Pith Number

pith:4MTKI66L

pith:2021:4MTKI66LCBVDJHG7JDCBAGTUMH

not attested not anchored not stored refs pending

Mean curvature flow of symmetric double graphs only develops singularities on the hyperplane of symmetry

Wolfgang Maurer

arxiv:2103.06072 v1 · 2021-03-10 · 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{4MTKI66LCBVDJHG7JDCBAGTUMH}

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	2026-07-05T02:22:01.268836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e326a47bcb106a349cdf48c4101a7461c32725f4fa6defcb96907a4204e5f316

Aliases

arxiv: 2103.06072 · arxiv_version: 2103.06072v1 · doi: 10.48550/arxiv.2103.06072 · pith_short_12: 4MTKI66LCBVD · pith_short_16: 4MTKI66LCBVDJHG7 · pith_short_8: 4MTKI66L

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/4MTKI66LCBVDJHG7JDCBAGTUMH \
  | 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: e326a47bcb106a349cdf48c4101a7461c32725f4fa6defcb96907a4204e5f316

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "589d813e9b446b174962d06fb0f33da2b03b5a14532c1f0200f5ebdfa892c339",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-03-10T14:18:28Z",
    "title_canon_sha256": "0a1992b75a3f2ed6d971e6fd40b4a3293da548aac4eea7af9912084498e81a8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.06072",
    "kind": "arxiv",
    "version": 1
  }
}