Pith Number

pith:XQ62SRQW

pith:2026:XQ62SRQWVOZXUDNLOKJHP2BYBN

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Projections of convex polytopes to a line and higher univariate Prony systems

Boris Shapiro

The directional moment variety of convex polytope projections equals the Hankel determinantal variety of measures on polytopes.

arxiv:2605.15917 v1 · 2026-05-15 · math.CA · math.AG

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Record completeness

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2 Internet Archive

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We identify the directional moment variety with the Hankel determinantal variety appearing in the theory of moment varieties of measures on polytopes.

C2weakest assumption

The pushforward to a line of the Lebesgue measure restricted to a convex d-polytope is a spline density of degree d-1 whose moments lead naturally to a family of higher univariate Prony systems.

C3one line summary

Pushforwards of Lebesgue measure restricted to convex d-polytopes onto a line produce spline densities whose moments obey higher Prony systems, with the directional moment variety identified as the Hankel determinantal variety from moment varieties of measures on polytopes.

References

11 extracted · 11 resolved · 0 Pith anchors

[1] C. Am´ endola, K. Ranestad, and B. Sturmfels,Algebraic identifiability of Gaussian mixtures, Int. Math. Res. Not. IMRN 2018, no. 21, 6551–6566 2018

[2] H. B. Curry and I. J. Schoenberg,On P´ olya frequency functions. IV. The fundamental spline functions and their limits, J. Analyse Math.17(1966), 71–107 1966

[3] De Concini and C 2011

[4] R. J. Gardner,Geometric Tomography, second edition, Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, Cambridge, 2006 2006

[5] N. Gravin, J. B. Lasserre, D. V. Pasechnik, and S. Robins,The inverse moment problem for convex polytopes, Discrete Comput. Geom.48(2012), 596–621 2012

Receipt and verification

First computed	2026-05-20T00:01:45.117604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc3da94616abb37a0dab729277e8380b5665509687c91b8fc58cb72a15854fa0

Aliases

arxiv: 2605.15917 · arxiv_version: 2605.15917v1 · doi: 10.48550/arxiv.2605.15917 · pith_short_12: XQ62SRQWVOZX · pith_short_16: XQ62SRQWVOZXUDNL · pith_short_8: XQ62SRQW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XQ62SRQWVOZXUDNLOKJHP2BYBN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: bc3da94616abb37a0dab729277e8380b5665509687c91b8fc58cb72a15854fa0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19b6e60d491036c989f9cd43aa6589314f6845298e6a20135e841af58c50ea8a",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-15T12:56:20Z",
    "title_canon_sha256": "426063278c1df99e51ecec6c0fb2dbb9d286f311f7f3862b406f4db83db8e6e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15917",
    "kind": "arxiv",
    "version": 1
  }
}