Pith Number

pith:4NJBYZZB

pith:2001:4NJBYZZB3JOVMLNEXSHNRFKE6I

not attested not anchored not stored refs pending

h-cobordisms between 1-connected 4-manifolds

Matthias Kreck

arxiv:math/0101163 v2 · 2001-01-19 · math.GT · 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{4NJBYZZB3JOVMLNEXSHNRFKE6I}

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	2026-05-18T02:38:00.873892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3521c6721da5d562da4bc8ed89544f21b160117efe1c4664ce3262dc2268bea

Aliases

arxiv: math/0101163 · arxiv_version: math/0101163v2 · doi: 10.48550/arxiv.math/0101163 · pith_short_12: 4NJBYZZB3JOV · pith_short_16: 4NJBYZZB3JOVMLNE · pith_short_8: 4NJBYZZB

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/4NJBYZZB3JOVMLNEXSHNRFKE6I \
  | 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: e3521c6721da5d562da4bc8ed89544f21b160117efe1c4664ce3262dc2268bea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c76c90d0bc70f8edfd2f232e1d3cb1280ae01e6bd675a5e81ad313230416aa1c",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2001-01-19T20:04:17Z",
    "title_canon_sha256": "6a91e3689d126e71c75392f5f1776ddd2fcef0ff78b5d30d8a3a165699b56025"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0101163",
    "kind": "arxiv",
    "version": 2
  }
}