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README.md

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+---
+license: mit
+tags:
+  - process-calc
+  - receipt
+  - exact-arithmetic
+---
+
+# rate-receipt
+
+Same kernel as `process-calc`, but every call returns a **receipt**:
+seed, value, channel, rate, gauge yes/no.
+
+```python
+from receipt_calc import mix, receipt
+print(receipt(lambda x: mix(x, x), 3))
+```
+
+Empty seeds and seed 0 are θ. Float is θ.
+
+Not an LLM. Sister of `process-calc`.

receipt_calc.py

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+#!/usr/bin/env python3
+"""Every rate write is a receipt. Stdlib only."""
+from __future__ import annotations
+
+from fractions import Fraction as F
+
+
+def as_exact(x):
+    if isinstance(x, bool):
+        raise TypeError("theta bool")
+    if isinstance(x, int):
+        return F(x)
+    if isinstance(x, F):
+        return F(x)
+    raise TypeError("theta not Q: %s" % type(x).__name__)
+
+
+def isolate(v, seed):
+    v, seed = as_exact(v), as_exact(seed)
+    if seed == 0:
+        raise ValueError("theta seed 0")
+    return (v, seed)
+
+
+def mix(a, b):
+    (v, r), (w, s) = a, b
+    return (v * w, r * w + v * s)
+
+
+def rate(top, bot):
+    if bot[1] == 0:
+        raise ValueError("theta dead isolator")
+    return top[1] / bot[1]
+
+
+def receipt(fn, v, seeds=(1, 2, F(1, 2), -1)):
+    """One row per seed, plus gauge (all rates equal or split)."""
+    if not seeds:
+        raise ValueError("theta empty seeds")
+    rows = []
+    for s in seeds:
+        x = isolate(v, s)
+        y = fn(x)
+        r = rate(y, x)
+        rows.append({"seed": s, "value": y[0], "channel": y[1], "rate": r})
+    rates = [row["rate"] for row in rows]
+    gauge = all(r == rates[0] for r in rates)
+    return {"at": as_exact(v), "gauge": gauge, "rate": rates[0] if gauge else None, "rows": rows, "theta": not gauge}
+
+
+if __name__ == "__main__":
+    sq = lambda x: mix(x, x)
+    rec = receipt(sq, 3)
+    print("gauge", rec["gauge"], "rate", rec["rate"])
+    for row in rec["rows"]:
+        print(row)
+    try:
+        receipt(sq, 3, seeds=())
+    except ValueError as e:
+        print(e)