Two design-only tickets opened together because they're tightly
coupled — pillar VII records bind to combinatorics@v1 via
pi_star_ref, and #000032 lands first to avoid rebind churn on
that field.
#000032 — combinatorics@v1 π*
=============================
A new π* kernel that canonicalizes pure-integer counting
expressions (binomial, factorial, permutations, partitions,
Catalan, Bell, Stirling) and FAILS CLOSED on any input whose
result is not a non-negative integer. Tighter domain than
algebra-symbolic@v1, which already accepts the same input
surface but happily returns symbolic / negative / rational
outputs.
Distinguishing feature: algebra-symbolic@v1 returns
binomial(n,k) → "binomial(n,k)" (symbolic), binomial(-3,2) → 6
(generalized). combinatorics@v1 rejects both. Operators choose
the kernel by what they want rejected.
Output format: integer string (b"10"). Compose with
arithmetic@v1 to get bytes-identical agreement (b"10/1") for
the multi-modality witness flow.
Estimated size: ~120 LOC module + ~80 LOC tests + ~22 fixtures.
Single-commit feasible.
#000033 — Claim-pack pillar VII (combinatorics)
================================================
Extend the claim-pack source (#000029) with a new combinatorics
pillar slotting into the documented gap (existing v2 bundles use
I, II, III, IV, V, VI, IX — VII and VIII reserved for
extension). Counting axioms (Pascal's rule, addition principle,
multiplication principle, pigeonhole, factorial / binomial
definitions) + classical theorems (binomial theorem,
inclusion-exclusion in counting form, hockey-stick, Vandermonde,
Catalan closed form, stars-and-bars).
Bundle provenance is the open question — three options
documented:
A. Commission a Grok-4 v3 bundle for parity with the existing
pack.
B. Hand-curate from textbooks (Stanley, Brualdi, Wilf, Knuth).
C. Hybrid — LLM draft + human curation.
Hard constraint: explicit authorship metadata. No silent
invention. Bundle landing is a config + data exercise; no
source-code changes to arborist/sources/claim_pack.py needed
since the source already iterates arbitrary pillar names.
Sequencing: #000032 first (kernel), #000033 next (records bind
to it from day one), #000031 stays parallel-track (textbook
ingest for warrant promotion).
Both tickets stay open · awaiting go/no-go pending fox's
implementation green-light.
russell@unturf.com
d34ecb27c1