# Pre-registration: the proton–electron mass ratio, the series closed — superseding entry

**Freeze date:** 2026-09-06
**Author:** G · Studio G · the420code.org
**Scope:** AP49 (*The Hold*), superseding by reference the entry of 2026-08-02 (*Pre-registration: the proton–electron mass ratio at order α³*, digest 6ea78dac4e47a4c9…), which stands beside this one, never in its place.
**Status:** frozen for commit with AP49 FINAL v1.0. The commit hash is the timestamp.

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## 1. What changed, per condition 5 of the entry of 2 August

The registered prediction D = 1836.152673444331 (the series truncated at α²) is superseded by

**D_closed = 1836.152673444951**,

the same formula with its series closed:

    m_p/m_e = 1836 + 21α·(1 − 1/(84π)) + 21α·r/(1 − r),  r = 16α/1836.

The change is the tail beyond second order, +6.20 × 10⁻¹⁰. The rule that produces it — every order beyond the first is the previous order times r — was given by the author on 6 September 2026 before any arithmetic was shown to him (AP49 §4 and PROV-HOLD.1).

## 2. The order-α³ coefficient, with its sign, per condition 3

**c₃ = 21·16²/1836² = +1.595 × 10⁻³**, sign positive, stated in advance. The measurement’s own constraint on c₃ (entry of 2 August, §5) is −0.047 ± 0.082; the registered value sits at 0.59σ inside it. The rank-3 continuation 4³ = 64, excluded at 9.5σ by the entry of 2 August, is not produced: the third holder’s share is of the repair, so its coefficient is 21·16²/1836², not 21·64/1836.

The chain adds at every order. It does not close the present gap and does not try to: D_closed sits 6 × 10⁻¹⁰ further from the CODATA 2022 central value than D did, +0.57σ → +0.59σ (the prediction above the measurement). No negative term exists in the chain and none will be offered.

## 3. The sixteen, per KS-30.3

Read in AP49 §3 as the four conditions of the record’s repair held through the four dimensional expressions: 4 × 4, a share of the whole. The pin of the entry of 2 August, 16 = 15.97 ± 0.05 and 336 = 21 × 16, stands. KS-30.3 → PAID at the structural register on the author’s rule (AP30’s dated note of this date).

## 4. Against measurement (CODATA 2022, 1836.152673426(32); H₂⁺ 2025, 1836.152673414(47))

| | D_closed − measured | σ |
|---|---|---|
| CODATA 2022 | +1.895 × 10⁻⁸ = +10.3 ppt | +0.59σ |
| H₂⁺ (Nature 644, 69, 2025) | +3.10 × 10⁻⁸ | +0.66σ |

Propagated uncertainty from α: 0.013 ppt.

## 5. Binding conditions (KS-HOLD.1, .2, .3 as printed in AP49 §7)

1. **KILL D_closed (KS-HOLD.1).** Dies at 3σ once the measurement uncertainty reaches **3.4 ppt** with the central value unchanged, and at 5σ at **2.1 ppt**. Current best is 17.4 ppt. The third-order term itself is resolved at one sigma at about 52 times today’s precision; the fourth at about 8 × 10⁵. Fires in either direction.
2. **THE BASE (KS-HOLD.3).** The chain holds against the repair’s bare coupling 21α, not the repair net of its returned leak; the leaked alternative gives 1836.152673408, 3.7 × 10⁻⁸ below. CODATA 2022 sits between the two at +0.59σ / −0.56σ. At 1.7 ppt they are twelve sigma apart; at 3 ppt, about seven. Fires if the measurement settles on the leaked value or on neither.
3. **THE READING (KS-HOLD.2).** A second-order support count is its object through the four dimensional expressions — 21 × 4, 2 × 4, 4 × 4. Fires if any such count in the corpus is found to require another form.
4. **NO POST-HOC c₃.** Inherited unchanged from the entry of 2 August. The coefficient above is the one and only, derived from the author’s rule and published with its sign before any measurement that can reach it.
5. **No retro-editing.** This file’s hash and date are the record.

## 6. The version chain anchored

AP49 v0.3 docx 4d159dd0f34bfa2e… and v0.5 md 254e493652506e54… (witnessed by an external reviewer, 6 September 2026); v0.6 md 71fb8ee049240ded…; FINAL v1.0 md 3f9b1b52907c6025…, docx 200110b324c1da8f…, pdf 290f143fba1a3ce6…. The full lineage v0.1–v0.6 is in the freeze bundle of this date.

*Copyleft 2026. Don’t be a cunt. Be kind.*