Elamur Groupantsmath-comb-recurrences
The groupant beside math/src/comb.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | ../syntax.json |
| descriptant | present | descriptant |
| invariant | partial | invariant |
| tests | executed bounded checks | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
stirling_state | stirling_state | partial source derived model | stirling_state |
partition_direction | partition_direction | partial source derived model | partition_direction |
empty_and_limit | empty_and_limit | partial source derived model | empty_and_limit |
doubling_cost | doubling_cost | partial source derived model | doubling_cost |
Model text
descriptant
math-comb-recurrences
Stirling/Bell/partition/derangement/Fibonacci retain distinct zero seeds and update directions. Outputs have recurrence-specific nonunique index preimages. DP table/row costs differ; Cassini is not a complete sequence certificate. Child uses parent nt sieve/product joins.
Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.
approximant
Scoped forward and cost
Stirling/Bell/partition/derangement/Fibonacci retain distinct zero seeds and update directions. Outputs have recurrence-specific nonunique index preimages. DP table/row costs differ; Cassini is not a complete sequence certificate. Child uses parent nt sieve/product joins.
No executable percent surrogate claimed.
invariant
Scoped invariant
Stirling/Bell/partition/derangement/Fibonacci retain distinct zero seeds and update directions. Outputs have recurrence-specific nonunique index preimages. DP table/row costs differ; Cassini is not a complete sequence certificate. Child uses parent nt sieve/product joins.
Source range[4466,10809) bound by manifest digest. Parent domain applies, not arbitrary public states.
models
Source-scoped typed relations
behavior_complement
stirling2(0,0) excludes0 and returns1; stirling2(n>3000,k>n) excludes zero shortcut because n limit wins. Empty Fibonacci seed excludes(1,1), returning(0,1).
reverse_reconstruction
Partition count1 admits n=0 and n=1; derangement1 admits n=0 and n=2. Cassini acceptance constrains f1*(f1-f)-f²=(-1)^n but does not uniquely recover Fibonacci sequence provenance.
stirling_state
S(i,j)=j*S(i-1,j)+S(i-1,j-1), descending j preserves previous row; reset row0=0 after each nonzero i. UnsignedI computes full row with multiplier i-1 and returns row sum.
partition_direction
Distinct partitions update sum descending for each part; odd partitions update ascending. Euler pentagonal recurrence alternates pairs of signs at k(3k±1)/2. Their equality checks different counting paths.
empty_and_limit
partitions0=1, partitions_k(0,0)=1, derangements0=1/1=0; Bell0=1. Each function has its own n gate; alternate Bell/partition/derangement checks cover smaller ranges.
doubling_cost
F pair recursion halves n; c=a*(2b-a),d=a²+b² and parity chooses(c,d) or(d,c+d). O(log n) big arithmetic steps does not mean O(log n) bit time or bounded result storage.
tests
Evidence
See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.
Stirling/Bell/partition/derangement/Fibonacci retain distinct zero seeds and update directions. Outputs have recurrence-specific nonunique index preimages. DP table/row costs differ; Cassini is not a complete sequence certificate. Child uses parent nt sieve/product joins.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/comb.rs.groupant/recurrences.groupant/