Pith Number

pith:MW2MMM5U

pith:2012:MW2MMM5U6C7WIFIJL4LQV6KZ4F

not attested not anchored not stored refs pending

Degenerate neckpinches in Ricci flow

Dan Knopf, James Isenberg, Sigurd B. Angenent

arxiv:1208.4312 v1 · 2012-08-21 · math.DG · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MW2MMM5U6C7WIFIJL4LQV6KZ4F}

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	2026-05-18T02:21:00.891710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65b4c633b4f0bf6415095f170af959e144439534cb1bffdaba7484515fc83b81

Aliases

arxiv: 1208.4312 · arxiv_version: 1208.4312v1 · doi: 10.48550/arxiv.1208.4312 · pith_short_12: MW2MMM5U6C7W · pith_short_16: MW2MMM5U6C7WIFIJ · pith_short_8: MW2MMM5U

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/MW2MMM5U6C7WIFIJL4LQV6KZ4F \
  | 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: 65b4c633b4f0bf6415095f170af959e144439534cb1bffdaba7484515fc83b81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "467622455026c3fb9e8b376a4d3868506f84fc2cb7585ce3ad78607262578407",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-08-21T17:31:55Z",
    "title_canon_sha256": "c26df1018f58e5fb6510bd43002623ad17a4651cff4c2d87a2080217c987bcb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4312",
    "kind": "arxiv",
    "version": 1
  }
}