Pith Number

pith:NQAVN4VG

pith:2025:NQAVN4VGGSF7P4EE54F7DV7I5T

not attested not anchored not stored refs pending

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group

Qi Zhou, Wei Zhang

arxiv:2509.08415 v1 · 2025-09-10 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NQAVN4VGGSF7P4EE54F7DV7I5T}

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.

Receipt and verification

First computed	2026-07-05T12:08:29.652525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c0156f2a6348bf7f084ef0bf1d7e8ecd21324b13948c59d99d9d7843e4742d7

Aliases

arxiv: 2509.08415 · arxiv_version: 2509.08415v1 · doi: 10.48550/arxiv.2509.08415 · pith_short_12: NQAVN4VGGSF7 · pith_short_16: NQAVN4VGGSF7P4EE · pith_short_8: NQAVN4VG

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/NQAVN4VGGSF7P4EE54F7DV7I5T \
  | 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: 6c0156f2a6348bf7f084ef0bf1d7e8ecd21324b13948c59d99d9d7843e4742d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7106afe8f8b283716ffc9a8418c2208ad51b1c945ad4020df42f51f46cdd31a5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-09-10T08:58:26Z",
    "title_canon_sha256": "c25b913537da8d69f00ca7a9b654be6e0f8687556e3895e41b120d13109e810a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.08415",
    "kind": "arxiv",
    "version": 1
  }
}