Pith Number

pith:HA43PGFH

pith:2026:HA43PGFHAMEQWIVHTLVLAAZUX3

not attested not anchored not stored refs resolved

Area of H\"older curves and coarea formula on the Heisenberg group

Gioacchino Antonelli, Robert Young

Lipschitz maps from the subriemannian Heisenberg group to R^{2n} obey the coarea formula.

arxiv:2605.15987 v1 · 2026-05-15 · math.MG · math.CA · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HA43PGFHAMEQWIVHTLVLAAZUX3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

We prove the coarea formula for Lipschitz maps from the subriemannian nth Heisenberg group H_n to R^{2n}.

C2weakest assumption

The geometric condition ensuring convergence of the new integral holds for almost every fiber of the map, established via beta-number estimates from the Fassler-Orponen Dorronsoro Theorem (abstract, final paragraph).

C3one line summary

Proves the coarea formula for Lipschitz maps from H_n to R^{2n} via a new integral defining symplectic area for 1/2-Holder curves and beta-number estimates showing convergence for almost every fiber.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] Rectifiable sets in metric and Ba- nach spaces 2000

[2] Antonelli.Rectifiability in Carnot groups 2022

[3] Vertical curves and vertical fibers in the Heisenberg group 2024

[4] A T (b) theorem with remarks on analytic capacity and the Cauchy integral 1990

[5] A reverse coarea-type inequality in Carnot groups 2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:47.864480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3839b798a703090b22a79aeab00334befffbe0fd48f2b32974cac8143251aa76

Aliases

arxiv: 2605.15987 · arxiv_version: 2605.15987v1 · doi: 10.48550/arxiv.2605.15987 · pith_short_12: HA43PGFHAMEQ · pith_short_16: HA43PGFHAMEQWIVH · pith_short_8: HA43PGFH

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/HA43PGFHAMEQWIVHTLVLAAZUX3 \
  | 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: 3839b798a703090b22a79aeab00334befffbe0fd48f2b32974cac8143251aa76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95bd7c43fad44c2658481ea24c7645daffbacba554e10f10d0ad56867d1956be",
    "cross_cats_sorted": [
      "math.CA",
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-05-15T14:20:09Z",
    "title_canon_sha256": "209e84ae29f09ce50e06f7a4a58df6c74cdb8cf00873f59560e569316f5fccca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15987",
    "kind": "arxiv",
    "version": 1
  }
}