# Operator Semantics

KRINEIA exposes exactly three first-class chain operators: `append`, `project`,
and `cut`. They are modes of **krinein** (κρίνειν) — the Greek verb meaning to
separate, judge, decide, distinguish. Same root as *critic, crisis, criterion*.

The etymology is interpretive: it explains why these three operators cohere as a
set. [`INVARIANTS.md`](INVARIANTS.md) is normative: it defines what each
operator does and what is disallowed. Where this file and `INVARIANTS.md`
appear to disagree, `INVARIANTS.md` wins.

## The three modes

| Operator | Semantics | Boundary |
|---|---|---|
| `append(receipt)` | Distinguish a new receipt from prior chain state by recording it immutably. | Mutates only by adding a receipt. |
| `project(filter)` | Distinguish a non-mutating view from the whole chain. | Returns a view; does not rewrite history. |
| `cut(scope)` | Distinguish a bounded evidentiary excerpt from the chain. | Returns an evidence pack; does not authorize, delete, punish, or steer. |

A `cut()` may be parameterized by drift or setpoint criteria, but the operator
returns evidence; it does not itself authorize, delete, punish, or steer. The
boundary between evidence and control is invariant #4 (External analysis only)
in [`INVARIANTS.md`](INVARIANTS.md).

### Krinein modes (interpretive)

The mapping below is an interpretive aid, not part of the chain schema or the
operator contract. Implementers consume the table above and `INVARIANTS.md`;
the table below explains why exactly these three operators cohere.

| Operator | Krinein mode |
|---|---|
| `append(receipt)` | distinguish-now |
| `project(filter)` | distinguish-for-view |
| `cut(scope)` | distinguish-as-evidence |

## Why exactly three

Within KRINEIA, these are the only first-class chain operators. Other useful
actions must either compose `append`, `project`, and `cut`, or remain outside
the receipt-chain surface. This preserves the append-only invariant and keeps
governance evidence separate from operational control.

Cross-chain composition (e.g., relating one chain's state to another's) is
modeled as externally verified composition plus `append()` on each affected
chain. It is not a first-class chain operator.

## Substrate, not just protocol

KRINEIA is a substrate, not only a message format. Receipts are generated at a
trust-root-controlled location by an authorized writer structurally independent
of the observed agent (invariant #5 in [`INVARIANTS.md`](INVARIANTS.md)).
Implementations may host the substrate anywhere (filesystem, append-only
database, distributed log, Merkle-rooted blob store) provided the five
invariants hold.

## See also

- [`INVARIANTS.md`](INVARIANTS.md) — the five governing invariants (normative)
- [`RECEIPT_SCHEMA.md`](RECEIPT_SCHEMA.md) — canonical receipt envelope, hash rule, event taxonomy
- [`README.md`](../README.md) — repo overview and project status