Pith Number

pith:YIWA4QMW

pith:2019:YIWA4QMWUJRDPGG4URKQ7CSDHE

not attested not anchored not stored refs pending

The behavior of harmonic functions at singular points of $\mathsf{RCD}$ spaces

Guido De Philippis, Jes\'us N\'u\~nez-Zimbr\'on

arxiv:1909.05220 v1 · 2019-09-11 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YIWA4QMWUJRDPGG4URKQ7CSDHE}

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	2026-07-05T04:24:20.306911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c22c0e4196a2623798dca4550f8a4339315cb5982e32997109b30e34dff1b397

Aliases

arxiv: 1909.05220 · arxiv_version: 1909.05220v1 · doi: 10.48550/arxiv.1909.05220 · pith_short_12: YIWA4QMWUJRD · pith_short_16: YIWA4QMWUJRDPGG4 · pith_short_8: YIWA4QMW

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/YIWA4QMWUJRDPGG4URKQ7CSDHE \
  | 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: c22c0e4196a2623798dca4550f8a4339315cb5982e32997109b30e34dff1b397

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c44024a3a82269c3027583e054d510d96e7975b9b8b84e1acc6da1439902163",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-09-11T17:18:39Z",
    "title_canon_sha256": "3d176de0b7b6a68f8c85e282b1b7ad720d38bce6b51ed837bfe79c48bcf9703e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.05220",
    "kind": "arxiv",
    "version": 1
  }
}