Dark energy is the account nobody can draw on.
Folio I called Λ the locked reserve: vacuum correlation that exists but can never be withdrawn — and therefore never produces a force, only a constant floor in the books. Until tonight that was a phrase. Two measurements have since given it hands and feet. In Folio V's 3+1D run, the interaction's distance-blind component converted account to energy at par (E/δI = −0.975): a reserve term, present in both columns, immune to separation. What remained was to show the reserve exists as a matter of entanglement theory: that the vacuum holds correlation which no local protocol can drain.
The distinction is sharp and standard. The account is mutual information — all correlation, drainable or not. The drainable part is distillable entanglement: what local operations can actually extract as usable entangled pairs. A nonzero account with zero drainable content is a reserve — on the books, generating nothing, refusing withdrawal. Distillability has a hard criterion: any distillable state must have a nonpositive partial transpose, so where the logarithmic negativity EN is exactly zero, nothing can be drawn, by any protocol, ever.
If the drainable part (EN) persists wherever the account (mutual information) persists — no sudden death, locked fraction never reaching 100% — then the vacuum has no locked sector, and this folio's reading of Λ loses its mechanism.
The drainable part dies. The account survives it.
Two intervals of 8 sites in the chain vacuum, separation d swept. Both columns of the pair's account, near-critical arm (m = 10⁻³):
| d | account MI(A:B) | drainable E_N(A:B) | locked |
|---|---|---|---|
| 1 | 1.0658 | 0.23973 | 77.5% |
| 4 | 0.7897 | 0.03097 | 96.1% |
| 8 | 0.6642 | 0.00802 | 98.8% |
| 16 | 0.5478 | 0.00054 | 99.9% |
| 32 | 0.4447 | 0.000003 | 100.0% |
| 64 | 0.3591 | 0.000000 | 100.0% |
Read the last row slowly. At eight times the regions' own size, the vacuum still holds a third of a nat of correlation between them — and every bit of it is locked. The negativity is zero to the sixth decimal; no local protocol, however clever, can convert that account into usable entanglement. It is not small money that can't be withdrawn — it is real money, a persistent, slowly-decaying (logarithmic) account, all of it reserve.
Three structural facts from the full run:
The vacuum is overwhelmingly reserve even at contact. At d = 1 — the intervals touching — only 22.5% of the account is drainable. The liquid part of the vacuum was always the minority.
The reserve is a massless-sector phenomenon. The gapped arm (m = 0.1) shows the same locking, but there the account itself dies exponentially — by d = 32 only 0.00007 nats remain. A vacuum keeps long-range reserve only if it has a massless sector. Our universe has two — photons and gravitons — so its large-scale accounts are precisely of the persistent, fully-locked kind.
Locking is scale-stable. Doubling the account size (16-site intervals) shifts nothing structural: the locked fraction still climbs to 100% while the account holds at ≈ 0.38 nats out to twelve times the region size.
Why the reserve gravitates as a constant.
Assemble the three folios that touch it:
Force is the gradient of the drainable account. FOLIO V
Bodies settle toward configurations that change what can be exchanged with the vacuum's books — the Yukawa equality. A gradient requires an account that responds to separation and to withdrawal.
The locked component cannot respond. THIS FOLIO
Beyond d*, the entire account is undrainable. No transaction can touch it; no body can deplete it; monogamy's withdrawal mechanism (Folio III) has nothing to grip. A correlation that cannot be traded generates no gradient — and a term with no gradient enters the field equations only one way: as a constant.
And it is already on the books at par. FOLIO V, 3D ARM
The measured distance-blind floor converts account to energy at E/δI = −0.975 ≈ −1: the reserve is not bookkeeping fiction — it carries energy, uniformly, everywhere, regardless of separation. Uniform energy with no gradient, sourced by correlation nobody can withdraw: that is a cosmological constant, described rather than fine-tuned.
It is the part of the vacuum's wealth that is structurally untouchable — and at cosmological range, that part is all of it.
Find the reserve yourself.
Source: n5_reserve.py · data: n5_results.json
- Locked ≠ necessarily bound-entangled. EN = 0 proves undistillability (PPT states cannot be distilled, period). It does not say whether the surviving account is bound entanglement or classical correlation — for 1×1 Gaussian modes PPT even implies separable. For the Ledger's mechanism the distinction is secondary (neither can be withdrawn as entanglement), but for the physics of what Λ is, it matters; the decomposition is owed.
- This is a lattice toy — one free boson chain, intervals, nats. The covariant statement (locked fraction of the QED + gravity vacuum, ball-shaped regions, all scales) is unwritten.
- No value of Λ is predicted. The folio supplies the mechanism — why the untouchable sector gravitates as a constant — not the magnitude. The magnitude is the long shot in §III, and it is owed, not promised.
- d* is resolution-limited: negativity falls through double precision before it formally hits zero; the quoted "exact zero" means < 10⁻¹² in a calculation whose smallest honest digit is ~10⁻¹³. An mpmath pass (the Folio IV lesson) would pin d* precisely.
- What this folio establishes: the vacuum's correlation account has a component that no local operation can withdraw; that component dominates everywhere and is everything beyond a finite range; it persists only in massless sectors — and it is already measured (Folio V) to carry energy at par. The cosmological constant has a candidate identity: the vacuum's bound account.