Informational Superiority of Schmittian Notation | Public Paper Page

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Parent page: Sequential Provenance Comparison (SPC) | Public Page

Published: September 26, 2026

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The mainstream profit notation “profit = sales revenue − production cost” is numerically correct but inadequate as a macroeconomic state description.

The equation represents profit of 20 only as the residual between sales revenue of 100 and production cost of 80. It does not represent the operation in which final expenditure of household income 100 simultaneously recovers costs of 80 and forms profit of 20, nor does it show whether formed profit remains in Department II or has completed its transfer to Department III. By comparing two such states, this paper identifies that informational omission and shows that Schmittian three-department notation preserves the information required to audit formed profit’s logical origin, department of record, conditions of use, and transfer completion.

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Version: 1.0 (September 2026) ｜ Status: Working Paper / pre-peer-review preprint

Author: Nyun (Independent Researcher)

DOI: 10.5281/zenodo.22983561 ｜ Zenodo: public record

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The Paper in 30 Seconds

Question: Can a notation determine whether formed profit has completed its transfer to Department III when two states have equal totals of deposits, claims on firms, profit, and goods?
Comparison: In State 1, profit of 20 is in Department II. In State 2, the same 20 has been transferred to Department III.
Central result: The mainstream equation “profit = sales revenue − production cost” reduces profit formation to a residual calculation and does not preserve the forming operation or departmental status. Schmittian notation retains departmental status and can therefore identify transfer completion.
Scope: The claimed superiority is limited to this audit purpose; the paper does not claim that Schmittian notation is superior for every accounting purpose.
Institutional condition: Recording profit in Department III marks it for exclusion, but effective exclusion from lending requires enforceable departmental restrictions.

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Central proposition

States 1 and 2 have equal totals of deposits, claims on firms, profit, and goods. Yet profit of 20 is in Department II in State 1 and in Department III in State 2.

Schmittian bookkeeping can identify this difference and determine whether the transfer has been completed; aggregate notation containing only totals cannot.

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Why must the banking system be divided into three departments?

The purpose is not to create three banks or three times as much money. It is to avoid treating equal sums as equivalent when their origins and permitted uses differ. The same 20 may be unspent income or ordinary saving, or it may be profit formed out of income that households have already spent.

Department II records income and ordinary saving. Profit formed through final expenditure is transferred to Department III. This makes a profit-deposit originating in spent income identifiable as something that should not be reused as if it were still ordinary loanable saving. The three departments therefore record not merely how much exists, but where a sum came from and what it may now be used for.

To the author’s knowledge, this may be among the first documents to explain the need for the three-department banking system in accessible terms through the simple comparison of States 1 and 2.

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From State 0 to State 2

Stage	Operation or state	Status of profit 20	Transfer completion
State 0	Before final expenditure	Not yet formed	—
Operation 1	Final expenditure of household income 100 recovers costs of 80 and forms profit of 20	Formed in Department II	Incomplete
State 1	Analytical intermediate state after profit formation and before immediate transfer	Department II	$C_T=0$
Operation 2	Transfer of profit 20 from Department II to Department III	Interdepartmental transfer	In progress
State 2	After transfer to Department III	Department III	$C_T=1$

State 1 is not an institutionally completed state assumed to persist through clock time. It is an analytical partial representation introduced to inspect profit formation separately from transfer. Treating State 1 as complete violates immediate Transfer Rule T; allowing financial use of its profit deposit additionally defeats the intended exclusion under Rule E.

Comparison of the Two Notations

Point of comparison	Aggregate notation without status	Schmittian notation
Totals of deposits, claims, profit, and goods	Represented	Represented
Departmental status of profit 20	Not preserved	Preserved as Department II or III
Distinction between States 1 and 2	Impossible	Possible
Completion of Rule T	Cannot be determined	Can be determined
Effective exclusion from loanable funds	Cannot be determined from totals	Recorded as excluded; effectiveness requires departmental restrictions

Comparative Proposition on Informational Sufficiency

Let $O$ denote the information observable through a notation and $C_T(s)\in\{0,1\}$ whether the required transfer has been completed.

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Comparative proposition

If $O(s_i)=O(s_j)$ while $C_T(s_i)\neq C_T(s_j)$, notation $O$ is informationally insufficient to determine whether formed profit has completed its transfer to Department III.

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Aggregate notation gives the same observation for States 1 and 2 even though transfer completion differs. Schmittian notation distinguishes the department in which profit is recorded.