Pith Number

pith:W6OJ7NB4

pith:2016:W6OJ7NB4OTRECNPC3NI7I62SUO

not attested not anchored not stored refs pending

Manifolds which admit maps with finitely many critical points into spheres of small dimensions

Cornel Pintea, Louis Funar

arxiv:1611.04344 v2 · 2016-11-14 · 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{W6OJ7NB4OTRECNPC3NI7I62SUO}

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	2026-05-17T23:55:39.081915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b79c9fb43c74e24135e2db51f47b52a3940d46660e47c0d34e35763fbe6d27b2

Aliases

arxiv: 1611.04344 · arxiv_version: 1611.04344v2 · doi: 10.48550/arxiv.1611.04344 · pith_short_12: W6OJ7NB4OTRE · pith_short_16: W6OJ7NB4OTRECNPC · pith_short_8: W6OJ7NB4

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/W6OJ7NB4OTRECNPC3NI7I62SUO \
  | 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: b79c9fb43c74e24135e2db51f47b52a3940d46660e47c0d34e35763fbe6d27b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be2d83a74c7be2fcf063824b7159f9d265dbcedaa353f4f427597d282853d83d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-11-14T11:30:04Z",
    "title_canon_sha256": "e3f23211a4da8d3476f3d8a32267e335f26f9a6896c949b64da30666dc50575a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04344",
    "kind": "arxiv",
    "version": 2
  }
}