Pith Number

pith:U4VL4HRW

pith:2013:U4VL4HRWNJOIFTKYBDF7IF23NR

not attested not anchored not stored refs pending

Closed BLD-elliptic manifolds have virtually Abelian fundamental groups

Enrico Le Donne, Pekka Pankka

arxiv:1312.1308 v2 · 2013-12-04 · math.MG · math.DG · 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{U4VL4HRWNJOIFTKYBDF7IF23NR}

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	2026-05-18T03:05:27.596959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a72abe1e366a5c82cd5808cbf4175b6c70dd023605db9134ea234afbe4bf1430

Aliases

arxiv: 1312.1308 · arxiv_version: 1312.1308v2 · doi: 10.48550/arxiv.1312.1308 · pith_short_12: U4VL4HRWNJOI · pith_short_16: U4VL4HRWNJOIFTKY · pith_short_8: U4VL4HRW

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/U4VL4HRWNJOIFTKYBDF7IF23NR \
  | 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: a72abe1e366a5c82cd5808cbf4175b6c70dd023605db9134ea234afbe4bf1430

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98a4a4e020a9671242f444e3b084ee44dc767758545d3d98d7898d0c21010d25",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-12-04T20:07:07Z",
    "title_canon_sha256": "c620ac5160ac344b91ba89d49d1cd6b4cb75ff6c8d571f670f0b7736b456e344"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1308",
    "kind": "arxiv",
    "version": 2
  }
}