The Separation Certificate
If independence is never free — if calling two things "separate" is a claim that has to be paid for — then there has to be a way to check whether a specific proposed separation has actually settled its bill. This page gives the public form of that check: a fixed set of seven questions any proposed separation must answer before it is treated as physically real rather than quietly assumed.
The seven questions
A proposed separation — of a system into subsystems, a geometry into a product of pieces, a spectrum into independent sectors, or an observer from an observed system — is asked to answer all seven of the questions below. An honest "not yet" to any single one of them means the separation is not established: it is a candidate, not a fact.
Six of the questions come straight from the core consistency principles every claim in the framework has to satisfy — Shape, Scale, Granularity, and Invariance, plus Nonseparability itself. The seventh, causal order, is added specifically for a proposed separation: it catches the case where a split was chosen only after the result it is supposed to explain was already known.
| Check | Question the separation must answer |
|---|---|
| Shape | What object is being split? Is this split part of the same fixed object — the same version, the same fingerprint — or did the argument quietly switch to a different object partway through? |
| Shape (cont.) | Is the split described precisely enough for someone else to check it, rather than merely gestured at? |
| Scale | Does the split smuggle in a new scale, threshold, or normalization that was not already on the books? A hidden second scale is a hidden second assumption, not a free description. |
| Granularity | What finite record proves the split exists? A distinction that cannot bottom out in a finite, auditable observation is not yet a physical distinction. |
| Invariance | Does the split survive the transformations it is supposed to survive — change of coordinates, gauge, basis, representation, or convention? A split that exists in only one convention is an artifact of the convention, not of the physics. |
| Causal order (the separation-specific question, not one of the core five) | Was the split fixed before the answer it is being used to explain was known? A split chosen to fit an answer already in hand is reconstruction after the fact, not a genuine structural finding. |
| Nonseparability | Is the independence of the two sides — the claim that they really are separate — proven, paid for by an observed anchor, and finitely recorded? Or is it still an open assumption? |
Four ways a separation can land
Running the seven questions against a concrete claim does not just return pass or fail. It sorts the separation into one of four honest boxes — the same bookkeeping the framework uses everywhere, so nothing gets quietly rounded up:
Paid
The separation is backed by an already-observed measurement. It is settled because the world has already recorded it — nothing further is owed.
Derived
The separation follows from the constraints themselves — it is forced, not merely allowed. The rarest and strongest outcome.
Open
The separation is admissible but not yet earned: at least one question answers "not yet." Its status is honestly open, and it is written down as open.
Inadmissible
The separation fails a question it cannot recover from — for example, no finite record could ever register it, or it lives only in one convention. It is ruled out, not shelved.
How to read a "no" answer
None of these questions is a trap designed to kill every separation. Ordinary, well-established separations in physics — two detectors at different locations, two decay channels with different final states, two particles with different measured masses — answer all seven questions easily, because they are backed by finite, invariant, causally-ordered, already-paid-for observations. The certificate is not skeptical of separation in general. It is skeptical only of separations that are assumed for convenience and never actually checked.
So a "no" or "not yet" on one question does not mean the separation is false. It means the separation's status is currently open — and the honest thing to do is say so, rather than write the split into a theory as though it were already settled.
The one-sentence version
For a general reader
A thing counts as separate only when the theory can say what separates it, at what scale, and by what finite record — and can show the split is genuine structure, not a hidden assumption dressed up as a description.
Where this has actually been applied
Two concrete places in the tested gate work have run this certificate against a real structural claim, and each landed in a named box — reported here at their actual, current status:
- The internal geometry's product structure — three separate geometric factors, one per force. Does treating them as separate pieces cost anything, or is it free? This lands as paid: the split we actually observe — the Standard Model's gauge group factoring into three parts — is backed by measurement and settled at the energies we can reach. Whether that observed product is also the low-energy face of one deeper unified geometry is a separate, openly-open question. See The Standard Model as Interface.
- Extra "spectator" matter sectors — proposed additions to the Standard Model that would sit alongside it without ever touching it. This is the strongest, rarest outcome: unpaid, disconnected spectator sectors are ruled out by the nonseparability constraint itself, not by a modeling choice. This does not, by itself, fix how many generations of matter there are. See Kinds of Separation.
Both are named on this site with their actual, current, unrounded status — including exactly what is still open.