Pith Number

pith:GWHXQN3T

pith:2018:GWHXQN3TRGLPR43DDAOLAIQAA2

not attested not anchored not stored refs pending

Phase transitions for a model with uncountable spin space on the Cayley tree: the general case

Benedikt Jahnel, Golibjon Botirov

arxiv:1803.02867 v1 · 2018-03-07 · 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{GWHXQN3TRGLPR43DDAOLAIQAA2}

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	2026-05-18T00:21:45.251084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

358f7837738996f8f363181cb022000685ff781ef7d4c4b1661927c6ad7a996e

Aliases

arxiv: 1803.02867 · arxiv_version: 1803.02867v1 · doi: 10.48550/arxiv.1803.02867 · pith_short_12: GWHXQN3TRGLP · pith_short_16: GWHXQN3TRGLPR43D · pith_short_8: GWHXQN3T

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/GWHXQN3TRGLPR43DDAOLAIQAA2 \
  | 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: 358f7837738996f8f363181cb022000685ff781ef7d4c4b1661927c6ad7a996e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0cc7cab023e96707521a224e7888876da519cf5b4573f19ba95a823a1433dfb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-03-07T20:35:18Z",
    "title_canon_sha256": "f5dc3f6c82ed92e1c4d458c078b1cd7183660281397f23d0a0cd7536187d8ee6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.02867",
    "kind": "arxiv",
    "version": 1
  }
}