An anomaly was sitting in the books, unnamed.
When the saturation test (N1) measured a single site's accounts, it found something it filed as a caution and moved past: summing the site's mutual information with all pairs over-counted its total budget by a factor of 27. An over-count of that size is not sloppy bookkeeping — sub-additivity does not fail by accident. It means the same information is copied, again and again, across the vacuum. The chain is not keeping one record; it is running a wire service. That is the signature Zurek named quantum Darwinism: classical, objective facts are the ones an environment broadcasts redundantly, so that many observers can read them independently without disturbing one another.
The outlier question, asked of the only ledger this house keeps: is geometry itself such a fact? Is the position of a mass classical and objective because the vacuum broadcasts it — and would a different vacuum keep it quantum and private?
If the massless vacuum does not show broadcast structure — if the number of disjoint fragments that can each independently distinguish two defect positions is comparable between massless and gapped vacua — the thesis is dead.
Every piece of the vacuum knows where the mass is.
Arena: the chain vacuum (N = 240), tiled into 28 disjoint 8-site fragments — disjointness is everything; it forbids double counting and models independent local observers. A mass = a pinned defect at site a or at a + 2. Per fragment, the discrimination power Dj = S(ρF(a) ‖ ρF(b)) — the quantum relative entropy between what that fragment alone holds in the two worlds: the operational rate at which that fragment, by itself, can tell where the mass sits. (Numerical gate: S(ρ‖ρ) = 6×10⁻¹⁴; Gaussian entanglement-Hamiltonian machinery throughout.)
| Vacuum | R(δ = 10⁻⁶) | R(δ = 10⁻⁸) | D_j vs distance |
|---|---|---|---|
| Massless (m = 10⁻³) | 22 / 28 | 28 / 28 | power law: 1.5×10⁻³ (d=12) → 3.5×10⁻⁷ (d=108) |
| Gapped (m = 0.3) | 1 / 28 | 2 / 28 | 5.97×10⁻⁷ (d=12), then machine zero (10⁻¹⁴) everywhere |
Read the contrast at full width. In the massless vacuum, every single fragment — out to the far end of the chain — independently records where the mass is, with discrimination decaying only as a power law: an inexhaustible supply of copies, one per neighbourhood, readable without consulting anyone else. Gap the vacuum and the broadcast stops dead at the correlation length: beyond ξ, no fragment holds any record — not a weak one, none, to fourteen digits. The same structure shows in the value channel (arm 1): the massless vacuum gives every fragment ≈ 0.4–0.7 nats about a probe site — a nearly flat profile, the wire-service signature, and the origin of N1's ×27 — while the gapped vacuum gives zero to all but the adjacent block.
In a gapped vacuum, geometry is private.
Our universe gravitates with a massless field. Spacetime is classical because it is broadcast.
The third sector, and the books reorganized.
This folio adds the missing column to the vacuum's trial balance. The day's earlier measurements split the books two ways: the thin liquid layer (pairwise negativity — where forces live, Folio V) and the dominant locked sector (undistillable — where Λ lives, Folio VI). The broadcast is the third entry, and it answers the question the other two could not:
| Sector | Its measure | Its physics |
|---|---|---|
| Liquid | pairwise negativity (2 shells only; 11–40% of the budget) | Forces — the Yukawa equality of Folio V |
| Locked | undistillable remainder (100% beyond finite range) | Λ — the reserve of Folio VI |
| Broadcast | redundant MI across disjoint fragments (×27; 28/28) | Classicality — objective geometry, this folio |
Three consequences, in ascending order of reach:
Why gravitational which-path information is unshieldable. The old shielding argument (gravity cannot be caged) returns with a mechanism: a superposition of mass positions is a superposition of publications — the which-path record is not in one place to be screened; it is in 28 places out of 28. Decoherence of massive superpositions (DSW, the horizon fee of Folio VIII) is the dynamics of an object whose location was never private to begin with.
The equivalence principle as editorial policy. Annex B measured that the far field forgets everything about a source except its energy (point-mass comparator 0.999). Combined with this folio: the vacuum does not broadcast everything — it broadcasts exactly the gravitational data (the stress moments) and discards the rest. What is public about an object is precisely its geometry. Einstein's principle, reread: geometry is the public sector of matter.
The Λ–objectivity link. CONJECTURE The broadcast and the locked reserve are both massless-sector phenomena — the same modes that publish geometry hold the undrainable account. If that is not a coincidence (and in the toy the gapped vacuum loses both at once), then dark energy and the classicality of spacetime are two faces of one sector: Λ is the standing cost of the publication — the universe pays a constant to keep geometry public. Stamped, quarantined, and pointed at the obvious test: compute the locked fraction and the redundancy together as the gap is dialled, and see whether they die at the same ξ.
Stamps, debts, ancestry.
- Ancestry, declared before any audit: quantum Darwinism is Zurek's (2003–2009); Riedel–Zurek showed scattered sunlight redundantly broadcasts object positions (why the Moon's location is objective); Korbicz et al. formalized spectrum-broadcast structures. What this folio adds — to our knowledge, unaudited: the static vacuum dressing version (no radiation, no scattering, the ground state itself as the broadcast medium), the massless/gapped dichotomy as the public/private switch for geometry, and the three-sector trial balance. Adversarial audit round 3 is owed before "new" is said in print.
- Relative entropy is an asymptotic rate (Stein exponent) — the right per-fragment, independent-observer measure, but a fragment with D_j = 10⁻⁸ needs ~10⁸ copies of the experiment to read its record; "objectivity" here is in-principle redundancy, as in all Darwinism literature.
- The defect is a static pin, not a superposed quantum source. The bridge from "two dressed vacua are fragment-wise distinguishable" to "a superposed source decoheres into a public pointer basis" is the standard which-path identification — stated, not re-derived.
- Scaling claim is extrapolated: the power-law D_j(d) implies R(δ) grows without bound with system size in the massless case (infinite redundancy in the thermodynamic limit) vs. R fixed ≈ ξ/|F| when gapped. Measured at N = 240 only; the N-scaling run is named, not done.
- One vacuum, one dimension, Gaussian throughout. The photon/graviton statement is the conjecture this toy points at, not what it proves.
- What this folio establishes: in the toy, geometric information is redundantly, independently readable everywhere if and only if the vacuum is massless — broadcast structure measured 28/28 against a 1/28 control, from a kill-gate written first. The ×27 anomaly of N1 is explained and promoted from caution to phenomenon.
Source: n10_broadcast.py · data: n10_results.json