Pith Number

pith:GPAAAUPQ

pith:2010:GPAAAUPQ22NAAZBOECGYCXOP4N

not attested not anchored not stored refs pending

The mean curvature at the first singular time of the mean curvature flow

Nam Le, Natasa Sesum

arxiv:1001.3682 v1 · 2010-01-20 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GPAAAUPQ22NAAZBOECGYCXOP4N}

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	2026-05-18T02:09:31.663286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33c00051f0d69a00642e208d815dcfe367bb1af9382ef9a7a9c421557c2f6bb2

Aliases

arxiv: 1001.3682 · arxiv_version: 1001.3682v1 · doi: 10.48550/arxiv.1001.3682 · pith_short_12: GPAAAUPQ22NA · pith_short_16: GPAAAUPQ22NAAZBO · pith_short_8: GPAAAUPQ

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/GPAAAUPQ22NAAZBOECGYCXOP4N \
  | 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: 33c00051f0d69a00642e208d815dcfe367bb1af9382ef9a7a9c421557c2f6bb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fbad5100ff7b85aa8ccd822d6d2476372d3c30d2cf3ee2b04c919f759faba62",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-01-20T21:39:11Z",
    "title_canon_sha256": "3536c0f2cd08737ee118bea06f119b72047feac169c10ca9827c7c67492ae984"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.3682",
    "kind": "arxiv",
    "version": 1
  }
}