Pith Number

pith:XD66ZRXS

pith:2016:XD66ZRXSDYGTQHSVYPQPO6VLAC

not attested not anchored not stored refs pending

Sizes of spaces of triangulations of 4-manifolds and balanced presentations of the trivial group

Alexander Nabutovsky, Boris Lishak

arxiv:1610.06130 v2 · 2016-10-19 · 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{XD66ZRXSDYGTQHSVYPQPO6VLAC}

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	2026-05-18T00:41:53.399138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8fdecc6f21e0d381e55c3e0f77aab008085bc9038e7762e8dfd9c1e82e345d3

Aliases

arxiv: 1610.06130 · arxiv_version: 1610.06130v2 · doi: 10.48550/arxiv.1610.06130 · pith_short_12: XD66ZRXSDYGT · pith_short_16: XD66ZRXSDYGTQHSV · pith_short_8: XD66ZRXS

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/XD66ZRXSDYGTQHSVYPQPO6VLAC \
  | 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: b8fdecc6f21e0d381e55c3e0f77aab008085bc9038e7762e8dfd9c1e82e345d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c540c27b0c2331aa96ec23229fdadd6d501a3000d3ac99a9bc5766d6698013d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-10-19T18:03:56Z",
    "title_canon_sha256": "c72c590f51ad356cc8d0370e1e787d42eab747cebe22ad3490851c23b4f865df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.06130",
    "kind": "arxiv",
    "version": 2
  }
}