Pith Number

pith:QG5LKSLF

pith:2011:QG5LKSLFS4JOYMSTKKD53MMFNK

not attested not anchored not stored refs pending

Critical sets of random smooth functions on compact manifolds

Liviu I. Nicolaescu

arxiv:1101.5990 v3 · 2011-01-31 · math.DG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QG5LKSLFS4JOYMSTKKD53MMFNK}

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	2026-05-18T02:56:12.883282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81bab549659712ec32535287ddb1856aaeb8d789f73220fb0ce47561947ade96

Aliases

arxiv: 1101.5990 · arxiv_version: 1101.5990v3 · doi: 10.48550/arxiv.1101.5990 · pith_short_12: QG5LKSLFS4JO · pith_short_16: QG5LKSLFS4JOYMST · pith_short_8: QG5LKSLF

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/QG5LKSLFS4JOYMSTKKD53MMFNK \
  | 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: 81bab549659712ec32535287ddb1856aaeb8d789f73220fb0ce47561947ade96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "933f7057ee8311f8d4506e332a96dea104feb3ffc45d9ea0c1a41c5697fe8964",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-01-31T15:27:29Z",
    "title_canon_sha256": "d99d2b9ce53844bec7978c122815169572e1168782d6bacb70d80505dfcf1720"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5990",
    "kind": "arxiv",
    "version": 3
  }
}