Pith Number

pith:2DU2T2HL

pith:2015:2DU2T2HLE3UEWKLEKTSRUHJM7X

not attested not anchored not stored refs pending

Minimal Graphs in Nil_3 : existence and non-existence results

Barbara Nelli, Eric Toubiana, Ricardo Sa Earp

arxiv:1508.01724 v1 · 2015-08-07 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2DU2T2HLE3UEWKLEKTSRUHJM7X}

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	2026-05-18T01:35:38.909639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0e9a9e8eb26e84b296454e51a1d2cfde03c9922edf6f70c307343e89bbbaf7d

Aliases

arxiv: 1508.01724 · arxiv_version: 1508.01724v1 · doi: 10.48550/arxiv.1508.01724 · pith_short_12: 2DU2T2HLE3UE · pith_short_16: 2DU2T2HLE3UEWKLE · pith_short_8: 2DU2T2HL

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/2DU2T2HLE3UEWKLEKTSRUHJM7X \
  | 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: d0e9a9e8eb26e84b296454e51a1d2cfde03c9922edf6f70c307343e89bbbaf7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0660d86efa2c8295ac3ec4108c7c24c217a4b1d3b7f38188263c90a0c9a36c28",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-08-07T15:25:11Z",
    "title_canon_sha256": "54bdfdd17862c28e27762923edd9db829c8f85155ed8f0c2de3c0c2cd0de4ef7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01724",
    "kind": "arxiv",
    "version": 1
  }
}