Pith Number

pith:ZZTHXW2H

pith:2010:ZZTHXW2HWFSS6NB42DDYLAQ5ZP

not attested not anchored not stored refs pending

Existence of random gradient states

Christof K\"ulske, Codina Cotar

arxiv:1012.4375 v4 · 2010-12-20 · 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{ZZTHXW2HWFSS6NB42DDYLAQ5ZP}

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	2026-05-18T03:45:01.250572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce667bdb47b1652f343cd0c785821dcbf38f3ff7c81d2278ae1190854b19e379

Aliases

arxiv: 1012.4375 · arxiv_version: 1012.4375v4 · doi: 10.48550/arxiv.1012.4375 · pith_short_12: ZZTHXW2HWFSS · pith_short_16: ZZTHXW2HWFSS6NB4 · pith_short_8: ZZTHXW2H

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/ZZTHXW2HWFSS6NB42DDYLAQ5ZP \
  | 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: ce667bdb47b1652f343cd0c785821dcbf38f3ff7c81d2278ae1190854b19e379

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44d7e7d6475550470f9064b9d7173fe3f922a6383fcca9ec4793a25d75978248",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-20T15:59:35Z",
    "title_canon_sha256": "728525a1e7ae6e59430d4ec6e20fc2235eea563845f5258262c5d3ccc0799314"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4375",
    "kind": "arxiv",
    "version": 4
  }
}