Pith Number

pith:ZBBQIZ7X

pith:2026:ZBBQIZ7XTSBT2FBWWUEHC6YBFR

not attested not anchored not stored refs pending

Canonical forms and moment-generating functions of plane polypols

Boris Shapiro

The polarity relation between canonical forms and Fantappie transforms for polygons extends to curved polypols, where the transform becomes a holonomic branched period controlled by vertex hyperplanes and dual curves.

arxiv:2605.10864 v2 · 2026-05-11 · math.AG · math.CO · math.CV

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\usepackage{pith}
\pithnumber{ZBBQIZ7XTSBT2FBWWUEHC6YBFR}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

For genuinely curved polypols the same dual-geometric mechanism survives, but the transform is no longer a rational logarithmic canonical form; rather, it is a holonomic, generally branched period whose singularities are controlled by vertex hyperplanes and by the projective dual curves of the nonlinear boundary components.

C2weakest assumption

The dual-geometric polarity mechanism that works for polygons continues to govern the relation between canonical forms and Fantappie transforms when the boundary arcs are genuinely curved rational curves.

C3one line summary

For plane polypols the normalized Fantappie transform is a holonomic generally branched period whose singularities are controlled by vertex hyperplanes and projective dual curves of the nonlinear boundary components.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:47.002870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8430467f79c833d1436b508717b012c56424ef708c4d4947343d0e78ffda63b

Aliases

arxiv: 2605.10864 · arxiv_version: 2605.10864v2 · doi: 10.48550/arxiv.2605.10864 · pith_short_12: ZBBQIZ7XTSBT · pith_short_16: ZBBQIZ7XTSBT2FBW · pith_short_8: ZBBQIZ7X

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/ZBBQIZ7XTSBT2FBWWUEHC6YBFR \
  | 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: c8430467f79c833d1436b508717b012c56424ef708c4d4947343d0e78ffda63b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2905d318eccfc7792df6e9957c7d3d26a51863b35cb054ebd2470c76ebdd189a",
    "cross_cats_sorted": [
      "math.CO",
      "math.CV"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-11T17:12:34Z",
    "title_canon_sha256": "edc81021595ce69091e47f0218ccc60dd01597f7746eb4e20eeb7722d5e344fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10864",
    "kind": "arxiv",
    "version": 2
  }
}