Framework page · status as of 3 September 2026
What follows from the fact that one claim is kept in two records.
Economics begins the moment one fact is written in two places. Actual economics is the complete account of what that forces and what it leaves to people.
When one person owes another, there are two written records of it: the creditor's, kept as an asset, and the debtor's, kept as a liability. Each is on its own books. Nothing makes them agree. Every accounting system on Earth has this structure; national accounting calls it quadruple entry. Every economic model drops it and writes one number per link.
We keep the second record and ask what it forces. Nothing else is added at the start: no preference, no utility, no market, no equilibrium, no money symbol. Money enters only as the unit the figures are written in. Those are not modelling choices we made; they are the words that do not appear in the calculus that the two records generate.
This is why we call it actual. A model of the economy is a simplified stand-in someone chose. Two records of one claim is not a stand-in for anything; it is what a receivable and a payable are. A theorem proved from it is a theorem about the economy, in the way arithmetic is about counting rather than a model of it.
Every economic object is placed on one side of a line: forced by the two-record structure, holding whatever any party chooses, or left to the parties. The theory is complete when every object has been placed with a proof. This is where the line stands today.
| Object | Status | What is proved |
|---|---|---|
| A disagreement between two records | forced | Unchanged by every move the two parties make together and by every internal entry either makes on its own free accounts. Closed only by a revaluation, and the two revaluations always sum to the gap. |
| The figures available in a dispute | forced | Exactly two, the two records. Settlement at any figure is two concessions summing to the gap; neither party concedes more than the gap exactly on the interval between the two records. |
| The cheapest rewriting of a cycle of obligations at fixed net positions | forced | Unique for every separable strictly convex cost minimised on empty lines. Determined by the cut space of the graph of standing relationships, including relationships carrying nothing. |
| Who a rewrite reaches | forced | A relationship carrying nothing is drawn into the rewrite exactly when the marginal costs circulate around a cycle it closes. A party who owed nothing and was owed nothing can be charged. A fixed cost of opening a position, or a one-sided line, suppresses this; the objective decides, not the network. |
| What a who-owes-whom table can see | forced | Any instrument reading only amounts owed, or net positions, takes the same value on two networks that differ on who a rewrite reaches and who consents. It is right about positions and about forests; it is blind to open lines carrying nothing. |
| The buffer that absorbs a revaluation | forced | A party's free-account balance is minus its own net. The buffers of all parties sum to zero exactly when the network's gaps cancel in aggregate. A party with no free account cannot post. |
| Where the two records come from | forced (form) | A transfer between two books is recorded by them in different periods; matched books are kept records with different stamps, never a simultaneous state. |
| The cost of a disagreement | postulate, then forced | An index that is indifferent to which party is called creditor, obeys the same law at every scale, and adds over relationships is J(x) = (x + 1/x)/2 - 1 of the ratio of the two records, up to a unit and an exponent. The three properties are postulated; the form is then a theorem. |
| Shares of a cost, the split of a revaluation, the settlement point, outside options, rents, which relationships are kept | free | Left to the parties. For each, a theorem states what no choice can change: the total of the shares, the sum of the revaluations, the interval, the stopping points of the pruning dynamics. |
| The size of the first claim | open | The located-unit model gives the transfer and its two stamps, not the magnitude of the unit. This is the same wall as the creation law in physics. |
| Whether the free rows stay free when the network is closed | open, next | If every cash account is an issuer's liability, so that no account is free anywhere, do any of the free rows become theorems? This is the question the program is on now. |
Three kinds of statement appear above, and they are not the same kind.
Three places where the difference between one record and two is a difference in what happens to people.
Actual Economics: one recognition, two records
Framework paper. The full account from the ground of Recognition Science, including the objective, the ethical reading, and genesis. 17 pages.
Two Records of One Claim: disagreement, rewriting, and the bystander in networks of bilateral obligations
The same theorems under stated postulates, for a reader who does not hold the ground. 15 pages.
Both papers carry every proof on the page. Where a result is known in another vocabulary (the assignment game of Shapley and Shubik, pairwise stability of Jackson and Wolinsky, the core of Gillies, separable convex flows after Rockafellar) the papers say so and say what the two records add.
This page is the standing statement of the theory and is revised when the line moves: a row goes from open to forced, or from free to forced, or a postulate is derived or dropped. The date at the top is the date of the last such change. Nothing is removed; a row that is refuted is marked refuted and stays.