Pith Number

pith:TBFXXZTR

pith:2026:TBFXXZTRJ7HTWQMEQFMBAJEING

not attested not anchored not stored refs pending

Liouville Rigidity for Real and Complex Degenerate Hessian Equations

Biao Ma, Hao Fang, Jinyang Wu

arxiv:2607.21024 v1 · 2026-07-23 · math.AP · 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{TBFXXZTRJ7HTWQMEQFMBAJEING}

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	2026-07-24T01:23:47.900354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

984b7be6714fcf3b4184815810248869a86ee18301698d44f6ffb17ad1589f31

Aliases

arxiv: 2607.21024 · arxiv_version: 2607.21024v1 · doi: 10.48550/arxiv.2607.21024 · pith_short_12: TBFXXZTRJ7HT · pith_short_16: TBFXXZTRJ7HTWQME · pith_short_8: TBFXXZTR

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/TBFXXZTRJ7HTWQMEQFMBAJEING \
  | 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: 984b7be6714fcf3b4184815810248869a86ee18301698d44f6ffb17ad1589f31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fe20f095f5b91d2a6d5633e8e57a6b087db414fd840f1a29b637890643d0c63",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-23T08:07:44Z",
    "title_canon_sha256": "ceef766690f735aa38501b17725b9ddc7c09aa66bba713336c67485307d5a89b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21024",
    "kind": "arxiv",
    "version": 1
  }
}