $h=30$ fails
  parity since $\kappa\cdot900=11$; $Y=5/2$, $r_y=2$, $C=44$, $\{1,5\}\ne3$): **all correct**; constants agree with
  Codex's `out/codex/c31/targets.json`.

## 4. Table integrity (Section 6) — `referee_table_check.py`, output `table_check_referee.txt`

Recomputed all 47 rows from `out/s4lat/allopen_open*.tsv`, `out/milgram_paper/rerun_v1.tsv`,
`parity_rows_v1.tsv`, `out/s4lat/kills_all_xcheck.txt`, `out/audit_milgram_fable/brouwer_scan_open.tsv`,
`rerun_v3.tsv`, `parity_rows_v3.tsv`, `out/codex/c31/targets.json` and my own parity test, with my own reader.
* Complements, eigenvalue/multiplicity columns, orientation ($2k<v$), ranks of all example representations,
  membership of every example representation in that program's kill set, grades H/C2/C1 (26/20/1): **all agree**.
  All 94 rows (both orientations) are "?" in the 8 Oct snapshot and in the 9 Oct snapshot where present
  ($v\le750$).
* One stale cell: **(235,52,9,12) V1 is 5/5 in the logs, 2/2 in the table** (the V1 rerun finished after the table
  was generated; `rerun_v1.tsv` also records one 600 s timeout for $(-8,1,2)$, correctly not counted).  (MINOR M3)
* One kill present in the logs but **absent from the table: (1072,391,150,138), "?", V1 kills both
  representations $(-11,1,1)$ and $(23,-1,1)$** (`allopen_open_0.tsv`, lines 1055–1056, written 10:58, after the
  10:45 table).  The "47" of the title/abstract/Section 6 is therefore already stale; either regenerate or date the
  snapshot to the minute.  (MINOR M4)
* V3 kills that come from odd-norm representations only: 96_35, 105_40, 112_36, 133_32, 456_195 — exactly the five
  the paper names.  Every table row has at least one even-representation kill (V1), as claimed.
* Timeouts touching table rows: 176_25 (V4 1), 235_52 (V1 1), 300_26 (V1 1, V4 1), 352_26 (V1 1), 560_247 (V1 1),
  616_205 (V1 2, hence "--"), 690_318 (V1 1), 780_369 (V1 1) — all correctly excluded from the denominators.
* Section 7 control counts recomputed (`referee_counts.py`, `counts_referee.txt`): V1 on existing rows 557 pairs /
  1114 reps / 1043 decided / 71 timeouts / 0 kills ✓; V3 existing 458 rows / 4034 reps / 0 kills / $v\le400$ ✓; V3
  open scan reached $v=381$ ✓; V4 112 rows / 222 admissible / 2 timeouts ✓; `compare_run2.txt` 1304 records / 0
  violations ✓; `realcheck.log` 112 pairs / 0 violations ✓; INDEX 254 graphs / 158 parameter sets ✓; the 560-record
  $\bar y$ check **rerun by me: 560 records, 0 violations, 386 skipped** ✓ (no log of it was archived — MINOR M5);
  W(3)/Q(4,3) records: $\det N=2$, orders [2] vs $\det N=72$, orders [6,6,2] in $A+4I$ ✓.
* Coverage sentence (Section 8, "586 of 1402 attempted both sides, 495 decided"): from the logs as they stand now,
  665 attempted both sides, 558 decided — the scan kept running; fine as a dated snapshot.

## 5. Novelty framing and bibliography (Section 9)

The framing follows `docs/novelty_milgram_obstruction_2026_10_09.md` faithfully: method = BMV/NV, new = the general
dual-vector identity with $\bar y$, the parity corollary's application, and the sweep.  I agree with it, with the
caveats the paper already states (no MathSciNet forward search, experts not consulted).  Bibliography:
* \cite{Akiyama}: the author is **Kay Akiyama** (arXiv:2609.08319v1, 8 Sep 2026, "Nonexistence of a strongly regular
  graph with parameters (266,45,0,9): a certificate-free Lean proof"), from `out/novelty_milgram/2609.08319.txt`.
  (MINOR M6)
* \cite{Elkies}: N. D. Elkies, *Math 272y: Rational Lattices and their Theta Functions*, lecture notes, Harvard,
  "7 October 2019: Gluing", Proposition 1 (from `out/novelty_milgram/elkies_oct07.txt`).  (MINOR M6)
* \cite{KRY}: check whether the 2018 preprint has since appeared (I believe in *Graphs and Combinatorics*, 2019);
  update if so.  (EDITORIAL)
* \cite{Hancock} is a pointer to a table entry, not a reference; fold it into \cite{BrouwerTable}.  (EDITORIAL)
* Consider citing Scharlau's *Quadratic and Hermitian Forms* (used by NV for the Gauss-sum/anisotropy facts) and
  Brouwer–Van Maldeghem §9.4 (SNF) next to \cite{BvE} for the "primes of $r-s$" remark.  (EDITORIAL)

## 6. Numbered findings

**FATAL** — none.

**MAJOR**
* **A1 (Remark 3.4, odd vertex norm).**  Four C2 grades (105_40, 112_36, 133_32, 456_195) and the V3 column of
  96_35 rest on a case the text calls "only sketched".  The content is correct (verified above, and V3's code
  implements exactly the stated conditions), so no downgrade is needed — but the remark must become a lemma with
  proof: (a) $L_0$ even of index 2, same rank; (b) dichotomy of $z$; (c) in the half-integral case
  $2\sigma\equiv v\pmod2$, $2B\sigma\in\mathbb Z$ (indeed $2B\sigma\equiv k-\theta\pmod 2$), $\sum(2z_i)^2\equiv v\pmod
  8$, and $x^2=(\sum z_i^2-\kappa\sigma^2)/e$ unchanged; (d) statement of the resulting value set $S$; (e) the
  parity obstruction "$T=0$, $\nu$ odd $\Rightarrow v$ even" that V3 also uses.  Five lines each.

**MINOR**
* **M1 (Remark 4.2, line 386).**  "The hypotheses force $v$ and $|\theta-\rho|$ to be odd" is false for $v$:
  $T(9)=\mathrm{srg}(36,14,7,4)$ with $\rho=-2$ has $a=9$, $G=9(A+2I)-4J$, $\nu=14$ even, $\ell=63$ odd, $v=36$
  (my PARI run: $\det L=3^{14}$, rank 8, (F5) satisfied).  Only $a$ and $|\theta-\rho|$ are forced odd.  Harmless
  for the results (all kills have odd $v$), but the sentence must go.
* **M2 (Section 4, after Cor. 4.1).**  "It is equivalent to Milgram's formula applied to $L$" is only right when all
  primes of $\ell$ are $\equiv1\pmod4$ (real Gauss sum); for a prime $\equiv3\pmod4$ Milgram gives information
  (F5) does not and vice versa is not claimed.  Say "it is the case ... in which Milgram's formula is applied to $L$
  itself".
* **M3** Table 6.1 row (235,52,9,12): V1 cell 2/2 should read 5/5 (logs).
* **M4** The kill of (1072,391,150,138) (V1, 2/2) postdates the table; the count 47 is stale.  Regenerate the table
  and the three places that say 47, or state the exact cut-off time.
* **M5** The 560-record $\bar y$ check has no archived log; archive the rerun output (I reproduced 560/0).
* **M6** Complete \cite{Akiyama} (Kay Akiyama) and \cite{Elkies} (Math 272y, 7 Oct 2019, "Gluing", Prop. 1).
* **M7** Theorem 3.1 assumes $b=\pm1$ but the proof never uses it; either drop the hypothesis (the theorem then
  covers Proposition 3.3's even rescaled case too) or say it is only to match V1.
* **M8** State the NL$_m(q)$ corollary of §2 above explicitly (14 of the 21 parity pairs, and Bondarenko–Radchenko's
  row, are instances); it is the most quotable consequence and makes the family structure of Table 6.1 transparent.
* **M9** "Every pair in the table has status ? in the snapshots of 8 and 9 October": the 9 Oct snapshot in the
  repository stops at $v=750$, so for the 13 pairs with $v>750$ only the 8 Oct snapshot supports this.  Say so, or
  archive a full 9 Oct snapshot.

**EDITORIAL**
* E1 Define $\gamma$ as the generator of $H$ (it equals the stated gcd because $T\in H$).
* E2 (F2) "All three implementations ... enumerate these by brute force": true for $p=2$ only; V1, V3, V4 hard-code
  the odd-$p$ list (V3 filters it for anisotropy).  Reword.
* E3 "1097 such rows" (lines 389, 626): both my parser and `parity_scan.txt` give 1096 existing rows with integral
  eigenvalues (187 '!' + 890 '+' + 19 'N!').
* E4 Table examples for H rows: the "example representation" is chosen arbitrarily among equal-rank kills (set
  iteration order), e.g. 96_35 shows V1 $(3,-1,3)_{33}$ while the hand proof is $(3,-1,1)_{33}$ (= $A'+4I$).  Show
  the representation of the proof.
* E5 Abstract, "No existing parameter set of the table fails": add "in any representation tested" (V1 has 71
  timeouts, V3 covers $v\le400$; only P covers everything).
* E6 Lemma 2.3(3): say explicitly that $v_2(r_y)=\lceil(1-\pi)/2\rceil$ and $v_p(r_y)=\lceil-\pi/2\rceil$ are the
  definitions unpacked; the reader otherwise has to re-derive them.
* E7 Section 5.2, "the blind auditor's weaker decider admits $\langle\tfrac12\rangle$ in this representation": give
  the log line (V3 rerun: $(96,60,38,36)$ R a=1 c=0) so the statement is checkable.
* E8 \cite{Hancock}, \cite{KRY} as in §5.

## 7. Files written by the referee (`out/referee_milgram_fable/`)

* `referee_parity.py` — own parity-corollary scanner; `parity_scan_referee.txt` (0 existing kills; 20 open + 1 "−").
* `referee_detL.gp`, `run_own.gp`, `run_files.gp` — PARI Smith-normal-form determinants of centred vertex lattices;
  `detL_own_constructions.txt` (13 own graphs), `detL_audit_graphs_v130.txt` (189 audit graphs, 378 records, 0
  violations).
* `referee_table_check.py` — recomputes Table 6.1 from the logs; `table_check_referee.txt`.
* `referee_counts.py`, `referee_coverage.py` — Section 7/8 numbers; `counts_referee.txt`, `coverage_referee.txt`.