← The blow-up search

Thirteen escalations in one cycle: what an adversarial audit family found, and what it did not

Nothing here resolves the Clay problem. This is one long-shot programme's working record, published at the confidence its own gates recorded. What this is →

Route PUB3, leg 223, v1. DRAFT, for the user's review. This leg's landing does not approve it.

Status. Third publication-scoping bundle, after leg 179 (ℓ¹_w-death) and leg 186 (space-axis). Unlike both of those, this note contains no certificate mathematics. It is about the audit family's own hit-rate discipline: what happens when you point adversarial and degenerate input at the modules underneath a research codebase's banked claims, and, the part that is actually load-bearing, how you decide whether any published number moved.

What this note is not. It is not a claim that any link of this project's L1 → L4 chain moved. None has, in 223 legs. It is not a security or reliability audit of a shipped product. And, stated first because it is the most important disclaimer, its general thesis is not new, see §0.

Provenance. Every magnitude is read from the escalating leg's own banked journal or JSON on its own branch, or from experiments/JOURNAL.md's orchestrator-audited pointer. Sources are named inline. Where two banked sources disagree, both numbers are printed and the disagreement is named rather than resolved (§6). The provenance rules were pre-committed in writeup/novelty/leg_223.md before this file was written.


0. The general claim is not novel, and the note is written to a published standard

The tempting headline (adversarial input against numerical modules reliably surfaces latent defects that ordinary use never triggers) is established prior art. Four literatures own it already:

  • Silent bugs as a named class. Wrong behaviour with no crash, no hang and no error message is a catalogued category with its own incidence studies (arXiv:2112.13314).
  • Numerical bugs in exactly this dependency stack. Franco et al.'s 269-bug dataset is drawn from six libraries including NumPy, SciPy and LAPACK.
  • Why construction-time testing misses them. The oracle problem: for most numerical code there is no independent ground truth, so absolute oracles are unavailable and testing must use metamorphic relations instead (Kanewala & Bieman, STVR 2016).
  • The standard this repository is answerable to. The computer-assisted-proof literature already states in print that any computer-assisted proof implicitly carries as a hypothesis the statement that the software encountered no bugs, and carries the cautionary cases, five papers retracted from a single software bug; a sign error reversing an influential economics result (arXiv:2502.07850).

So the finding here is not that the defects exist. It is the ledger: a per-cycle census of a claim-bearing research codebase in which every defect is graded by a pre-committed question, does this move a banked number?, rather than by severity-to-the-code. None of the four prior literatures grades on that axis. That is a bookkeeping contribution and is claimed as nothing more.


1. The census, and the inclusion rule

Inclusion rule, stated so the count is auditable: a leg counts as an audit-family escalation this cycle if (a) its work was an adversarial/degenerate-input audit of a solver/ module, a consistency audit of a shared ledger, or a repair leg closing one of those findings, and (b) it ended parked on its own branch with main untouched rather than landing.

Count: thirteen. Not seven.

The dispatch that commissioned this note named seven (188, 198, 199, 200, 201, 204, 205) and warned that the number had grown. It had, by six. §7 explains why the number was stale, and it is not because anyone was careless.

One escalation is deliberately excluded, and named so the exclusion is auditable: leg 211 (XU11) escalated this cycle, but it is a literature cross-validation (Xu arXiv:2607.19762 against leg 185's a* = 0.38649640), not an input audit. It is not counted, and the count would be fourteen under a looser rule.

[POINTER ADDED 2026-08-07 BY LEG 283 (Route-M2SR): APPEND-ONLY; the paragraph above is preserved verbatim and its counting argument is unaffected, since nothing in it depends on a*'s value or provenance.] Two corrections to the parenthetical a* label, for readers who follow it out of this document. (i) Provenance: 0.38649640 is leg 125's / Route-M2P's number (the Δ(a) sweep at ν = 0, relative residual 1.933e-15, TECHNICAL_P2_ROUTEM2P_V1.md §3.5), not leg 185's own measurement. (ii) Status: leg 185's claim that its ν(a) zero crossing lands on that value is UNPINNED, its own two starts straddle zero at a = 0.3865 (+0.00000035 / −0.00425080), and leg 210's independent bracket between converged points is [0.36, 0.37]. The sign flip itself is confirmed and is now gauge-independent (ν → μ²ν under dilation, μ² > 0). Separately, leg 185's a = 1/2 ν magnitudes are downgraded to sign-only (not quoted in this document). Source: leg 210 (Route-M2SV), parked leg/210-m2sv-v1 @ 6e06880; index writeup/CORRECTIONS.md #9.

Two audit-family legs are not escalations and are counted separately: legs 206 (GSA) and 207 (DPA) found real defects and landed directly, judged not claim-adjacent. They belong in the denominator, not the escalation list: see §5, where they matter a great deal.

# leg route module contamination status
1 188 SURV dealias floor, 4 modules not a contamination question (a pending ruling
2 198 BHA bordered_hl.py zero banked impeached (magnitude contested, §6)
3 199 CGA certificate_guards.py zero banked impeached
4 200 PCA port_certification.py zero banked impeached
5 201 ICA2 interval_certificate.py zero banked impeached
6 202 PNA profile_newton.py MATERIALLY EXPOSED) Route-D v11
7 203 RSA rescaled_spectrum.py claim-adjacent, no number confirmed wrong
8 204 TNA2 target_norm.py zero banked impeached
9 205 BVR boussinesq_rescaled.py UNCERTAIN: never re-run
10 208 TSA target_selection.py zero banked impeached
11 209 SCA2 spectral_certificate.py zero; proof confirmed safe
12 213 LGC2 literature_gates.py (ledger) zero (cosmetic)
13 215 CGR nk_bounds.py (repair) zero; repair incomplete, 1 of 16

Critical, and verified at write time rather than assumed: not one repair leg has landed. git log origin/main carries no Leg 216/217/218/219/220/221/222/225/226 commit. Legs 218 and 221 have pushed a novelty pass only; 217, 219, 220, 222 and 225 have branches sitting at their base commit with no leg commit at all. Every "zero" in the table above is therefore the finding leg's own measurement, independently re-confirmed by nobody. That is a weaker epistemic state than "confirmed zero" and the note does not use that phrase.


2. The twelve module audits, and what each actually measured

202 (PNA), profile_newton.py. The one that is different in kind.

This is the only item this cycle that materially exposes a banked claim, and it is not softened here into "latent" for symmetry with the others.

continuation returns off-branch, grid-scale spurious roots as converged=True, satisfying both gauges to 0.0e+00 exactly and every residual row to machine precision. The module computes no decay-class or smoothness diagnostic, so a lattice artifact is indistinguishable from the physical branch in every field the module returns.

a n converged relres far-field sup inflation vs anchor
first departure 0.45 101 True 1.77e-15 1.35e-02 2079×
worst 1.05 101 True 4.17e-16 9.02 1.39e+06

At a = 1.05 the returned profile's supremum is attained at the domain edge, 9× larger than at the origin, with node-to-node oscillation 0.80 against the anchor's 0.09, and it is reported with a better residual than the physical branch has. The banked consequence: c(a = 1.50) returns 0.20427 / 0.23717 / 0.97282 at n = 101 / 201 / 301, all three converged=True at machine zero (6.0e-16 / 5.8e-16 / 4.1e-15). 376% between the extremes, and grid refinement does not close them, because they are different branches.

The delivery vehicle is the rescue clause. When the warm start stalls, continuation retries from the cold anchor and accepts the result because alt["relres"] < r["relres"] (which the spurious root satisfies better than the physical branch does) then re-seeds the whole remainder of the ladder from it. A clause written to make the sweep robust is what walks it off the branch and keeps it off.

Exposure, from leg 202's own git grep, not from its dispatch's candidate list:

consumer exposure
Route-D v11 (p2_route_d_v11_anchor.py) (banks a_max_machine, grid_converged_a_max, GA_boundary on a relres < 1e-8 verdict DIRECT AND MATERIAL. Its own banked v3_boundary shows the signature: relres oscillating 1e-14 → 1e-7 → 1e-14 as a rises (a = 0.54–0.60 fail, then 0.62/0.64 "converge" at 1e-14)) a branch jump, not a boundary.
Route-D v12 (p2_route_d_v12_defect.py): consumes sol["relres"], sol["c"] at a ≤ 0.55 PLAUSIBLY EXPOSED at its upper rows; M1's first measured departure is a = 0.45. Not re-run.
Route-ASA (leg 122) NOT materially affected, checked, not assumed: substrate is a = 0.0/0.3, on-branch at every grid measured.

The second consumer is recorded here because the shared ledger omits it. experiments/JOURNAL.md's pointer and every DM summary name Route-D v11 only. Route-D v12's plausible exposure appears solely in leg 202's own journal. It is an open, un-re-run question.

Resolved 2026-08-07 (leg 295). The a_max_machine exposure named in the table row above is closed: two independent methods confirm the corrected value 0.55 (leg 236's dependency-trace row-exclusion; leg 226's adversarial D2/D3 repair, both landing on the same number from different code paths), reconciled and provenance-tiered by leg 294's consolidated report (writeup/data/p2_route_v11x_v1_consolidated.json). This note adds the resolution; the table row's own text, above, is unchanged.

The corroboration that makes this hard to argue with: Route-D v11 already computed the diagnostic that catches this, externally, as a weighted_defect, and banked values that blow up exactly where leg 202 measures the departure, 0.50 at a = 0.5, 4788 at a = 0.8, 73372 at a = 1.0. The information needed to reject those profiles was sitting in the caller's own JSON and never reached the module's verdict, because the diagnostic lived in the experiment and never in the module. That is the finding, and it generalises past this module.

Repair leg 226 (PNR) is drafted and ranked first in the whole backlog (and has not been dispatched.

Two further mechanisms, latent: M2, a small-amplitude start escapes the scaling family at default parameters (Ω(0) = −0.750000 not −1, gauge residual 0.25, c wrong by up to 6.15e+05× and a sign, with c ~ 1/eps exactly identifying the mechanism as the scaling degeneracy rather than roundoff); M3, c0 never range-checked) solve(c0=1e9) hands 1e9 straight back as a converged wave speed.

203 (RSA), rescaled_spectrum.py. Claim-adjacent, and stated at exactly its own weight.

Eight mechanisms. R1: converged_spectrum has no guard on K_fine vs K_coarse, so the degenerate comparison certifies the entire continuum (n_kept goes from the correct 2 to all K (24/24 at K = 48, a 24× inflation), every match distance identically 0.0, including a spurious ±40.4623i pair) the exact Hopf-crossing signature the module exists to rule out. This is lesson 90 in the module's own code.

R2 is the claim-adjacent one, and leg 203's own journal marks it NOT LATENT. spectrum and converged_spectrum discard newton's converged flag; the worst silently-accepted iterate sits 2.632e-01 from the exact −1 and puts 44 eigenvalues in the right half plane (max Re +0.3437) where the truth has none. 5/7 banked Route-E E5_sweep rows (residuals 6.187e-04 … 1.135e-02) and 7/7 banked Route-G g4_cross_model rows (9.094e-05 … 2.275e-03) were computed at points whose residual exceeds the module's own 1e-8 threshold.

Two things cut the other way and are stated because they do: both routes banked their residuals alongside their values, so the condition is discoverable from the JSON and was never hidden; and both are already flagged converged=False by the module's own separate, conservative check. Leg 203 explicitly does not claim any banked number is wrong: the sign and size of any resulting error in those rows is not measured, and the one place it could be checked cheaply (a = 0.5) comes out right to 8 digits. The exposure is that those rows are discoverably less precise than a bare convergence label suggests. Repair leg 225 (RSR) is dispatched; its branch carries no commit.

205 (BVR), boussinesq_rescaled.py. The uncertain one.

Two independent, separately-confirmed silent-fabrication mechanisms in odd_field_x_slope. Defect A (second occurrence of leg 99's class, at the exact line leg 99 flagged and declined to test): an empty fit window sends lstsq to return exactly 0.0 against truth 2.0, 2000× tolerance. Defect B is the alarming one and is new: a hard-coded absolute r_win = 0.4 with a discarded lstsq residual drives modulation()'s c_l to +0.188 against truth 1.4 (86.5% error, 1731× tolerance) on a fully resolved grid, with rank and condition number constant throughout. Leg 99's own fix is provably blind to B.

Contamination status: UNCERTAIN, and it is not written as zero. Leg 205's own journal is explicit: "This leg did not re-run any banked result and does not claim any banked number moves." The unguarded reduction is public and called outside modulation by p2_route_l_v1_precond.py:222-229 (which additionally divides by its return value) and by spike1_stepB_evidence.py:84-85. Whether the Spike-1 Step-B/C numbers were computed on fields concentrated enough for B to bite is a separate question needing its own leg; the profiles in play use exp(-r²)-class envelopes, i.e. the safe scale, which the leg calls "a reason to expect no movement but not a measurement of it. Flagging, not claiming." Repair leg 221 (BVRR) carries the re-confirmation in its own gate; it is live and has committed a novelty pass only.

198 (BHA), bordered_hl.py. Largest nominal magnitude; contested (§6).

A negative border weight is accepted with no check, and induced_sup_norm can return a negative "operator norm": −1.0 to −4.0e9 on hand-checked cases whose true weighted norm is 101.0. The same-magnitude sign flip corrupts Z₂ by up to 1.189e17× and can flip a certificate's own closure verdict (no root → root at 2.217e-11). Three further silent sites (permuted-grid velocity_matrix, arity-truncating pin, NaN-dropping tail_exponent mask). Zero banked numbers impeached: no live caller passes a negative weight.

199 (CGA), certificate_guards.py. 16/67 silent accepts, four mechanisms.

M1, the headline: four of the five exported guards test finiteness explicitly; unit_range_violation does not, and nk_bounds.py:430 asks it for a closed lower endpoint at minus infinity, so the test is -inf < -inf = False and alpha = -inf is admissible. At the consumer, farfield_modelling_error_bound(-inf, 0.5, 1.0) returns bound = NaN, 40 of 40 window samples NaN, and does not raise: against an honest 2.537396530974982 at alpha = 1.5. The localisation is itself a gate: the same function refuses both infinities at the gamma site, where the endpoint is finite. Zero banked numbers impeached: 8/8 live alphas lie in [1.1, 1.8].

Also: M2, radius_violation accepts '0.5', Decimal('0.5'), Fraction(1,2) and True as admissible radii (4 of 4) while its sibling refuses 2 of them; M3, bool is numbers.Real, so gamma=True returns a claimed upper bound 1.2605493138651522× smaller than at the live gamma = 0.5, and budget(Y_0=False, …) narrates the boolean into a mathematical claim; M4, a negative rational underflows to -0.0 before the sign test, real accept, magnitude ≤ 1 ULP, and leg 199 pins it at that weight rather than inflating it; M5, the empty container is a vacuous pass in two guards.

200 (PCA), port_certification.py. Four mechanisms.

radii_polynomial_status returns closes=True on a ball of radius exactly 0 at Y_0 = 0 (leg 51's own a=0 CLM value): it reads the discriminant alone and never forms r_min. line_sweep_solve inverts a different operator when s_rho < 0 (18820× relative error, no exception); leading_order_solve truncates integer rhs (relative error 1.000); stall_verdict's NaN < 2.0 gives poisoned ladders a confident "bending" verdict. Two of the four are catchable by guards that already exist in-repo and are never called here. Zero banked numbers move: the live PORT run's min(s_rho) = 0.3896 > 0 sits in the corner where all four are dormant.

201 (ICA2), interval_certificate.py. An unrepaired clone of leg 69's defect 1.

matmul_point_interval silently returns a non-containing enclosure in the subnormal band (containment escape 200 η = 24.63% of the returned magnitude at the shipped BorderedHL N = 405) driving Y₀ 19.66% below the quantity it claims to upper-bound while still flagged rigorous=True. A repaired sibling routine encloses at 0 η on identical input. Zero banked numbers wrong: the live minimum row mass sits 292.9 decades above the failing band.

204 (TNA2), target_norm.py. A guard that defeats three legs of prior guard work.

The domain guard windows on max|X| rather than the true data interval, so an asymmetric grid silently extrapolates 535 of 16384 θ-samples while reporting n_outside_grid = 0 and domain_valid = True. Result: p = -0.0889 against exact 1.4, a 386× systematic error of the wrong sign, defeating legs 55/84/94's guard work while reporting clean. Three further silent-wrong mechanisms (frac_outside_grid threading; a negative analytic_tail bound with finite=True; fit_exponent overstating n_points 3.0× when dropping NaN bins). 0 of 7 mechanisms reachable from the banked call path: leg 55's +0.394/+0.094 margins uncontaminated.

208 (TSA), target_selection.py. The sixth uncensused guard-class member.

certificate_guards.py's own docstring claims to cover every function of this class; this one was never on the list. 9/9 forbidden (Y₀,Z₁,Z₂) triples return feasible=True, five with a negative certified radius (worst −1413.71); y0_budget(2.0,1.0) == y0_budget(0.0,1.0) == 0.5 bit-for-bit against a true budget of 0; unknowns() understates the dim-2 count by 598.5×. Latent: 85/85 banked Z₁ records lie in [0,1). Checked and confirmed, not assumed: leg 63's "exactly one candidate passes" and the whole γ = 2 line (63/125/174/185/ 187/193) are not at risk, that predicate lives on a disjoint, parked branch this defect never touches.

209 (SCA2), spectral_certificate.py. The module Theorem NGX is proved against.

Four latent mechanisms. Headline: an unordered NaN comparison (nan > 0 is False) sends sigma_min from 0.0349 to +inf and inverts counterexample_norm_floor from 14.3206 to a plausible-looking 0.0, exactly the theorem's own conclusion, reversed. The proof is confirmed safe, and this is the careful part: measured rather than assumed, 0 shipped (class, param) pairs produce NaN/Inf or a negative weight, the nearest shipped s is 0.263852 clear of the failing band, and clean-input float64 matches exact rational Gauss–Jordan to 7.24e-16. Theorem NGX rests on an exact folklore inequality and an analytic tail estimate; neither touches this code path. The theorem is untouched, only the numerical module has an adversarial-input gap.

206 (GSA) and 207 (DPA): the two that landed directly

Counted in the denominator (§5), not in the escalation list.

206: ga_search.py returns a wrong value on 12 of 41 adversarial cases across six mechanisms (a -inf optimum demoted to worst rank; a NaN gene surviving in a "converged" individual at finite fitness; inverted bounds collapsing offspring onto a point; elite_frac ≥ 1 freezing the breeding loop at 864347× worse while reporting 40 generations). All six are orthogonal to the standing GA ban, and all 9 live call sites were audited safe by static AST parse.

207: dissipative_profile.py, 4 latent sites. Most severe: Y₀/Z₂ are measured at the constructor's stored a, not the solved one, inflation up to 1.144e+12× when they drift; and a zero profile silently echoes Chen's exact Δ = −1/3 at residual_rms exactly 0.0, with no health indicator distinguishing it from real convergence. A static call-site audit of legs 125/185/187 found 0 exposed sites.

188 (SURV) and 213 (LGC2) and 215 (CGR): the three that are not module audits

188 is a necessity audit, and its status line is not a contamination claim. Its gate answered (a) FORCED, (b) NO: n = 3's exclusion under the strict Bowman 2/3 rule is mathematically forced. Its real contribution is a correction to the scope of escalation #4, and the correction runs in the direction people do not expect: leg 129's blast radius is wider than originally scoped, not narrower. Four solver modules consume the two masks leg 129 touches (gclm.py, fractional_gclm.py, fractional_boussinesq.py, boussinesq.py), and critically solver/gclm.py has no grid guard at all: solve_gclm(n=3) runs clean today and would raise post-repair. So the ruling the user owes is about a four-module refusal boundary, one of them going from unguarded to raising for the first time, not a single Boussinesq verdict.

Leg 188's own novelty pass also caught its dispatch's premise being false before running: the dispatch asserted the strict rule was "already used elsewhere, e.g. leg 120's own repair", but leg 120 wrote no repair (it escalated, unpatched), and grep -rn "// 3" solver/*.py returns nothing: no shipped module on main uses the strict cut. It survives only in the adversarial batteries, which pin the loose cut as a measured defect rather than adopt the strict one. Leg 188 is also the one escalation with no journal file on its branch, only a runner and a novelty pass, so its record lives in DM prose rather than in a leg artifact.

213 is a ledger-consistency audit and its finding is cosmetic and honestly labelled so: EGM_PRIMARY_READ's own sign_correction_leg_190 field describes 5 prose sites as still carrying the wrong bracket, true when written, false since leg 214 fixed all five (2c901c4). The ledger's claim about the repository's current files is backwards. 0 banked numbers move; a one-tense-word fix (reserve leg 227).

215 is a repair leg whose gate answered NO, and it is in this list because it escalated rather than landing. The one-line isinf repair at nk_bounds.py:430 closes leg 199's M1 cleanly: alpha=-inf now raises, 8/8 live call sites bit-identical at 0 ULP. But M1 is only 1 of the 16 gaps leg 199 found; the other 15 live in certificate_guards.py, outside leg 215's territory. The repair is sound; the gate's premise is what failed: that all 16 were the missing-isinf family. Leg 216 (CGF) owns the remainder and has not started.


3. The distribution, which is the actual result

Twelve legs this cycle ran a gate of the form "under adversarial and degenerate input, does this module ever silently return a wrong value rather than reject or visibly propagate?": legs 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209.

All twelve answered YES.

That is the number worth publishing, and it needs stating carefully, because it is a claim about this codebase, not a discovery about method (§0). Twelve modules were selected as load-bearing and audited; twelve had at least one mechanism that returns a finite, plausible, wrong value with no exception, no warning and no flag. Several had four to eight. The prior selection was not adversarial: these are the modules underneath banked results, chosen for being load-bearing rather than for being suspect.

Against that, the grading:

grade count legs
materially exposes a banked claim 1 202
claim-adjacent; no number confirmed wrong 1 203
contamination never measured (uncertain) 1 205
zero banked numbers impeached, per the finding leg's own measurement 9 198, 199, 200, 201, 204, 208, 209, 213, 215
not a contamination question (pending ruling) 1 188

Both halves matter, and reporting either alone would be dishonest. A 12/12 defect rate with a 1/12 material-exposure rate is a different story from either number by itself. The contamination discipline (measuring reach at live parameters instead of reasoning from severity) is what separated them, and it repeatedly reversed the intuitive ranking: leg 198 has the largest nominal magnitude in the cycle (Z₂ to 1.189e17×) and contaminates nothing, while leg 202's mechanism produces machine-zero residuals, the most innocuous-looking diagnostic possible, and is the one that reaches a banked headline.

The mechanism behind that inversion is worth naming. In every latent case, the defect needed an input no caller produces: a negative weight, alpha = -inf, a subnormal row mass, an asymmetric grid, s_rho < 0. Leg 202's needed nothing: it fires on the module's own default path, on a warm start, at a parameter the caller genuinely sweeps. Reachability, not magnitude, is the variable that predicts contamination, and it is cheap to measure and was measured in eleven of twelve cases.

The twelfth is leg 205, and its absence is exactly why its status stays UNCERTAIN.


4. What the discipline caught that a severity ranking would have missed

Four cases where measuring reach changed the answer:

  1. Leg 209 separated the module from the theorem. The mechanism reverses Theorem NGX's own conclusion (counterexample_norm_floor 14.3206 → 0.0). A severity ranking stops there. The leg instead established that the theorem rests on an exact folklore inequality and an analytic tail estimate, neither of which touches this code path, so the proof is untouched and only the numerical module has a gap.
  2. Leg 208 checked the γ=2 line rather than assuming it. The natural fear, leg 63's "exactly one candidate passes", was confirmed safe because that predicate runs on a disjoint, parked branch the defect never reaches.
  3. Leg 199 declined to inflate M4. A real silent accept whose magnitude is ≤ 1 ULP, reported at that weight and explicitly flagged as unreachable from float64.
  4. Leg 202 rejected its own dispatch's candidate list. The brief named legs 125/185/187; git grep showed none of them imports the module, and leg 202 recorded leg 187's status as unresolved-at-merge-base rather than absent, because 187 was in flight elsewhere. It then found the real consumers itself.

And one where it cut against the leg's own convenience: leg 202 also recorded a correction against its own intermediate scouting note, in the artifact rather than quietly dropping it.


5. Where the banked record disagrees with itself

Printed rather than resolved, per this leg's pre-committed provenance rule.

(a) Leg 198's Z₁ ratios are contested by leg 218's in-flight re-measurement. Leg 198 reports Z₁ corruption up to 1.198e9×; leg 218's novelty pass, re-running both modules in the same process, measures 2.287e8×, a factor 5.24× apart, and 1.505e12 vs 2.651e12 (1.76×) on the second case. Leg 218's own explanation: Z₁ = ‖I − A·DF‖ with A = inv(DF) is a near-total cancellation whose honest and flipped values (5.518e-09, 5.099e-15) both sit at the round-off floor, so the ratio is environment-dependent while the verdict is not, lesson 86. Leg 198's ‖A‖ (6.671e9×, 6.066e10×) and Z₂ (+1.188608e+17 / −1.779456e+07) columns reproduce exactly to 4–6 s.f. Neither number is adopted here; the verdict (a sign flip corrupts these constants catastrophically) is not in dispute, and the contamination status (zero) is not affected.

Update: 2026-08-07, leg 279 (Route-Z1X). Item (a) is now CLOSED AS EXPLAINED. Append-only; nothing in the paragraph above is altered, and §5's framing ("printed rather than resolved") was correct as of leg 223. Item (a) was resolved elsewhere, by leg 228 (experiments/journal/leg_228.md §4), not by this document. Leg 228 treated leg 218's variance explanation as the falsifiable claim it is, with the falsification condition fixed before the numbers were looked at, and measured the disputed quantity under mathematics-neutral perturbations only (algebraically identical re-associations of the same matrix products, plus BLAS thread counts). The ratio spans 11.77×, 2.6422e8 to 3.1108e9, against a disagreement of only 5.239×; thread count alone moves it from 2.6422e8 (1 thread) to 3.1108e9 (4 threads), same code, same machine, same inputs. The control is the sharp number: the ‖A‖ ratio, the column legs 198 and 218 agree on, moves by 7.2e−12 relative under those same perturbations. So the disputed Z₁ ratio is round-off-floor noise in a near-total-cancellation denominator, and neither 1.198e9× nor 2.2867e8× should be adopted as the ratio: there is no such number to adopt. The reproducible columns, and the ones this and any other prose should quote, are ‖A‖ = 6.6712e+09× (and 6.0663e+10× on the w_om case) and Z₂ = +1.188608e+17 / −1.779456e+07, which both legs reproduce to 4–6 s.f. Both legs' verdicts, and the contamination status (zero), are unaffected: exactly as the paragraph above already says. See writeup/CORRECTIONS.md, leg 279 entry.

(b) The DM's blast-radius framing for leg 198 is measured false. DIRECTION.md ranks 218 first "given that this module sits directly upstream of every bordered-certificate battery this repository has run (54, 58, 127)". Leg 218 measured it: legs 54/58/127 do not import solver/bordered_hl.py at all, 0 of 7 of their runners/evidence files mention it; they rest on solver/spectral_certificate.py via p2_route_tc_v1_assemble. Answering the gate's clause (b) on those three would have been a lesson-90 tautology. The live caller set, enumerated by import, is port_v1/port_v2/l1_v1/l1rh_v1 plus two test files, every one of which passes w_om = w_r = 1.0. The priority ranking stands on other grounds; its stated reason does not.

UPDATE: 2026-08-07, leg 282, carrying leg 228 §3 (flagged forward by leg 279 §5). This paragraph's finding is unaffected; its parenthetical caller list is incomplete. The six-name set above is leg 218's, and leg 228 re-enumerated it from the callers themselves: 13 direct importers of solver/bordered_hl.py in the worktree, of which 10 existed contemporaneously with leg 218 (membership decided by git cat-file -e d9a20fb:<path>, not a hardcoded name list). Leg 218 named six; five of the ten were missed. The verified ten-importer set is p2_route_port_v1_bordered.py, p2_route_l1_v1_interval.py, p2_route_l1rh_v1_construction.py, test_bordered_hl.py, test_interval_certificate.py (the five leg 218 had by import), plus test_bordered_hl_adversarial.py, p2_route_bhn_v1_adversarial.py, p2_route_hlb_v1_contraction_lit.py, p2_route_nb_v1_targetnorm.py and p2_route_tn_v1_consistency.py (missed). The mechanism of the gap is named: leg 218's sixth name, p2_route_port_v2_reach.py, imports p2_route_port_v1_bordered and not solver.bordered_hl, correct as a transitive caller, but it means the set was not purely "by import" as this paragraph describes, and four direct importers fell through that gap.

Three things this update does NOT change, each checked rather than assumed. (1) This paragraph's actual claim (that legs 54/58/127 do not import solver/bordered_hl.py, 0 of 7 runners/evidence files) is untouched: 0 of the five missed importers belongs to leg 54, 58 or 127. (2) The w_om = w_r = 1.0 observation survives, with its wording sharpened: none of the five missed importers mentions w_om or w_r at all, so all five take BorderedHL.weights' defaults, which are w_om = 1.0, w_r = 1.0 (solver/bordered_hl.py:312), the values are as stated; "passes" should read "passes or inherits by default". (3) Leg 218's repair is not impeached. One missed importer does touch the weight surface (p2_route_tn_v1_consistency.py:219 calls b.weights(p=P_STAR, w_l=0.01*|X|max), which made leg 228's pre-fixed material/cosmetic split come out MATERIAL) but leg 218's differential is caller-agnostic, and leg 228 re-earned it over the full ten-importer configuration space, tn_v1_consistency's live configuration (n = 201, p = 0.39, w_l = 0.01 |X|max) included: 45 configurations, 77,040 float leaves, 0 bit mismatches, compared on IEEE-754 payloads rather than ==. What is corrected is the enumeration; the hazard recorded is that a verification leg trusting it would have inherited the hole. See writeup/CORRECTIONS.md §8–§9.

(c) Route-D v12's exposure is absent from every shared ledger. §2 above. It appears only in leg 202's own journal and has not been re-run.

(d) One "the fix is one line" estimate was wrong by 15/16. Leg 199's report stated its M1 fix was a one-line isinf check. It was, and closing M1 closed 1 of 16 gaps (leg 215). The estimate was accurate about the line and misleading about the finding.


6. Why the count was stale, which is a finding about the process

The dispatch commissioning this note named seven escalations. The true figure at write time is thirteen. The cause is structural, not carelessness, and it is worth recording because it is the kind of defect this cycle's own audits were looking for, in the bookkeeping rather than the code.

DIRECTION.md states 26 times that escalations are "recorded in PROGRESS.md's NEEDS YOU". PROGRESS.md is not in the repository. .gitignore:33 excludes it by design, with the comment "PROGRESS.md is rewritten every cycle (the committed snapshot is reports/STATUS.md)". No commit in the repository's whole history has ever touched it.

So the committed register is reports/STATUS.md: whose header reads "committed snapshot (sections 1-3 of PROGRESS.md)". It was last refreshed at commit 4b6f4d8, with the summary "6 landings, 3 escalations", and its NEEDS YOU section lists exactly three: 188, 199, 198. main has since advanced to b8eae4f and the escalation count has gone from 3 to 13.

The only committed escalation register is stale by ten items, including the one materially exposed banked claim. Anyone reconstructing the backlog must instead read DIRECTION.md's DM narrative and experiments/JOURNAL.md's pointers in commit order and take the union, which is what this leg did, and which is why the count moved by six.

This is a bookkeeping observation, not a criticism of any leg: every individual escalation was recorded correctly somewhere, each in at least two places, by legs and an orchestrator working exactly to spec. What is missing is a single committed place where they are recorded together. The audit family found silent-wrong values in twelve of twelve modules by asking what happens under input nobody expected; the same question asked of the process finds a register that silently reports 3 when the answer is 13.


7. The honest ceiling

  • No link of the L1 → L4 chain moved. Not in this cycle, not in 223 legs. Clay stays at ~0.05%, behind Walls 1 and 2.
  • Nothing here is a positive result about the mathematics. The best case for a repaired module is that a guarantee is restored, not that a margin improved.
  • The 12/12 rate is a statement about this codebase, from a sample of twelve non-adversarially-selected load-bearing modules in one repository. It is not an estimate of any population rate, and §0's prior art already establishes the phenomenon generally.
  • Nine "zero contamination" statuses rest on the finding leg's own measurement, since no repair leg has landed and none has independently re-confirmed one.
  • One status is uncertain (205) and one is materially exposed (202). Neither is written as zero anywhere in this note.
  • Whether Route-D v11's headline survives is open, and cannot be settled from here. It requires leg 226's re-derivation using a repaired module. Leg 226 is ranked first in the entire backlog and has not been dispatched.

Provenance table

claim read from
202's mechanisms, tables, exposure, v12 experiments/journal/leg_202.md @ origin/leg/202-pna-v1
203's R1–R8 table, R2 NOT LATENT experiments/journal/leg_203.md @ leg/203-rsa-v1
205's "flagging, not claiming" experiments/journal/leg_205.md @ leg/205-bvr-v1
199's M1–M7, blast-radius table experiments/journal/leg_199.md @ leg/199-cga-v1
198's magnitudes experiments/JOURNAL.md pointer (leg 198 entry)
198's contested Z₁, caller set novelty commit 7a32718 @ leg/218-bhr-v1
188's premise correction, loose-cut grep writeup/novelty/leg_188.md @ leg/188-surv-v1
188's 4-module scope DIRECTION.md DM update (no leg journal exists on 188's branch)
200, 201, 204, 206, 207, 208, 209, 213, 215 experiments/JOURNAL.md orchestrator-audited pointers
repair-leg landing status git log origin/main; branch tips for 216–222, 225
register staleness .gitignore:33, reports/STATUS.md header + NEEDS YOU, git log --all -- PROGRESS.md (empty)