Pith Number

pith:GKQ3NBML

pith:2016:GKQ3NBMLJ42S4J4ZTNDMTKO2OI

not attested not anchored not stored refs pending

Positively ratioed representations

Giuseppe Martone, Tengren Zhang

arxiv:1609.01245 v4 · 2016-09-05 · math.GT · math.DS · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GKQ3NBMLJ42S4J4ZTNDMTKO2OI}

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	2026-05-17T23:48:34.707408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32a1b6858b4f352e27999b46c9a9da721d13c412d7a802f3408c653c2fe6dec0

Aliases

arxiv: 1609.01245 · arxiv_version: 1609.01245v4 · doi: 10.48550/arxiv.1609.01245 · pith_short_12: GKQ3NBMLJ42S · pith_short_16: GKQ3NBMLJ42S4J4Z · pith_short_8: GKQ3NBML

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/GKQ3NBMLJ42S4J4ZTNDMTKO2OI \
  | 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: 32a1b6858b4f352e27999b46c9a9da721d13c412d7a802f3408c653c2fe6dec0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "981437247daa0b9865380e603d1b603c21be259d29544bd5073a4fdc828b6adf",
    "cross_cats_sorted": [
      "math.DS",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-05T18:21:39Z",
    "title_canon_sha256": "10869ef1958a3a9a4b145f0a573d3e6b53c06ea19c33caf72e87d3886fbbba03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01245",
    "kind": "arxiv",
    "version": 4
  }
}