Study 11 Ehrhart Volume Corpus

Study 11 — Corpus: lattice polytope vertex pins

Status: CORPUS SEALED — 2026-08-22
Charter: Study 11 · Results: Results

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Corpus inventory

All vertices are integer tuples in (\mathbb{Z}^d). No float coordinates. Reproducible from this page alone.

ID	dim	Vertices	Sealed volume
unit_square	2	(0,0),(1,0),(1,1),(0,1)	1
unit_triangle	2	(0,0),(1,0),(0,1)	1/2
simplex3	3	(0,0,0),(1,0,0),(0,1,0),(0,0,1)	1/6
hle_poly_d2	2	(0,0),(1,0),(0,1),(-1,1)	1
hle_poly_d3	3	(0,0,0),(1,0,0),(0,1,0),(0,0,1),(-1,0,1),(0,-1,1)	2/3

The hle_poly_* rows are the Humanity's Last Exam polytope family (integer lattice formulation).

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Machine ledger

Artifact	Path
Grade script	corpus/study-11/study11_grade.py
Sealed ledger JSON	corpus/study-11/study11_ledger.json
Boundary schema	corpus/peer-review-conjecture/schemas/ehrhart_polytope_boundary.json

python3 corpus/study-11/study11_grade.py

Expected summary: primary_win: 5, primary_total: 5, adversary_miss: 5.

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Gaps (VOID)

Slot	Reason
Dimension (d \ge 4) HLE polytope	Not yet pinned — prospective registry OPEN
Barvinok-style high-dimensional corpus	Charter extension; enumeration suffices for this seal