Pith Number

pith:VLNZDA6L

pith:2012:VLNZDA6L2AESHDKOBRXMTMPHEG

not attested not anchored not stored refs pending

On 4-Manifolds, Folds and Cusps

Stefan Behrens

arxiv:1205.5192 v1 · 2012-05-23 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VLNZDA6L2AESHDKOBRXMTMPHEG}

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	2026-05-18T02:21:09.963758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aadb9183cbd009238d4e0c6ec9b1e721a9409fe00c2a15b20164bf621df4e82e

Aliases

arxiv: 1205.5192 · arxiv_version: 1205.5192v1 · doi: 10.48550/arxiv.1205.5192 · pith_short_12: VLNZDA6L2AES · pith_short_16: VLNZDA6L2AESHDKO · pith_short_8: VLNZDA6L

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/VLNZDA6L2AESHDKOBRXMTMPHEG \
  | 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: aadb9183cbd009238d4e0c6ec9b1e721a9409fe00c2a15b20164bf621df4e82e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e5fb852cfb452bdaa58a11ace8376453c3565191eb09ef2e6779ef895333f2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-05-23T14:53:52Z",
    "title_canon_sha256": "ae0aad7b13d11744680e697f936f3a1a8f83e3224b6d8321cc44b4f5bea5a15e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5192",
    "kind": "arxiv",
    "version": 1
  }
}