Pith Number

pith:4H5CKDJZ

pith:1999:4H5CKDJZVDCCUJZ5M3QPGKIX7H

not attested not anchored not stored refs pending

Harmonic Functions on Manifolds with Nonnegative Ricci Curvature and Linear Volume Growth

Christina Sormani

arxiv:math/9903172 v1 · 1999-03-29 · 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{4H5CKDJZVDCCUJZ5M3QPGKIX7H}

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	2026-07-04T14:41:06.140812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1fa250d39a8c42a273d66e0f32917f9e0dfc84b5463acf3a7f9661701a36911

Aliases

arxiv: math/9903172 · arxiv_version: math/9903172v1 · doi: 10.48550/arxiv.math/9903172 · pith_short_12: 4H5CKDJZVDCC · pith_short_16: 4H5CKDJZVDCCUJZ5 · pith_short_8: 4H5CKDJZ

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/4H5CKDJZVDCCUJZ5M3QPGKIX7H \
  | 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: e1fa250d39a8c42a273d66e0f32917f9e0dfc84b5463acf3a7f9661701a36911

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8213c1882969eea32bd8cb2d952e496bd1cc45e23eb267e80f06de577550a9e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1999-03-29T21:33:21Z",
    "title_canon_sha256": "fdbdc97c036e85cc44b3bbca725400bee435471a2009cfa24442c74cd22c0959"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9903172",
    "kind": "arxiv",
    "version": 1
  }
}