Merge pull request #929 from AdaWorldAPI/claude/jirak-math-theorems-harvest-rfii13

weather-p1: CT-F16 kills the steering rescue — and the 0.684 plateau was the instrument, not the data

Author: AdaWorldAPI

.claude/board/EPIPHANIES.md

@@ -1,3 +1,67 @@
+## 2026-08-12 — E-THE-CONTROL-SCORED-THE-HEADLINE-1
+
+**Status:** FINDING `[G]` — `comet_tail_f16.py` / `.json`, bars committed
+BEFORE the run (`05f09005`); report §5.12. EXPLORATORY, not an EV.
+
+**The arc's leading rescue was measured and it failed — and the anti-vacuity
+control accidentally calibrated the instrument that had been judging it.**
+
+CT-F16 swapped ONE variable: the dipole's motion reference, from 6h surface
+displacement to the 500/600/700 hPa steering flow, on CT-F14's OWN 19 storms
+(paired; stored centres reused, so selection and disk geometry cannot move).
+Report §9.2 had named this *"the single most promising fix"*. Measured:
+**sign consistency 0.579 against a 0.70 bar** (worse than surface's 0.684),
+**residual sd 68.29° → 87.71°, 28.4 % WIDER** where a ≥10 % tightening was
+predicted, and a level sweep improving **monotonically toward the SURFACE** —
+best at 850 hPa, outside the 400–650 hPa band the height ladder predicted,
+converging exactly on the surface-displacement figure. There is no
+mid-tropospheric optimum on this sample.
+
+**The control is the larger finding.** F16c scored two deliberately WRONG
+references through the identical pipeline. The **90°-rotated** steering
+reference returned **13/19 = 0.684, p=0.0835** — *numerically identical to
+CT-F14's headline*, the number this arc has carried as "suggestive" since
+§5.11 (a different set of 13 storms, so the count coincides, not the
+identity). At n=19 the one-sided ladder is 11→p=0.324, 13→p=0.0835,
+**14→p=0.0318**. So **CT-F14 was never one storm short of significance; it was
+one storm short of distinguishability from an answer built to be wrong.**
+
+**Rule: an anti-vacuity control does not only guard the test it is attached to
+— it measures the RESOLVING POWER of the instrument.** This one was written to
+protect CT-F16 and instead retro-calibrated CT-F14. Attach a
+deliberately-wrong reference to any claim whose headline is a rate, and read
+the control's score as the floor that headline must clear. Had F16c existed at
+§5.11, "0.684, suggestive" would have been reported as "0.684, indistinguishable
+from a rotated control".
+
+**Second finding, independent of the first: the sign test conflates a
+SYSTEMATIC ROTATION with a correct prediction.** Stratified by steering
+strength — weak flow (<10 m/s, n=6) **sign 0.833 / median |err| 103°**; strong
+flow (≥10 m/s, n=13) **sign 0.462 / median |err| 55°**; `corr(speed,|err|) =
+−0.407`. The prediction gets **more accurate in magnitude** as steering
+strengthens, exactly as the physics expects, while sign consistency moves the
+**opposite** way. High sign consistency in the weak subset is errors clustered
+near −103°: a systematic rotation, which a sign test reports as success. **A
+one-sided sign test on a distribution not centred at zero measures which SIDE
+the bias falls on, not whether the prediction holds** — and this arc has used
+it as the primary instrument since §4. The apparatus story told since §5.9
+(*slow storms have noisy bearings → filter on displacement*) is not what these
+data show: the well-steered storms are the ones whose signs split at chance
+while their magnitudes are best.
+
+**What is NOT falsified.** The height ladder (§5.2/5.8) decomposed the FIELD at
+each level about that level's own centre; CT-F16 keeps the SURFACE dipole and
+swaps the FLOW reference. Different quantities — the ladder stands as a
+measurement (n=2, unreplicated), and what died is the operational reading §9.2
+built on it. The structural claim (§9.1: ring profile, wn-1 dominance, the
+12-byte carrier) is untouched; nothing in CT-F16 touches it.
+
+**Cross-ref:** `E-ZERO-FOR-ELEVEN-THE-AUTHOR-CANNOT-AUDIT-HIS-OWN-FALSIFIERS-1`
+(the author is the wrong person to find a spec's vacuous pass routes — here a
+control found a *live* one, in a number already published);
+`E-THE-HEADLINE-NUMBER-MEASURED-A-MODEL-NOBODY-CLAIMED-1` (the other time this
+arc's headline described something other than what was claimed).
+
 ## 2026-08-11 — E-THE-BYTE-WAS-ONLY-THE-SELECTOR-THE-PAIR-IS-THE-CARRIER-1
 
 **Status:** FINDING `[H]` — operator correction + `l4_rail_probe.py` (commit

probes/weather-p1/COMET_TAIL_REPORT.md

@@ -770,6 +770,140 @@ this quantity. No stronger attribution is claimed at n = 2.
 
 ---
 
+### 5.12 CT-F16 — the steering-level moderator, measured: **it makes the directional claim WORSE**
+
+`comet_tail_f16.py` / `.json`. Bars pre-registered and **committed before the
+run** (`05f09005`). §9.2 named this "the single most promising fix" for the
+directional claim. It has now been tested and it **fails on both bars.**
+
+**Design.** A *paired* re-scoring of CT-F14's OWN 19 qualifying storms with
+**only the motion reference changed** — same storms, same stored centres, same
+decomposition, byte-identical `err_deg`. Surface 6h displacement → disk-mean
+500/600/700 hPa steering flow. Reusing the stored centres removes storm
+selection and disk geometry as variables. **This is a mechanistic test, NOT a
+verdict** — a fresh steering-scored sample is CT-F17 and is not run.
+
+| bar | prediction | measured | verdict |
+|---|---|---|---|
+| **F16a** sign consistency vs steering flow | ≥ 0.70 | **0.579** (11/19), p=0.324 | **FAIL** — and *worse* than surface's 0.684 |
+| **F16b** paired residual tightening | sd drops ≥ 10 % | **68.29° → 87.71°, +28.4 % WIDER** | **FAIL** — opposite direction |
+| **F16c** anti-vacuity | permuted & rotated both < 0.70 | 0.421 / 0.684 | PASS — but see the caution below |
+| **F16d** level sweep (descriptive) | optimum inside 400–650 hPa | **monotone toward the SURFACE; best 850 hPa** | outside the predicted band |
+
+The level sweep is the clearest signal, and it points the wrong way:
+
+| level | 400 | 500 | 600 | 700 | 850 |
+|---|---|---|---|---|---|
+| sign frac | 0.579 | 0.579 | 0.632 | 0.632 | **0.684** |
+| sd (deg) | 89.5 | 87.8 | 82.1 | 80.3 | **77.0** |
+
+Both columns improve **monotonically as the reference level approaches the
+surface**, converging at 850 hPa on exactly the surface-displacement figure.
+There is no mid-tropospheric optimum. On this sample the surface displacement
+was already the best available motion reference, and mid-level flow is a
+*worse* one.
+
+**⚠ Does this falsify the height ladder (§5.2/5.8)? No — and the distinction
+matters.** The ladder decomposed the **field at each level about that level's
+own centre**; CT-F16 keeps the **surface dipole** and swaps only the **flow
+reference**. Those are different quantities, so the ladder is untouched as a
+measurement. What CT-F16 falsifies is the **application** §9.2 proposed on top
+of it — "score the dipole against steering-level motion". That inference is now
+measured and dead. The ladder (n=2) remains an unreplicated observation whose
+operational reading has failed its first test.
+
+**⚠ The anti-vacuity arm accidentally calibrated the noise floor — and CT-F14's
+headline sits exactly on it.** The deliberately **90°-rotated** steering
+reference scored **13/19 = 0.684, p=0.0835** — numerically identical to
+CT-F14's own headline figure (on a *different* set of 13 storms, so the count
+coincides rather than the identity). **A reference constructed to be wrong
+produces this arc's "suggestive" number on this sample.** F16c's bar was
+`< 0.70` and 0.684 clears it, so the gate passes as written — but the margin is
+the finding. At n=19 the one-sided ladder is 11/19 → p=0.324, 13/19 → p=0.0835,
+**14/19 → p=0.0318**: the test only separates from chance at 14. CT-F14's
+0.684 was never one storm short of significance; it was one storm short of
+*distinguishability from a deliberately wrong answer*.
+
+**⚠ And the sign test is not measuring what the arc assumed.** Stratifying by
+steering-flow strength inverts the two statistics against each other:
+
+| subset | n | sign frac | median \|error\| |
+|---|---:|---:|---:|
+| weak flow (< 10 m/s) | 6 | **0.833** | **103°** |
+| strong flow (≥ 10 m/s) | 13 | **0.462** | **55°** |
+
+`corr(steering speed, |error|) = −0.407` — the prediction gets **more accurate
+in magnitude** as the flow strengthens, which is physically sensible. But sign
+consistency moves the *opposite* way. High sign consistency in the weak-flow
+subset is not the prediction working: those errors cluster near **−103°**, a
+systematic rotation, and a sign test on a distribution centred far from zero
+reports the *side* of the offset, not its correctness. The apparatus story this
+arc has told since §5.9 — *slow storms have noisy bearings, so filter on
+displacement* — is not what these data show; the well-steered storms are the
+ones whose signs split at chance while their magnitudes are best.
+
+**Consequence for the arc.** The directional claim does not merely remain
+unproven; its **leading mechanistic rescue is now measured and failed**, and
+the instrument used to judge it is shown to conflate a systematic rotation with
+a correct prediction. §9.2's ranking of the dry moderators is superseded to
+that extent: steering level is no longer "the single most promising fix". The
+**structural** claim (§9.1) is untouched — nothing here involves the ring
+profile, the wn-1 dominance, or the 12-byte carrier.
+
+### 5.13 The instrument was the collapse: circular resultant vs sign test, same 19 storms
+
+`comet_tail_resultant_instrument.py` / `.json`. **Post-hoc re-analysis of
+stored rows — explicitly NOT a verdict.** Operator framing: *"die irrationale
+Aufsummierung hilft, dass der Dipol nicht auf 0.68 kollabiert."* Measured:
+
+| referent | sign < 0 | R̄ | μ | μ 95 % CI | Rayleigh p |
+|---|---:|---:|---:|---:|---:|
+| **surface (CT-F14)** | 0.684 | **0.516** | **−30.2°** | ±36.5° | **0.0050** |
+| steering (CT-F16) | 0.579 | 0.343 | −40.5° | ±64.3° | 0.107 |
+| CONTROL rot+90° | **0.684** | 0.343 | **−130.5°** | ±64.7° | 0.107 |
+| CONTROL permuted | 0.421 | 0.142 | — | ±152° | 0.689 |
+
+(uniform-expectation R̄ at n=19 ≈ 0.203)
+
+Three things, in order of importance:
+
+1. **The 0.684 plateau was a property of the STATISTIC, not the data.** The
+   sign test collapses each storm's error vector to one bit; 19 bits saturate
+   below the 14/19 distinguishability floor (§5.12). The circular resultant —
+   the *Aufsummierung*: sum the unit error vectors, read length and direction
+   — resolves the identical rows at **p = 0.0050**, because concentration (R̄)
+   and offset (μ) come out as two numbers instead of eating each other. The
+   systematic ≈−30° offset the arc has chased since §5.1 is now *estimated*
+   (−30.2° ± 36.5°) instead of *penalizing the score*.
+2. **The wrong referent is now visible.** F16c's rotated control scored
+   0.684 = indistinguishable under the sign test. Under the resultant it has
+   the same R̄ (rotation preserves concentration, by construction) but μ
+   shifted **100.3°** — separated by well over both CIs. The instrument
+   hierarchy is clean: real referent (0.516) > structured-but-wrong (0.343,
+   wrong μ) > permuted (0.142, below the uniform floor).
+3. **NOT a promotion.** Same sample, post-hoc — the p=0.0050 demonstrates the
+   instrument, it does not establish the directional claim. CT-W6 is the
+   pre-registered use of circular statistics on these rows (with the
+   two-component Faltung decomposition); a fresh-sample verdict is CT-F17.
+
+**The Faltung reading (operator, same exchange):** the resultant IS the first
+circular Fourier coefficient — a Faltung of the empirical error distribution
+with `e^{iθ}`. The generalization is the full harmonic/kernel readout (von
+Mises smoothing = circular Faltung; n=19 supports the first 2–3 harmonics),
+and the W6 decomposition is a DEconvolution: the measured dipole distribution
+= (referent component mix) ⊛ (apparatus noise, ±3–7° measured in CT-F4).
+Components add linearly in the transform domain, which is exactly what makes
+the multi-referent separation solvable — and on the palette ring `Z_256` the
+circular convolution is native to the substrate (`DistanceLut::circular()`'s
+own domain, FFT-able at 256 points).
+
+**Consequence for every prior sign-consistency number in this document:**
+§4's 2/2, §5.9's 6/10, §5.10's 8/10, §5.11's 13/19 were all read through an
+instrument that (a) cannot estimate the offset it penalizes and (b) cannot
+distinguish a rotated referent at these n. They stand as recorded, but their
+evidential weight is bounded by this section, in both directions — the sign
+test neither established the claim nor could it have.
+
 ## 6. Product / encoding consequence `[S]`
 
 > **⚠ Read with §5.9–5.11 AND the compression correction in §1.** The figures
@@ -1119,7 +1253,7 @@ already more explicit structure than a learned model exposes.
 
 | moderator | measured evidence | wiring |
 |---|---|---|
-| **Steering level** (baroclinic tilt) | the 92–102° monotone height ladder, zero-crossing 400–650 hPa (§5.2/5.8) | score the dipole against the *steering-level* motion (500–700 hPa flow) instead of the 6h surface displacement — the single most promising fix, **CT-F16** |
+| ~~**Steering level** (baroclinic tilt)~~ **— TESTED, FAILED (§5.12)** | the 92–102° monotone height ladder, zero-crossing 400–650 hPa (§5.2/5.8), n=2 | ~~score the dipole against steering-level motion — the single most promising fix, **CT-F16**~~ **RUN: 0.579 vs a 0.70 bar, residual 28.4 % WIDER, level sweep monotone toward the SURFACE (best 850 hPa, outside the predicted band). The ladder as a measurement stands; this operational reading of it is dead.** |
 | **Displacement magnitude** (label noise) | 6/7 pooled at ≥250 km vs 14/20 unfiltered; CT-F14 0.684 | model the motion-bearing *uncertainty* explicitly instead of a hard cutoff |
 | **Surface type / friction** | +14° ocean vs +34° land inflow, paired within one disk (§5.7) | a wind-level correction; second-order on the pressure dipole |
 | **Latitude / f, regime** | the low-wn1 July cases; the 75°N outlier | intake covariates, already computed per storm |