Pith Number

pith:PUEE6X3I

pith:2011:PUEE6X3IQIGOOKDAHZJNNCYJMB

not attested not anchored not stored refs pending

Waist of the sphere for maps to manifolds

A.Yu. Volovikov, R.N. Karasev

arxiv:1102.0647 v1 · 2011-02-03 · math.MG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PUEE6X3IQIGOOKDAHZJNNCYJMB}

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	2026-05-18T03:15:21.268700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d084f5f68820ce728603e52d68b0960741447bc65cf05558fbaead28cb7d7c7

Aliases

arxiv: 1102.0647 · arxiv_version: 1102.0647v1 · doi: 10.48550/arxiv.1102.0647 · pith_short_12: PUEE6X3IQIGO · pith_short_16: PUEE6X3IQIGOOKDA · pith_short_8: PUEE6X3I

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/PUEE6X3IQIGOOKDAHZJNNCYJMB \
  | 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: 7d084f5f68820ce728603e52d68b0960741447bc65cf05558fbaead28cb7d7c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d008de4af77713bdec5b1d7999d5546723b1b987d2d8dd6a2ef7e45dc7bf303d",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-02-03T11:12:36Z",
    "title_canon_sha256": "965ecaefce5fb0d8eade974bc4f76509f6f88a184069f9d982b0eb17eb561c51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0647",
    "kind": "arxiv",
    "version": 1
  }
}