Pith Number

pith:344OFHFX

pith:2021:344OFHFXPQBC2WO3TUNJMA3JC6

not attested not anchored not stored refs pending

Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature

Xian-Tao Huang

arxiv:2109.07534 v1 · 2021-09-15 · 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{344OFHFXPQBC2WO3TUNJMA3JC6}

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.

Cited by

1 paper in Pith

Eigenvalues on spheres

Receipt and verification

First computed	2026-07-05T03:14:58.058113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df38e29cb77c022d59db9d1a9603691784f9404d34d8ef6efa78d3d4282fc6bb

Aliases

arxiv: 2109.07534 · arxiv_version: 2109.07534v1 · doi: 10.48550/arxiv.2109.07534 · pith_short_12: 344OFHFXPQBC · pith_short_16: 344OFHFXPQBC2WO3 · pith_short_8: 344OFHFX

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/344OFHFXPQBC2WO3TUNJMA3JC6 \
  | 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: df38e29cb77c022d59db9d1a9603691784f9404d34d8ef6efa78d3d4282fc6bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c03518d9dd5ae2efb4d433c9f523e4e1f5008a0e4fabd8a923b8957231887321",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-09-15T19:02:26Z",
    "title_canon_sha256": "a09ced776f9df545f50d7ae55233699d1eb41d0ed89bf89f9ff6f3fe5da0dc9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.07534",
    "kind": "arxiv",
    "version": 1
  }
}