Pith Number

pith:T5MLHKZP

pith:2025:T5MLHKZPMAIPUBRUKRXFYEQFQX

not attested not anchored not stored refs pending

On critical maps of the horizontal energy functional between Riemannian foliations

Hui Liu, Tian Chong, Xin Huang, Yuxin Dong

arxiv:2504.01498 v1 · 2025-04-02 · 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{T5MLHKZPMAIPUBRUKRXFYEQFQX}

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	2026-07-05T10:43:16.299171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f58b3ab2f6010fa0634546e5c120585ebf426cd122c31a9bfa3c65b30cdb71f

Aliases

arxiv: 2504.01498 · arxiv_version: 2504.01498v1 · doi: 10.48550/arxiv.2504.01498 · pith_short_12: T5MLHKZPMAIP · pith_short_16: T5MLHKZPMAIPUBRU · pith_short_8: T5MLHKZP

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/T5MLHKZPMAIPUBRUKRXFYEQFQX \
  | 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: 9f58b3ab2f6010fa0634546e5c120585ebf426cd122c31a9bfa3c65b30cdb71f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4998cea1cf992220c259fd9ce135342d312c16d36c7ecd16949a53ae9e4974a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-04-02T08:50:59Z",
    "title_canon_sha256": "5027382ec07a5bef381d3fb979c5df2287aa8cc41c4f98518d587bc09091f452"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.01498",
    "kind": "arxiv",
    "version": 1
  }
}