Pith Number

pith:KRHNL4AR

pith:2015:KRHNL4ARY2PJOM5WP5LHF3CHAO

not attested not anchored not stored refs pending

On the spatial Markov property of soups of unoriented and oriented loops

Wendelin Werner

arxiv:1508.03696 v2 · 2015-08-15 · 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{KRHNL4ARY2PJOM5WP5LHF3CHAO}

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	2026-05-18T00:40:08.559930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

544ed5f011c69e9733b67f5672ec470397eda07885009e5223cd294cd3924d7a

Aliases

arxiv: 1508.03696 · arxiv_version: 1508.03696v2 · doi: 10.48550/arxiv.1508.03696 · pith_short_12: KRHNL4ARY2PJ · pith_short_16: KRHNL4ARY2PJOM5W · pith_short_8: KRHNL4AR

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/KRHNL4ARY2PJOM5WP5LHF3CHAO \
  | 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: 544ed5f011c69e9733b67f5672ec470397eda07885009e5223cd294cd3924d7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9477b3e22d481ecb7151d960048153f3828765177f56da2e539b0eb77ece8b94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-15T05:05:34Z",
    "title_canon_sha256": "070f546aa64706cacddba41f173703f193ee07e1ed3a8defb21cc27b882eedf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03696",
    "kind": "arxiv",
    "version": 2
  }
}