Pith Number

pith:GMXDXU6T

pith:2013:GMXDXU6TVC7RW3ATBF5ZVBANM5

not attested not anchored not stored refs pending

Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups

Grigori Avramidi, T. Tam Nguyen Phan, Yunhui Wu

arxiv:1309.0043 v1 · 2013-08-30 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GMXDXU6TVC7RW3ATBF5ZVBANM5}

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	2026-05-18T03:14:28.978428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

332e3bd3d3a8bf1b6c13097b9a840d67534ff1e1f946ab1015d5c5f336ba4185

Aliases

arxiv: 1309.0043 · arxiv_version: 1309.0043v1 · doi: 10.48550/arxiv.1309.0043 · pith_short_12: GMXDXU6TVC7R · pith_short_16: GMXDXU6TVC7RW3AT · pith_short_8: GMXDXU6T

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/GMXDXU6TVC7RW3ATBF5ZVBANM5 \
  | 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: 332e3bd3d3a8bf1b6c13097b9a840d67534ff1e1f946ab1015d5c5f336ba4185

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a86da413b6ea4fc504fd299cf96b057cf97f516fffb4329baf057ac5321f7486",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-08-30T22:49:25Z",
    "title_canon_sha256": "81beadf14ca46348b008337fbada43ab046f5aab087855b5723c09174a676541"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0043",
    "kind": "arxiv",
    "version": 1
  }
}