# Correspondence — the eligibility-plus-hash shape, measured

Run 2026-09-12, before any spec change. Real generator, shipped projection,
definition C (the residual), resonance night as defined — a world's own
baseline, one-sided z ≥ z\*, MAD floor 0.75 reading points.

**The shape measured here is not the one in §3.** §3 selects on *sustained*
co-movement: r ≥ k(n) shared resonance nights in a trailing window of W. This
measures a different rule:

> **Candidates** — same region, **both resonant tonight**. No window, no k.
> **Selection** — the night's finalised block hash draws pairs from the
> candidate set, once per pair ever, at a rate τ(N) chosen for a per-world
> median wait of about two years.

**No spec value is set by this report.**

---

## 1 · The headline — the rate follows from the promise, not from the parameters

This is the structural result and it is why the shape works where the
k-schedule did not.

Fix a per-world median wait `T` and the sky-wide rate is forced:

```
  contacts per night  ≈  N · ln2 / (2T)
```

A world is in half the pairs it belongs to; setting its median wait sets the
sky's total. Measured against that prediction:

| | predicted | measured (z\* = 1.0 / 1.5 / 2.0) |
|---|---|---|
| **43 worlds** | 0.020 / night | 0.016 / 0.018 / 0.017 |
| **10,000 worlds** | 4.75 / night | 4.53 / 4.62 / 5.37 |

**τ(N) is not a free parameter to be tuned — it is solved for.** Choose the
wait a world should expect and τ falls out; z\* then decides only whether the
candidate pool is *deep enough* to sustain it.

That is the whole difference from §3. There, τ was a bound on false pairs per
night, `k` had to be read off a tail nobody had measured, and no value worked
at both catalogue sizes. Here the promise is the input.

**At 43 worlds: ~6 contacts a year. At 10,000: ~1,700 a year.** Both follow
from the same two-year promise.

---

## 2 · The numbers

**43 worlds, the live catalogue's own names, 5 years**

| z\* | mute | cand. pairs/night | partners/world/night | τ (draw rate) | contacts/night |
|---|---|---|---|---|---|
| 1.0 | 1 (2.3%) | 2.97 | 0.138 | 1.04e-2 | 0.0162 |
| 1.5 | 1 (2.3%) | 1.15 | 0.053 | 6.32e-2 | 0.0184 |
| 2.0 | 1 (2.3%) | 0.46 | 0.021 | 2.07e-1 | 0.0167 |

| z\* | contacted in 5y | wait p25 / median / p75 | never in 1 yr |
|---|---|---|---|
| 1.0 | 62.8% | 0.81 / **1.81** / >5y | 58.1% |
| 1.5 | 67.4% | 0.31 / **1.79** / >5y | 58.1% |
| 2.0 | 65.1% | 0.27 / **1.35** / >5y | 55.8% |

**10,000 worlds, 3 years**

| z\* | mute | cand. pairs/night | partners/world/night | τ (draw rate) | contacts/night |
|---|---|---|---|---|---|
| 1.0 | **6 (0.1%)** | 250,160 | 50.03 | 1.80e-5 | 4.53 |
| 1.5 | **23 (0.2%)** | 102,608 | 20.52 | 4.46e-5 | 4.62 |
| 2.0 | 351 (3.5%) | 42,395 | 8.48 | 1.27e-4 | 5.37 |

| z\* | contacted in 3y | wait p25 / median / p75 | never in 1 yr |
|---|---|---|---|
| 1.0 | 60.4% | 0.89 / **2.19** / >3y | 72.5% |
| 1.5 | 56.8% | 0.95 / **2.35** / >3y | 74.5% |
| 2.0 | 55.7% | 0.89 / **2.29** / >3y | 72.2% |

Percentiles are over **all** worlds with the uncontacted censored, not over the
contacted subset — that would report the median of the lucky.

---

## 3 · Mute worlds — the shape's biggest gain

A mute world can never be contacted, assigned by seed, with no recourse. Under
the window rule this was the worst finding of the previous report. Here it
nearly disappears:

| z\* | mute at 10,000, **window rule** | mute at 10,000, **this shape** |
|---|---|---|
| 2.0 | 734 (7.3%) | **351 (3.5%)** |
| 1.5 | — | **23 (0.2%)** |
| 1.0 | — | **6 (0.1%)** |

Two reasons. Co-resonance on **one** night is enough to be a candidate, where
the window rule needed a world to reach r ≥ k repeatedly. And z\* = 1.0–1.5
is a far shallower cut than the 2.0–2.5 the window rule needed to keep M·q
under control — it did not have that freedom, because a lower z\* made q
explode. Here a lower z\* only makes the pool deeper, and τ absorbs it.

**z\* = 1.5 strands 23 worlds in ten thousand.** That is the first parameter
set in this whole exercise that does not permanently exclude somebody.

---

## 4 · The alignment attack

Target `martynas`; an aligned name at cos 0.9997 found in **2,344 tries**; a
field of 600 unchosen worlds in the same region; 1,095 nights.

| z\* | target's resonance nights | co-resonant: aligned | field mean | field max | **lift** |
|---|---|---|---|---|---|
| 1.0 | 152 | 143 | 45.84 | **144** | **3.1×** |
| 1.5 | 34 | 30 | 6.85 | **32** | **4.4×** |
| 2.0 | 10 | 6 | 0.86 | **8** | **6.9×** |

Two things, and the second matters more than the first.

**The lift is 3–7× and it is real.** A chosen name genuinely co-resonates more
often with its target, and the search costs milliseconds.

**But the aligned world never beats the field.** At every z\* the best
*unchosen* world in the region co-resonates at least as often — 144 against
143, 32 against 30, 8 against 6. **Aiming buys what the luckiest stranger
already has**, and the draw itself is uniform over candidates, so it cannot be
aimed at all. An attacker buys more *chances*, never a better one.

**Lower z\* suppresses the attack**: 3.1× at z\* = 1.0 against 6.9× at 2.0.
When everybody resonates often, co-resonance stops being distinguishing. So the
z\* that strands fewest worlds is also the z\* that most blunts the attack —
the two pull the same way, which they did not under the window rule.

**This does not make §2 true as written.** *"The selection is made by the sky.
Not by sender"* is still doing work a 3× lift argues with. It is a much weaker
version of risk 1 than the window rule had, and it is quantified rather than
suspected.

---

## 5 · Recomputability — confirmed

A stranger reproduces a night's contacts from three published things: the
**block hash**, that night's **resonance flags**, and each world's **region**,
which is its catalogId's prefix and needs no lookup.

```
  inputs read: the night's block hash, its 6 resonance flags, and each id's region prefix.
  candidate pairs (same region, both resonant): 4
    CD-0A1B2C3 + CD-0M5N6P4   [Cygnus Drift]
    CD-0A1B2C3 + CD-0Z9Y8X7   [Cygnus Drift]
    CD-0M5N6P4 + CD-0Z9Y8X7   [Cygnus Drift]
    LC-0Q1R2S3 + LC-0T4U5V6   [Lyra Cluster]

  drawn: CD-0A1B2C3 + CD-0Z9Y8X7
  recomputed from the same inputs: IDENTICAL
  with a different block hash:      different, as it must be
```

**Two implementation requirements** fall out, and both are cheap:

1. **The candidate list needs a canonical order**, because the hash indexes
   into it. Sort regions, then catalogIds within a region. Two readers who
   build the list in different orders get different contacts from the same
   hash, and neither would know.
2. **The hash must be stretched by counter** — `sha256(blockHash | index)` —
   so one 32-byte value decides any number of pairs. At 250,000 candidates a
   night this is not optional.

It is **strictly more checkable than §3's rule**: no q table, no simulation
report, no trailing window to reconstruct. One hash, one night's flags, one
prefix.

---

## 6 · What this shape fixes, and what it does not

**Fixes**

- **No tail to measure.** The previous report's central finding was that q(k)
  is unmeasured exactly where the schedule reads it. There is no q here.
- **One rule at both sizes.** The same two-year promise gives 6 contacts a year
  at 43 worlds and 1,700 at 10,000, and neither is a flood or a silence.
- **Mute worlds nearly gone** — 23 in ten thousand at z\* = 1.5.
- **τ is solved, not tuned.**

**Does not fix**

- **The seed link.** The alignment lift is 3–7×. Smaller than before,
  suppressed by low z\*, and never better than the luckiest stranger — but not
  zero, and §2's sentence still has to survive it.
- **"Most worlds wait longer than a year"** is now *true* rather than wildly
  understated: 72–75% at 10,000, 56–58% at 43. §5's published sentence fits
  this shape and did not fit the last one.

**Open, and not mine**

- **The two-year target itself.** Everything above is downstream of it. Two
  years gives 1,700 contacts a year at ten thousand worlds; five years gives
  680; one year gives 3,400.
- **z\*.** 1.0 and 1.5 are close on every measure; 1.5 halves the candidate
  pool and raises the attack lift from 3.1× to 4.4× while costing 17 more mute
  worlds in ten thousand. I would take **1.0**, and it is not my call.
- **Whether the sustained-co-movement idea is lost.** §1 says contact is
  *"sustained co-movement… past a published threshold"*. One shared night is
  not sustained. This shape may be better engineering and a worse promise, and
  that is the trade to weigh — a middle form (candidates need r ≥ 2 in a short
  window, then the hash draws) was not measured here and is the obvious next
  run if the word *sustained* is load-bearing.

---

*Report only. No spec change. The harness takes every parameter as a flag;
`--wait`, `--z` and `--worlds` re-run any of the above in minutes at 43 and
about ten at 10,000.*