# INVARIANTS — Laws, Proofs, Derivations

> Law in `docs/architecture/*.md`, proof in `test/*.test.mjs`.

| #  | Law                                  | Where defined (src symbol)                                                                                                            | Pins (test/N)       | Doc (docs/architecture/*.md) |
| -- | ------------------------------------ | ------------------------------------------------------------------------------------------------------------------------------------- | ------------------- | ---------------------------- |
| 1  | Determinism                          | `src/config.ts:seed` `src/alphabet.ts:Alphabet` `src/mind/traverse.ts:guidedFirst`                                                    | `test/20` `test/42` | `determinism.md`             |
| 2  | Derived thresholds                   | `src/geometry.ts:mergeThreshold,identityBar,reachThreshold,significanceBar,consensusFloor,dominates`                                  | `test/64` `test/40` | `thresholds.md`              |
| 3  | Exact decides / approximate proposes | `src/mind/primitives.ts:resolve` `src/mind/match.ts:locate,alignGraded` `src/mind/resonance.ts:bridge`                                | `test/51`           | `exact-vs-approximate.md`    |
| 4  | One cost currency                    | `src/mind/graph-search.ts:MICRO,STEP,CONCEPT,PASS` `src/derive:lightestDerivation` (min,+) `src/mind/attention.ts:poolVotes` (+,+)    | `test/55` `test/04` | `cost-model.md`              |
| 5  | Bounded reads                        | `src/store.ts:AbstractStore:nextFirst,parentsFirst,containersSlice,hasNext,bytesPrefix` `src/mind/traverse.ts:hubBound,hubCap`        | `test/90` `test/14` | `bounded-reads.md`           |
| 6  | Fold contract                        | `src/geometry.ts:contentLevels` `src/mind/canonical.ts:canonicalWindows,chainReach` `src/canon.ts:canonicalizer`                      | `test/59` `test/63` | `fold-contract.md`           |
| 7  | Mechanism market                     | `src/mind/pipeline-mechanism.ts:PipelineMechanism,Precomputed` `src/mind/pipeline.ts:think,worthRunning`                              | `test/01` `test/04` | `mechanism-market.md`        |
| 8  | Two commonality measures             | `src/mind/traverse.ts:reachOf,dominates,corpusN` (global) `src/mind/match.ts:depth[],MIN_WEAVE` (weave-local)                         | `test/17` `test/34` | `commonality.md`             |
| 9  | Memoization idempotence              | `src/mind/pipeline-mechanism.ts:Precomputed` `src/mind/mind.ts:beginResponse,endResponse,_resolvedSubtrees`                           | `test/42`           | `memoization.md`             |
| 10 | Caches as budgets                    | `src/store.ts:BoundedMap` `src/config.ts:StoreConfig:bytesCacheMax,recCacheBytes,haloCacheBytes`                                      | `test/96` `test/91` | `caches.md`                  |
| 11 | Honest degradation                   | `src/mind/pipeline.ts:weight=moves+PASS*unaccounted` `src/store.ts:BoundedMap:miss→re-derive`                                         | `test/28` `test/84` | `store.md`+`caches.md`       |
| 12 | Meter contracts                      | `src/meter.ts:Meter,PhaseCost,time` `src/mind/pipeline-mechanism.ts:Precomputed.shared`                                               | `test/55`           | `meter.md`                   |
| 13 | Saturation                           | `src/mind/traverse.ts:edgeAncestors:SaturationReason` `src/mind/junction.ts:junctionContainersFrom` `src/mind/resonance.ts:pivotInto` | `test/27` `test/16` | `saturation.md`              |