numeric-rule-finder 0.1.2

Discover the conservation/balance rules a set of numbers must satisfy, find where they break, and honest-stop when there is no such structure.

Numeric Rule Finder

An exact, dependency-light library that discovers the conservation laws latent in structured movement/transaction data, instead of making you declare one.

You declare nothing. It recovers the complete lattice of independent conservation laws the data actually obeys — including laws nobody wrote down — finds where they break, types each break (a re-attributable slip vs. a genuine hole), and honest-stops when there is no structure to exploit.

📖 There's a book. Read the ebook → — what it is, how it works, runnable worked examples (with real output), three machine-learning head-to-heads, a raw-XML showcase, and a mathematics appendix.

Two front doors

Just want answers? (no maths).

• See it in action — the headline walkthrough, Closing the month at Northwind Retail, in BUSINESS_GUIDE.md: six plain-English checks, each ending in an action (run it: examples/northwind_close/).
• On your own data — python -m numeric_rule_finder.cli (or from numeric_rule_finder import Reconciler); hand it a CSV and two column names.
• What you get — what balances, where it breaks and probably why, and any hidden separate sub-systems — found exactly in one pass (independent_groups, or the groups command).
• It's intelligent — when ordinary balancing finds nothing, it silently escalates to the deeper maths (e.g. modular/parity structure) and reports it in plain words.
• Across domains — accounting, energy, supply chain, ETL, clinical trials, elections, …: python examples/gamut/gamut_demo.py.

Want the mathematics? — read the ebook Appendix — The mathematics. The engine lives in the numeric_rule_finder/ package.

How it works (in brief)

Numeric Rule Finder treats your data as signed movements — a group, a bucket, an amount — and finds the weighted combinations of buckets that every movement leaves unchanged (the conservation laws), then measures exactly where they break. It climbs only as far as it needs:

• balance & structure — which groups don't net out; which buckets form hidden separate books (the exact independent groups, in one linear pass);
• modular laws — patterns invisible to ordinary arithmetic ("moves only in cases of 12", parity), via Smith Normal Form;
• typed residuals — is a break re-attributable (a coboundary) or a genuine hole (an obstruction that names the violated law)?
• multi-source consistency — whether independent reconciliations can all be true at once (an H¹ obstruction);
• substrate generality — the same engine over ℤ, ℚ, 𝔽ₚ, and ℚ[t] (parametric, rate-dependent laws).

Everything is exact (integer/rational arithmetic, never floating point) — and it scales: a modular-rank fast path certifies the honest stop (no conservation structure) in machine-integer arithmetic, skipping the exact rational solve where there is nothing to find. The actual mathematics — definitions, theorems, the coker(S) / H¹ residual typing, Smith Normal Form, and a map of the code — is in the ebook Appendix — The mathematics.

Real data carries more than one law

Point it at a dataset and it reports how many independent conservation laws hold. Real data routinely has several — separate books, conserved moieties, per-SKU stock — not just the one obvious balance:

the data	laws found	what that means
a clean double-entry ledger	1	every transaction nets to zero
two ledgers that never share a transaction	2	they are really separate books — nobody had declared that
a stock network with two products	2	each product's stock is conserved on its own
an enzyme reaction network	2	two conserved quantities (the enzyme, and total substrate)
a shared-resource / mutex process	3	each client's work-item plus the resource invariant
data with no balancing structure	0	honest stop — it refuses to invent a reconciliation

With and against machine learning

Where the signal is an exact law this beats statistical anomaly detection; where the job is partly fuzzy, it makes the model's job easier; and where the answer is an exact structure, it replaces a slow unsupervised job outright. Three reproducible head-to-heads (all walked through in Chapter 7 of the ebook):

• it beats an Isolation Forest outright on skim fraud — examples/fraud_vs_ml/;
• it feeds a Random Forest as an exact pre-filter + feature, lifting its score — examples/ml_assist/;
• it finds the exact groups in one pass — Reconciler.independent_groups — where a clustering k-sweep is thousands of times slower and wrong — examples/grouping_vs_ml/.

Run

numeric_rule_finder has no third-party dependencies; petra_adapter uses petra-nn only to read Petri nets, and the ML examples use scikit-learn.

pip install -e .                                      # optional (pure-stdlib core)
python -m numeric_rule_finder.cli check  data.csv --group txn_id --amount amount
python -m numeric_rule_finder.cli groups data.csv --group txn_id --account account  # exact independent groups
python examples/northwind_close/close_the_books.py    # a worked example
python examples/gamut/gamut_demo.py                   # the same engine across domains
python -m pytest tests examples -q                    # the suite

License

MIT-with-attribution — see LICENSE.