Pith Number

pith:6YLFEXLM

pith:2018:6YLFEXLMJ42JUOYDQ46QU5IKUP

not attested not anchored not stored refs pending

On the uniqueness class, stochastic completeness and volume growth for graphs

Marcel Schmidt, Matthias Keller, Xueping Huang

arxiv:1812.05386 v1 · 2018-12-13 · math.MG · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6YLFEXLMJ42JUOYDQ46QU5IKUP}

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	2026-05-17T23:58:20.417046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f616525d6c4f349a3b03873d0a750aa3f77d1360081099c6dd2080ad9bfb74b2

Aliases

arxiv: 1812.05386 · arxiv_version: 1812.05386v1 · doi: 10.48550/arxiv.1812.05386 · pith_short_12: 6YLFEXLMJ42J · pith_short_16: 6YLFEXLMJ42JUOYD · pith_short_8: 6YLFEXLM

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/6YLFEXLMJ42JUOYDQ46QU5IKUP \
  | 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: f616525d6c4f349a3b03873d0a750aa3f77d1360081099c6dd2080ad9bfb74b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9690ef75d800775b0bd44a9caffa24215b291be8d39efaf98935ff396a479cd",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2018-12-13T12:40:30Z",
    "title_canon_sha256": "ed6cd69ebb0ce289ef0dbb4fbcdc25f33427b725a621786614a3d08eaf362775"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.05386",
    "kind": "arxiv",
    "version": 1
  }
}