findings · e 002c findings

E-002c — findings

The first pre-registered positive result this programme has produced. All six gates passed, all twenty-four briefs analysed, all four registered hypotheses resolved.

Three of the four came back supported. The fourth failed, and its failure is the most useful thing here: it corrects a sentence this repository was already saying.

1. The registered result

H1 and H2 carry no p-value by design: the claim is about a magnitude, and a p-value against a nil null answers a question nobody asked. They are decided by where the interval falls, which is what the pre-registration says.

β pooled     +0.1299   CI [+0.0474, +0.2234]
β sender     −0.0200   CI [−0.0903, +0.0490]     contains zero
β receiver   +0.2797   CI [+0.1386, +0.4391]     excludes zero
β pooled, corrected for attenuation (reliability 0.7153)   +0.1816

β is the calibration slope: how far a claim moves when the outcome moves. Perfect calibration is 1.0; total unresponsiveness is 0.0.

2. The outcome the pre-registration named in advance

Its §7 lists four ways the run could land. This is the second:

H1 holds, H2 fails — responsiveness is real but far below calibration. Also a result, and a more interesting one for engineering: a partial signal can be amplified.

Writing that down before collecting is why this section can be short. There is no argument to have about whether a nonzero-but-small β counts as a finding.

3. This corrects something we were already saying

E-002b §6 reported a post-hoc slope and concluded, in a pull-quote:

The parties' confidence is very nearly unresponsive to how much actually transferred.

That was honest about its own status — labelled post-hoc, flagged as needing a successor to commit it before collecting. The successor has now run, and the sentence is too strong.

The direction replicates and the magnitude does not. E-002b's interval contained zero, so "very nearly unresponsive" was the most that data could say. With a better-powered instrument the interval clears zero: confidence does respond to transfer, at about an eighth of the rate calibration requires.

The corrected sentence is:

The receiver's confidence tracks transfer at a bit over a quarter of the rate calibration requires — β = 0.28. The sender's does not track it at all — β = −0.02, interval spanning zero.

Both halves are measured, and the second is the sharper claim: β_sender's interval contains zero and its point estimate is faintly negative, on 24 briefs spanning observed agreement from 0.485 to 0.970.

4. The sender and the receiver are not the same instrument

This is the part E-002b could not resolve and this run can.

                mean     sd       range            variance vs outcome
observed        0.7475   0.1591   0.485 – 0.970    —
claimed sender  0.9752   0.0357   0.845 – 1.000    19.8 : 1
claimed receiver 0.8843  0.0740   0.731 – 0.983     4.6 : 1

The sender sits at 0.975 and barely moves while the outcome moves across half its range. The receiver moves twice as much and its slope clears zero. H3 puts a number on the gap: +0.2997, [+0.151, +0.471], Holm-corrected p = 0.0009, by a paired sign-flip on the per-brief β contributions. That p-value is not the one this document first reported — see §6.

Per rung, the asymmetry is visible without any statistics:

Observed agreement climbs 0.26 and fidelity climbs 0.62 across the ladder. The sender's claim ends lower than it started at rung 110 and never leaves the 0.957–0.994 band.

5. H4: the earlier resolution was not a granularity artifact

E-002b measured per-probe resolution at +0.1408 on a four-value claim grid where 91.2% of cells sat at exactly 1.0, and said plainly that the signal rested on 8.8% of the data. H4 asked whether that was signal or grid.

At n_c = 9, which admits ten distinct claim values:

all ten values were used
1270 of 1584 probe-party cells at 1.0     80.2%
 314 moving                               19.8%
resolution  +0.3074   CI [+0.2156, +0.4035]

Resolution more than doubled on the finer instrument. The parties do know something about which probes diverged, and the coarse grid was hiding it rather than manufacturing it.

The pinning is still the dominant feature — four cells in five are at 1.0 — but it is weaker than E-002b's 91.2%, and the sender/receiver split above shows where the remaining pinning lives.

6. H3 was tested on the wrong quantity, and it is the same shape as last time

Found by re-reading this run's own code after the findings were written, not by a check. The conclusion does not move. What was published for two days was a p-value belonging to a different quantity.

H3's value and interval are a difference of slopes: β_receiver − β_sender = +0.2997, bootstrapped over briefs. Both correct, both what the hypothesis claims.

Its p-value came from a paired sign-flip on the per-brief claim levels — C_receiver − C_sender — which is a difference of means. It was numerically identical to recorded_sender_worse_than_receiver, sign-flipped: −0.0909 against +0.0909, p 0.0001 against 0.0001. So a registered hypothesis was being significance-tested by a statistic the analysis plan explicitly excludes from the hypothesis family, and Holm was dividing alpha over it.

The plan says H3 is tested "by a paired sign-flip permutation on the per-brief β-contributions". An OLS slope is a sum of per-brief terms, so the difference decomposes exactly:

d_i = (O_i − Ō)·[(C_r,i − C̄_r) − (C_s,i − C̄_s)] / Σ(O − Ō)²      Σ d_i = β_r − β_s

Checked against the reported effect before use: the contributions sum to +0.299731, the reported value is +0.299731. Sign-flipping them, 10 000 draws, same seed:

as registered   p = 0.0009   (Holm 0.0009)   19 of 24 contributions positive
as computed     p = 0.0001   — the level gap, a different quantity

H3 still holds. One number moved in the results file and nothing else: raw draws, gates, every other value, interval and p are byte-identical across the correction.

The part worth keeping is not the repair. It is that this is E-002b's H4 again — an interval on one quantity and a test on another — in the experiment registered to avoid exactly that, in a function whose comment three lines above the defect cites that defect by name. Knowing the failure mode, writing it down, and citing it in the code did not prevent committing it a second time.

What would have caught it is not vigilance. It is a check that asserts the statistic a hypothesis reports and the statistic it tests are computed from the same numbers — and no such check exists. Recorded as a task, not performed here, because inventing it while correcting an instance of it is how a fix gets fitted to one case.

7. What this settles in the theory

E-002b §8 recorded a debt:

Φ is defined as a level — claimed minus observed — and §5 contains no derivative, variance or slope term anywhere. So "confidence does not respond to transfer" cannot be reported as a measurement of Φ as currently defined. It needs a companion quantity, and naming it is a theory change.

β is that quantity, and it is now measured under a registration that named it before the data existed. It is added to definitions and lexicon in the same commit as this file, which is the review that debt asked for.

Φ and β are independent and both are needed. Φ says how far belief sits from outcome; β says whether belief moves when outcome moves. A party can have Φ = 0 and β = 0 — claiming the mean every time — and that party is maximally uninformative while scoring perfectly on the older quantity. That is the same argument PRINCIPIA §7.2 makes for bias versus resolution, one level up.

8. What must not be claimed

• Not that confidence is unresponsive. It responds; the interval excludes zero. The unresponsive party is the sender, and that is a narrower claim than the one E-002b's post-hoc made.
• Not that β = 0.13 is a property of language models. One model in both roles (gpt-oss:120b), one probe measure (MERIDIAN-33), one domain, 24 briefs. A model predicting its own copy is the easiest case for calibration, which makes a low β conservative and everything else narrower than it looks.
• Not that the attenuation correction is the headline. Reliability is 0.7153 and the corrected β is +0.1816; both are reported because the pre-registration says to report both and correct neither silently.
• Not that H3 shows senders are worse calibrated in general. It shows one model, given the sender's framing and the artifact it wrote, claims 0.975 and does not move. Whether that is about the role or about having authored the text is a separate experiment nobody has run.
• Not that the ladder shows a causal dose-response. Rung is message cost and the briefs were composed per rung; fidelity rising with cost is L1's territory, and L1 is not what this run registered.

9. Provenance

Collection ran 2026-07-31 19:06 to 2026-08-02 16:58 local, 28 512 model calls, zero retries used. The results file is what that run wrote.

A third file is the current record: the same analysis with H3 tested on the quantity §6 describes. One p-value differs from the second file; the draws and every other field are identical.

A second file carries the same analysis re-run from the completed cache after three reporting defects were fixed in the runner: H1 could not print as supported because the summary gated on a p-value it deliberately does not have, H3's verdict was computed and never recorded, and the declared multiplicity family listed five members where the correction was applied to the registered four. Both files are kept. Every computed field — every value, p, Holm-adjusted p, CI, gate, and all 28 512 raw draws — is identical between them; the diff is verdicts and one declaration.

The re-run made zero model calls: ollama was not running while it executed, so any attempt would have failed loudly rather than quietly redrawing.

Raw record: results/. This document is licensed CC BY 4.0.

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