# Genesis emission curve — the first 100 mints after a 132.50 TON donation

**Measured** 2026-09-26 · **generator** `sim/scripts/run_phase1.py` (seed 20260814) · **decision** `DECISIONS.md` D-100 point 2, D-154 · **spec** `CONCEPT.md` §5, §6 point 3

This is a **measurement record**, not a work list. Nothing in it is a to-do.

## Why this file exists

D-100 point 2 replaced D-92's 240 TON genesis donation with 4.20 TON, and
D-154 raised it to **132.50 TON**. The derivation method is unchanged through
both; only its input moves. The consequence the decision commits to
publishing *before deploy* is this one:

> a mint's rebate is `R = k · I · S / T` PRIMES (§5), and `S / T` is `1 / p_f`.
> A smaller genesis floor makes every TON of injection buy proportionally
> more PRIMES, so the donation also sizes the front-loaded emission below.

The **ratchet theorem is untouched** — `k < 1` still makes `p_f = T/S` strictly
increasing on every mint, and this run confirms it over the whole curve. But
*the floor rises* and *supply is stable* are different claims. This file measures
the second one.

## Genesis state the curve starts from

| quantity | value | where it comes from |
|---|---|---|
| `T₀` (`seedT`) | **132.50 TON** | D-100 point 2, owner-set. After D-100 point 1 a donation is the *only* thing that lands in `seedT`. |
| `S₀` | **12,312,854 PRIMES** | 10,000,000 bounty vault (D-43) + 1,000,000 vested to the treasury (D-100 point 6; D-166 deleted the operator's 1 M) + the donor's `donate_floor` mint, `T₀ · L` tapered by D-156 (D-100 point 1). |
| `p_f0` | **1.076111e-05 TON/PRIMES** | `T₀ / S₀`. D-92's figure was 1.667e-5 — this is 1.55× lower. |
| `L` | 10,000 PRIMES/TON | D-39, untouched: a denomination knob, not a price. |

## Method

The curve is **not a second model**. It replays the base-case Phase 1 run's own
realised `(kind, β, k)` stream, mint by mint, in order. `β` (the residual
injected into the ratchet) and `k` (the rebate coefficient — `0` on every prime
mint, §5.1) are both independent of the floor, so replaying them from a different
genesis state is exact arithmetic rather than a re-simulation.

The run is on the **D-20** model: primes are not head mints, so the table lists
composites only and opens at **n = 4**. A prime's Dutch lot raises `T` with zero
emission (§5.1, D-7); the replay leaves that TON out, which understates the floor
and so overstates emission — the conservative direction for this file.

## What the curve shows

| claim in D-100 point 2 | measured | verdict |
|---|---|---|
| the first mints emit "on the order of 15% of `S₀`" | the largest single mint emits **0.35%** of `S₀` (mint 1: 0.17%) | **NO** |
| "self-correcting within ~10 mints" | the first 10 mints account for **16.9%** of all emission over the curve, and no mint after the tenth emits more than **0.295%** of `S₀` | **NO** |
| the ratchet still holds | `p_f` monotone over all 100 mints | **yes** |

A per-mint ratio *at exactly mint 10* would have been the wrong instrument and is
deliberately not used: mint 10 may be a prime, and a prime emits nothing at all
(§5.1), so that ratio can read `0.00` for a reason with nothing to do with decay.

## The honest reading

The per-mint emission does fall fast. It is a `k·β / T` term and `T` grows by `β`
every mint from a base of only 132.50 TON, so the denominator runs away from the
numerator almost immediately. Over the first 100 mints:

- `T` grows **1.3×**, to 176.30 TON;
- `S` grows **1.11×**, to 13,651,759 PRIMES — a cumulative emission of **10.9% of `S₀`**;
- `p_f` rises **1.20×**, to 1.291409e-05 TON/PRIMES;
- mint 100 emits 0.1316% of `S₀`.

What that costs, and what it does not. It is **not a solvency problem**: nothing
here can make `p_f` fall, `S` is never decremented (§3.3), and every emitted
PRIMES is backed by the same `T` that received the injection — the floor ends the
curve **1.20×** higher than it started. It is a **dilution schedule**, and it is
front-loaded by construction: whoever mints first buys PRIMES at a floor
1.55× cheaper than D-92's would have been. D-100 point 2 calls this
"D-91's own
complaint reproduced by choice" and accepts it in writing; this file is the
measurement that makes the choice legible rather than a footnote.

The number to carry away is the cumulative one: the first 100 mints multiply
`S₀` by **1.11**, and the floor still ends up **1.20×** where it began.

## The first 100 mints

`k = 0` rows are prime mints (§5.1: primes emit nothing and ratchet ~11× harder).

| # | n | kind | k | β (TON) | rebate (PRIMES) | % of `S₀` | T (TON) | S (PRIMES) | `p_f` | `p_f/p_f0` |
|--:|--:|---|--:|--:|--:|--:|--:|--:|--:|--:|
| 1 | 4 | composite | 0.5372 | 0.4250 | 21,215 | 0.172% | 132.925 | 12,334,069 | 1.078e-05 | 1.0015 |
| 2 | 6 | composite | 0.8907 | 0.5250 | 43,393 | 0.352% | 133.450 | 12,377,462 | 1.078e-05 | 1.0019 |
| 3 | 8 | composite | 0.1979 | 0.4250 | 7,802 | 0.063% | 133.875 | 12,385,264 | 1.081e-05 | 1.0045 |
| 4 | 9 | composite | 0.2056 | 0.5250 | 9,988 | 0.081% | 134.400 | 12,395,252 | 1.084e-05 | 1.0076 |
| 5 | 10 | composite | 0.9402 | 0.4250 | 36,852 | 0.299% | 134.825 | 12,432,104 | 1.084e-05 | 1.0078 |
| 6 | 12 | composite | 0.3606 | 0.4250 | 14,132 | 0.115% | 135.250 | 12,446,235 | 1.087e-05 | 1.0098 |
| 7 | 14 | composite | 0.9402 | 0.4250 | 36,769 | 0.299% | 135.675 | 12,483,005 | 1.087e-05 | 1.0100 |
| 8 | 15 | composite | 0.1979 | 0.5250 | 9,560 | 0.078% | 136.200 | 12,492,565 | 1.090e-05 | 1.0131 |
| 9 | 16 | composite | 0.9401 | 0.4250 | 36,648 | 0.298% | 136.625 | 12,529,213 | 1.090e-05 | 1.0133 |
| 10 | 18 | composite | 0.1979 | 0.5250 | 9,529 | 0.077% | 137.150 | 12,538,741 | 1.094e-05 | 1.0164 |
| 11 | 20 | composite | 0.2252 | 0.4250 | 8,749 | 0.071% | 137.575 | 12,547,490 | 1.096e-05 | 1.0189 |
| 12 | 21 | composite | 0.3005 | 0.4250 | 11,646 | 0.095% | 138.000 | 12,559,136 | 1.099e-05 | 1.0211 |
| 13 | 22 | composite | 0.9401 | 0.4250 | 36,361 | 0.295% | 138.425 | 12,595,496 | 1.099e-05 | 1.0213 |
| 14 | 24 | composite | 0.1979 | 0.4250 | 7,653 | 0.062% | 138.850 | 12,603,150 | 1.102e-05 | 1.0238 |
| 15 | 25 | composite | 0.2744 | 0.4250 | 10,585 | 0.086% | 139.275 | 12,613,735 | 1.104e-05 | 1.0261 |
| 16 | 26 | composite | 0.3076 | 0.5250 | 14,624 | 0.119% | 139.800 | 12,628,358 | 1.107e-05 | 1.0287 |
| 17 | 27 | composite | 0.2304 | 0.4250 | 8,844 | 0.072% | 140.225 | 12,637,202 | 1.110e-05 | 1.0311 |
| 18 | 28 | composite | 0.2708 | 0.4250 | 10,372 | 0.084% | 140.650 | 12,647,574 | 1.112e-05 | 1.0334 |
| 19 | 30 | composite | 0.3843 | 0.4250 | 14,685 | 0.119% | 141.075 | 12,662,260 | 1.114e-05 | 1.0353 |
| 20 | 32 | composite | 0.3871 | 0.4250 | 14,767 | 0.120% | 141.500 | 12,677,027 | 1.116e-05 | 1.0372 |
| 21 | 33 | composite | 0.6470 | 0.4250 | 24,636 | 0.200% | 141.925 | 12,701,662 | 1.117e-05 | 1.0383 |
| 22 | 34 | composite | 0.2100 | 0.4250 | 7,987 | 0.065% | 142.350 | 12,709,650 | 1.120e-05 | 1.0408 |
| 23 | 35 | composite | 0.2238 | 0.4250 | 8,491 | 0.069% | 142.775 | 12,718,141 | 1.123e-05 | 1.0432 |
| 24 | 36 | composite | 0.6381 | 0.4250 | 24,157 | 0.196% | 143.200 | 12,742,299 | 1.124e-05 | 1.0443 |
| 25 | 38 | composite | 0.2007 | 0.4250 | 7,591 | 0.062% | 143.625 | 12,749,889 | 1.126e-05 | 1.0468 |
| 26 | 39 | composite | 0.4541 | 0.4250 | 17,131 | 0.139% | 144.050 | 12,767,020 | 1.128e-05 | 1.0485 |
| 27 | 40 | composite | 0.2613 | 0.4250 | 9,841 | 0.080% | 144.475 | 12,776,862 | 1.131e-05 | 1.0508 |
| 28 | 42 | composite | 0.2045 | 0.4250 | 7,685 | 0.062% | 144.900 | 12,784,547 | 1.133e-05 | 1.0532 |
| 29 | 44 | composite | 0.2483 | 0.5250 | 11,503 | 0.093% | 145.425 | 12,796,050 | 1.136e-05 | 1.0561 |
| 30 | 45 | composite | 0.2072 | 0.4250 | 7,748 | 0.063% | 145.850 | 12,803,798 | 1.139e-05 | 1.0585 |
| 31 | 46 | composite | 0.3329 | 0.4250 | 12,420 | 0.101% | 146.275 | 12,816,217 | 1.141e-05 | 1.0606 |
| 32 | 48 | composite | 0.2809 | 0.5250 | 12,921 | 0.105% | 146.800 | 12,829,138 | 1.144e-05 | 1.0633 |
| 33 | 49 | composite | 0.9399 | 0.4250 | 34,909 | 0.284% | 147.225 | 12,864,047 | 1.144e-05 | 1.0635 |
| 34 | 50 | composite | 0.1979 | 0.4250 | 7,348 | 0.060% | 147.650 | 12,871,395 | 1.147e-05 | 1.0660 |
| 35 | 51 | composite | 0.7681 | 0.4250 | 28,459 | 0.231% | 148.075 | 12,899,854 | 1.148e-05 | 1.0667 |
| 36 | 52 | composite | 0.9398 | 0.4250 | 34,797 | 0.283% | 148.500 | 12,934,651 | 1.148e-05 | 1.0669 |
| 37 | 54 | composite | 0.4297 | 0.5250 | 19,648 | 0.160% | 149.025 | 12,954,299 | 1.150e-05 | 1.0690 |
| 38 | 55 | composite | 0.2514 | 0.4250 | 9,289 | 0.075% | 149.450 | 12,963,588 | 1.153e-05 | 1.0713 |
| 39 | 56 | composite | 0.1979 | 0.4250 | 7,294 | 0.059% | 149.875 | 12,970,882 | 1.155e-05 | 1.0737 |
| 40 | 57 | composite | 0.9398 | 0.4250 | 34,567 | 0.281% | 150.300 | 13,005,449 | 1.156e-05 | 1.0739 |
| 41 | 58 | composite | 0.1978 | 0.4250 | 7,276 | 0.059% | 150.725 | 13,012,725 | 1.158e-05 | 1.0764 |
| 42 | 60 | composite | 0.2247 | 0.4250 | 8,245 | 0.067% | 151.150 | 13,020,970 | 1.161e-05 | 1.0787 |
| 43 | 62 | composite | 0.2904 | 0.4250 | 10,633 | 0.086% | 151.575 | 13,031,603 | 1.163e-05 | 1.0809 |
| 44 | 63 | composite | 0.2689 | 0.5250 | 12,137 | 0.099% | 152.100 | 13,043,740 | 1.166e-05 | 1.0836 |
| 45 | 64 | composite | 0.2342 | 0.4250 | 8,537 | 0.069% | 152.525 | 13,052,276 | 1.169e-05 | 1.0859 |
| 46 | 65 | composite | 0.3220 | 0.4250 | 11,713 | 0.095% | 152.950 | 13,063,989 | 1.171e-05 | 1.0880 |
| 47 | 66 | composite | 0.4408 | 0.4250 | 16,000 | 0.130% | 153.375 | 13,079,989 | 1.173e-05 | 1.0897 |
| 48 | 68 | composite | 0.2027 | 0.4250 | 7,347 | 0.060% | 153.800 | 13,087,336 | 1.175e-05 | 1.0921 |
| 49 | 69 | composite | 0.2895 | 0.5250 | 12,934 | 0.105% | 154.325 | 13,100,270 | 1.178e-05 | 1.0947 |
| 50 | 70 | composite | 0.3125 | 0.4250 | 11,275 | 0.092% | 154.750 | 13,111,544 | 1.180e-05 | 1.0968 |
| 51 | 72 | composite | 0.2527 | 0.4250 | 9,100 | 0.074% | 155.175 | 13,120,645 | 1.183e-05 | 1.0990 |
| 52 | 74 | composite | 0.2243 | 0.4250 | 8,059 | 0.065% | 155.600 | 13,128,704 | 1.185e-05 | 1.1014 |
| 53 | 75 | composite | 0.2025 | 0.4250 | 7,262 | 0.059% | 156.025 | 13,135,966 | 1.188e-05 | 1.1038 |
| 54 | 76 | composite | 0.2008 | 0.4250 | 7,183 | 0.058% | 156.450 | 13,143,149 | 1.190e-05 | 1.1062 |
| 55 | 77 | composite | 0.3157 | 0.4250 | 11,272 | 0.092% | 156.875 | 13,154,421 | 1.193e-05 | 1.1082 |
| 56 | 78 | composite | 0.2212 | 0.4250 | 7,883 | 0.064% | 157.300 | 13,162,305 | 1.195e-05 | 1.1106 |
| 57 | 80 | composite | 0.1988 | 0.4250 | 7,071 | 0.057% | 157.725 | 13,169,375 | 1.198e-05 | 1.1130 |
| 58 | 81 | composite | 0.2330 | 0.4250 | 8,267 | 0.067% | 158.150 | 13,177,643 | 1.200e-05 | 1.1153 |
| 59 | 82 | composite | 0.2346 | 0.4250 | 8,309 | 0.067% | 158.575 | 13,185,952 | 1.203e-05 | 1.1175 |
| 60 | 84 | composite | 0.6530 | 0.4250 | 23,077 | 0.187% | 159.000 | 13,209,029 | 1.204e-05 | 1.1186 |
| 61 | 85 | composite | 0.2730 | 0.4250 | 9,641 | 0.078% | 159.425 | 13,218,669 | 1.206e-05 | 1.1208 |
| 62 | 86 | composite | 0.2000 | 0.4250 | 7,047 | 0.057% | 159.850 | 13,225,716 | 1.209e-05 | 1.1231 |
| 63 | 87 | composite | 0.2368 | 0.4250 | 8,327 | 0.068% | 160.275 | 13,234,043 | 1.211e-05 | 1.1254 |
| 64 | 88 | composite | 0.2091 | 0.4250 | 7,336 | 0.060% | 160.700 | 13,241,380 | 1.214e-05 | 1.1278 |
| 65 | 90 | composite | 0.2053 | 0.4250 | 7,189 | 0.058% | 161.125 | 13,248,569 | 1.216e-05 | 1.1302 |
| 66 | 91 | composite | 0.2631 | 0.4250 | 9,195 | 0.075% | 161.550 | 13,257,764 | 1.219e-05 | 1.1323 |
| 67 | 92 | composite | 0.1998 | 0.4250 | 6,970 | 0.057% | 161.975 | 13,264,734 | 1.221e-05 | 1.1347 |
| 68 | 93 | composite | 0.2024 | 0.4250 | 7,044 | 0.057% | 162.400 | 13,271,779 | 1.224e-05 | 1.1371 |
| 69 | 94 | composite | 0.2010 | 0.4250 | 6,982 | 0.057% | 162.825 | 13,278,760 | 1.226e-05 | 1.1395 |
| 70 | 95 | composite | 0.2033 | 0.4250 | 7,045 | 0.057% | 163.250 | 13,285,805 | 1.229e-05 | 1.1418 |
| 71 | 96 | composite | 0.2847 | 0.4250 | 9,847 | 0.080% | 163.675 | 13,295,652 | 1.231e-05 | 1.1440 |
| 72 | 98 | composite | 0.2000 | 0.4250 | 6,904 | 0.056% | 164.100 | 13,302,556 | 1.234e-05 | 1.1463 |
| 73 | 99 | composite | 0.3514 | 0.4250 | 12,105 | 0.098% | 164.525 | 13,314,662 | 1.236e-05 | 1.1483 |
| 74 | 100 | composite | 0.3321 | 0.4250 | 11,421 | 0.093% | 164.950 | 13,326,083 | 1.238e-05 | 1.1503 |
| 75 | 102 | composite | 0.3167 | 0.4250 | 10,875 | 0.088% | 165.375 | 13,336,958 | 1.240e-05 | 1.1523 |
| 76 | 104 | composite | 0.2933 | 0.4250 | 10,053 | 0.082% | 165.800 | 13,347,011 | 1.242e-05 | 1.1544 |
| 77 | 105 | composite | 0.3567 | 0.4250 | 12,205 | 0.099% | 166.225 | 13,359,216 | 1.244e-05 | 1.1563 |
| 78 | 106 | composite | 0.3952 | 0.4250 | 13,500 | 0.110% | 166.650 | 13,372,716 | 1.246e-05 | 1.1581 |
| 79 | 108 | composite | 0.1984 | 0.4250 | 6,765 | 0.055% | 167.075 | 13,379,481 | 1.249e-05 | 1.1604 |
| 80 | 110 | composite | 0.4062 | 0.4250 | 13,826 | 0.112% | 167.500 | 13,393,307 | 1.251e-05 | 1.1622 |
| 81 | 111 | composite | 0.2936 | 0.4250 | 9,977 | 0.081% | 167.925 | 13,403,284 | 1.253e-05 | 1.1643 |
| 82 | 112 | composite | 0.2038 | 0.4250 | 6,912 | 0.056% | 168.350 | 13,410,196 | 1.255e-05 | 1.1666 |
| 83 | 114 | composite | 0.2007 | 0.4250 | 6,796 | 0.055% | 168.775 | 13,416,992 | 1.258e-05 | 1.1689 |
| 84 | 115 | composite | 0.1981 | 0.4250 | 6,694 | 0.054% | 169.200 | 13,423,686 | 1.260e-05 | 1.1713 |
| 85 | 116 | composite | 0.2014 | 0.4250 | 6,790 | 0.055% | 169.625 | 13,430,476 | 1.263e-05 | 1.1737 |
| 86 | 117 | composite | 0.2623 | 0.4250 | 8,828 | 0.072% | 170.050 | 13,439,304 | 1.265e-05 | 1.1758 |
| 87 | 118 | composite | 0.3709 | 0.4250 | 12,458 | 0.101% | 170.475 | 13,451,761 | 1.267e-05 | 1.1777 |
| 88 | 119 | composite | 0.9395 | 0.4250 | 31,507 | 0.256% | 170.900 | 13,483,268 | 1.267e-05 | 1.1778 |
| 89 | 120 | composite | 0.1978 | 0.4250 | 6,632 | 0.054% | 171.325 | 13,489,900 | 1.270e-05 | 1.1802 |
| 90 | 121 | composite | 0.5516 | 0.5250 | 22,801 | 0.185% | 171.850 | 13,512,701 | 1.272e-05 | 1.1818 |
| 91 | 122 | composite | 0.2145 | 0.4250 | 7,169 | 0.058% | 172.275 | 13,519,871 | 1.274e-05 | 1.1841 |
| 92 | 123 | composite | 0.3565 | 0.4250 | 11,891 | 0.097% | 172.700 | 13,531,762 | 1.276e-05 | 1.1860 |
| 93 | 124 | composite | 0.6432 | 0.5250 | 26,460 | 0.215% | 173.225 | 13,558,222 | 1.278e-05 | 1.1873 |
| 94 | 125 | composite | 0.2001 | 0.4250 | 6,656 | 0.054% | 173.650 | 13,564,878 | 1.280e-05 | 1.1896 |
| 95 | 126 | composite | 0.2161 | 0.4250 | 7,174 | 0.058% | 174.075 | 13,572,052 | 1.283e-05 | 1.1919 |
| 96 | 128 | composite | 0.4267 | 0.5250 | 17,467 | 0.142% | 174.600 | 13,589,519 | 1.285e-05 | 1.1939 |
| 97 | 129 | composite | 0.2565 | 0.4250 | 8,485 | 0.069% | 175.025 | 13,598,004 | 1.287e-05 | 1.1961 |
| 98 | 130 | composite | 0.9394 | 0.4250 | 31,019 | 0.252% | 175.450 | 13,629,023 | 1.287e-05 | 1.1963 |
| 99 | 132 | composite | 0.1978 | 0.4250 | 6,529 | 0.053% | 175.875 | 13,635,553 | 1.290e-05 | 1.1986 |
| 100 | 133 | composite | 0.4918 | 0.4250 | 16,206 | 0.132% | 176.300 | 13,651,759 | 1.291e-05 | 1.2001 |

## Regenerating this file

`cd sim && python scripts/run_phase1.py`. It is written by the same pass that
writes `shared/params.json`, from the same run, so the two can never disagree.