# Correspondence — the calibration report

Run 2026-09-12 against the **real generator** (`bypDerivePlanet`, lifted from
`functions/index.js` the way `seed-parity` lifts it) and the **shipped projection**
(`observatory-project.js`, unmodified). A simulated year — 365 nights from
`GENESIS` through the real RK4 integrator — at 43 worlds using the live
catalogue's own names, and at 10,000.

**No value in this report is a spec value.** §3 says the era parameters are
provisional until the report publishes; this is the report, and what it mostly
publishes is that **two of them cannot be set as the rule is written.**

---

## 0 · What the brief did not reach me, and what I did instead

The brief naming **"definitions A and B"** and **"the two τ schedules"** is not
in my context. Rather than guess silently I defined all three readings and both
τ explicitly below and ran everything, so whichever pair was meant is covered.
If A and B were meant to be something else, the harness takes them as a flag and
the run is about ninety seconds.

| | definition of the working reading R′ |
|---|---|
| **A** | `R − median` of the region — **the spec as signed** (§3) |
| **B** | `R − mean` of the region — the obvious alternative centre |
| **C** | the **residual** of R regressed on the region's median over the trailing 30 nights — removes the world's *loading* on the regional current rather than only the *level*. This is the definition risk 1 asks for. |

| τ | reading |
|---|---|
| **0.05** | one false pair expected every 20 nights, sky-wide |
| **1.0** | one false pair expected per night, sky-wide |

Everything else is the spec's: baseline 30 nights, W = 30, k(n) = min{k ≥ 2 :
M(n)·q(k) ≤ τ}, q measured against **all** same-region pairs.

---

## 1 · The headline — the rule does not survive the change of scale

`M(n)` is the count of eligible same-region pairs and grows as **N²**. `q(k)`'s
tail does not grow to meet it. So the same τ lands in two different worlds:

| | 43 worlds (M = 80) | 10,000 worlds (M = 4,163,351) |
|---|---|---|
| **τ = 0.05** | k = 7 · **q = 0 · no contact, ever** | k = 13 · 6 contacts a year · a world waits **804 years** |
| **τ = 1.0** | k = 3 · **136 contacts a year across 80 pairs** | k = 12 · 154 a year · a world waits **31 years** |

*(definition A, z\* = 2.5, floor 0.75)*

At 43 worlds τ = 1.0 contacts **every pair within weeks** and τ = 0.05 contacts
nobody. At 10,000 both τ land where 96.8%–99.9% of worlds are never contacted in
a year. **There is no τ that behaves at both sizes**, which is exactly what the
plan's risk 4 predicted and what §3's "provisional pending calibration" is
carrying.

This is structural, not a tuning failure: τ bounds *expected false pairs per
night across the whole sky*, so as the sky grows the rule must demand more of
each pair, and each pair has no more to give.

---

## 2 · q(k) is unmeasured exactly where the schedule reads it

This is the finding that matters most, and it is a property of the method rather
than of any parameter.

**The windows overlap.** Consecutive 30-night windows share 29 nights, so
pair-windows are not independent observations. Over 365 nights there are 305
windows and about **11 independent** ones — the raw count over-states the
evidence by **27.7×**.

**Pairs overlap too.** At 10,000 worlds a world sits in 865 same-region pairs,
and pairs sharing a world are correlated. No factor is applied for this below;
it makes the effective sample smaller still.

**Multiple testing is already handled** — `M(n)·q(k) ≤ τ` *is* the correction,
applied by the rule itself. That part is sound.

Applying only the window factor, at **10,000 worlds, z\* = 2.0**:

| k | q(k) | M·q(k) | pair-windows seen | **independent obs** |
|---|---|---|---|---|
| 5 | 3.19e-3 | 13,298 | 4,055,805 | 146,275 |
| 8 | 2.00e-4 | 832 | 253,764 | 9,152 |
| 11 | 1.12e-5 | 46.5 | 14,178 | 511 |
| 12 | 1.53e-6 | 6.36 | 1,940 | 70 |
| **13** | 3.06e-7 | 1.27 | 388 | **14** |
| **14** | 3.94e-9 | 0.016 | 5 | **0** |

**Both τ choose k = 14**, where the estimate rests on five overlapping windows of
what is essentially **one pair**. The schedule reads q in precisely the region
where the simulation has not measured it.

At **43 worlds it is worse**: *every* k from 2 upward has fewer than 30
independent observations, and k = 5 and above rest on one or two. The entire
schedule at the catalogue's real size is built on noise.

**A longer simulation does not fix this cheaply.** Independent windows scale
with nights ÷ W, so measuring q at k = 14 to ±10% needs of the order of a
hundred thousand independent windows — roughly **eight thousand simulated
years**. Either the tail is modelled rather than measured, or k is capped where
measurement actually reaches.

---

## 3 · Mute worlds and the floor

A mute world can never be contacted. It is assigned by seed, and nothing an
owner does changes it.

| definition | z\* | mute at 43 | mute at 10,000 |
|---|---|---|---|
| **A** | 2.0 | 5 (11.6%) | 1,312 (**13.1%**) |
| **A** | 2.5 | 8 (18.6%) | 2,897 (**29.0%**) |
| **B** | 2.0 | 10 (23.3%) | 1,525 (15.3%) |
| **B** | 2.5 | 14 (32.6%) | 3,139 (31.4%) |
| **C** | 2.0 | 2 (4.7%) | **734 (7.3%)** |
| **C** | 2.5 | 9–10 | 2,104 (21.0%) |

**z\* = 2.5 strands between a fifth and a third of the catalogue** under every
definition. z\* = 2.0 is materially better and still strands 7–15%.

**The floor barely matters.** Across 0.50 / 0.75 / 1.00 reading points the mute
count moves by 0–2 worlds at 43 and the flag rate by under half a point. It is
not a lever; it is a guard against a zero divisor, and 0.75 is as good as any.

**The repo has already ruled on this shape of decision.** The `NORM` divisor was
set to 12 rather than 20 because /20 "strands two worlds with a flat line
forever, assigned by seed with no recourse — a permanent outcome for one person,
which decides it against." Two worlds decided that. This is seven hundred to
three thousand.

---

## 4 · p₁ — the per-world-night flag rate

| definition | z\* | 43 worlds | 10,000 worlds | flags/night at 10,000 |
|---|---|---|---|---|
| A | 2.0 | 6.47% | 4.62% | 462 |
| A | 2.5 | 4.02% | 2.28% | 228 |
| B | 2.0 | 4.32% | 4.28% | 428 |
| B | 2.5 | 1.90% | 2.08% | 208 |
| C | 2.0 | 4.60% | 4.68% | 468 |
| C | 2.5 | 2.62% | 2.57% | 257 |

Well above the normal-theory tail — z ≥ 2.0 on a Gaussian is 2.3%, not 4.6% —
because R′ is not Gaussian and the flags arrive in **bursts**. On a burst night a
large share of a region flags together, which is what makes q(k) fat at low k
and empty at high k.

Typical own-spread (1.4826·MAD of R′) at 10,000: **A 6.07 points, B 6.24,
C 3.99**. C is the tightest, which is why it strands fewest worlds.

---

## 5 · Pair co-resonance, and risk 1

Mean cosine similarity of the two worlds' projection constants, by the highest r
the pair reached in any window. 1,200 worlds, z\* = 2.5.

| | random same-region pair | pairs reaching r ≥ 5 | lift |
|---|---|---|---|
| **A** | −0.0039 | 0.7543 | **0.758** |
| **B** | −0.0039 | 0.7793 | 0.783 |
| **C** | −0.0039 | **0.6509** | **0.655** |

**The residual definition does not break the seed link.** It reduces the lift by
14% and leaves it overwhelming: pairs that co-resonate are still near-parallel in
constants where random pairs are orthogonal.

**So risk 1 is not solved by this estimator change**, and the plan's proposed
remedy does not work as hoped. Removing the world's *loading* on the regional
current leaves the part of the correlation that comes from two worlds reading the
*same three-component sky* through similar constants — which is most of it. Any
fix has to act on that, and it is not a subtraction.

C remains the better reading on every other axis measured here.

---

## 6 · Activation — the census

How many signals before two-thirds of regions hold two or more signal-bearing
worlds, drawn uniformly at random from the real region distribution, 400 trials:

| catalogue | median | p10 | p90 |
|---|---|---|---|
| 44 | **26** | 22 | 31 |
| 200 | 25 | 21 | 31 |
| 1,000 | 26 | 21 | 31 |

**Stable at about 26 signals**, and it barely depends on catalogue size — it is a
property of the twelve-region distribution, not of how many worlds exist.

Production has **7**. So roughly **19 more signals**, and then the earliest
possible activation is night 31 of the archive. Production has 2 nights.

---

## 7 · The two τ schedules, side by side

Definition A, floor 0.75. "A world waits" is 1 ÷ (its own pairs × q).

**43 worlds, M = 80**

| z\* | τ | k | q(k) | contacts/night | contacts/year | a world waits | never contacted after 1 yr |
|---|---|---|---|---|---|---|---|
| 2.5 | 0.05 | 7 | 0 | 0 | 0 | never | 100% |
| 2.5 | 1.0 | 3 | 4.7e-3 | 0.374 | **136** | 0.1 years | 0.0% |
| 2.0 | 0.05 | 10 | 0 | 0 | 0 | never | 100% |
| 2.0 | 1.0 | 4 | 9.1e-3 | 0.728 | **266** | 0.0 years | 0.0% |

**10,000 worlds, M = 4,163,351**

| z\* | τ | k | q(k) | contacts/night | contacts/year | a world waits | never contacted after 1 yr |
|---|---|---|---|---|---|---|---|
| 2.5 | 0.05 | 13 | 3.9e-9 | 0.016 | 6.0 | 804 years | 99.9% |
| 2.5 | 1.0 | 12 | 1.0e-7 | 0.423 | 154 | 31 years | 96.8% |
| 2.0 | 0.05 | 14 | 3.9e-9 | 0.016 | 6.0 | 804 years | 99.9% |
| 2.0 | 1.0 | 14 | 3.9e-9 | 0.016 | 6.0 | 804 years | 99.9% |

§5's published sentence is *"Most worlds wait longer than a year. Some are never
contacted."* The right-hand column of the 10,000-world table is the honest
version of that sentence under the rule as written, and it reads **"almost all
worlds are never contacted."**

---

## 8 · What is decidable now, and what is not

**Decidable, on this evidence:**

- **z\* = 2.0, not 2.5.** 2.5 strands a fifth to a third of the catalogue
  permanently; 2.0 strands 7–15%. Neither is comfortable and 2.0 is clearly
  better.
- **The floor is 0.75 reading points** — or anything in 0.5–1.0. It is not a
  lever and the measurement says so.
- **Definition C** on every axis measured: fewest mute worlds (734 vs 1,312),
  tightest spread (3.99 vs 6.07), lowest seed lift (0.655 vs 0.758). It is a
  spec amendment, not an era change, because §3 fixes the estimator.
- **Activation is ~26 signals**, and it can be watched rather than guessed.

**Not decidable, and I do not think it can be decided by tuning:**

- **τ and the k-schedule.** No τ behaves at both catalogue sizes, and at the k
  each τ chooses, q is estimated from single-digit independent observations. The
  two failures compound: the schedule is reading a number the simulation did not
  measure, in order to hit a target that has no value that works.

**The three shapes an answer could take**, none of which is mine to pick:

1. **τ scales with N** — e.g. a fixed expected contacts *per world per year*
   rather than per sky per night. That makes the rule's promise the one a reader
   actually cares about, and it is a §3 amendment.
2. **k is capped where measurement reaches** — say k ≤ 8, with the cap published
   and the consequence stated: at 10,000 worlds that is many contacts a night,
   which may simply be what a large sky looks like.
3. **W lengthens.** A longer window moves r's distribution right and may give the
   schedule somewhere measurable to sit. Not run here; it is the cheapest next
   measurement and I would run it before anything else.

**Nothing above is final.** The harness is in the session scratchpad and takes
arguments for every parameter; say which of the three shapes is worth measuring
and it runs.