Pith Number

pith:OLD2NUSO

pith:2004:OLD2NUSOSCQL57C7SGUIXLTWN5

not attested not anchored not stored refs pending

Robust Phase Transitions for Heisenberg and Other Models on General Trees

Jeffrey E. Steif, Robin Pemantle

arxiv:math/0404092 v1 · 2004-04-05 · 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{OLD2NUSOSCQL57C7SGUIXLTWN5}

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	2026-05-18T01:05:26.454273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72c7a6d24e90a0befc5f91a88bae766f46b80c5ec7f273c9b7fb1e76c56109e1

Aliases

arxiv: math/0404092 · arxiv_version: math/0404092v1 · doi: 10.48550/arxiv.math/0404092 · pith_short_12: OLD2NUSOSCQL · pith_short_16: OLD2NUSOSCQL57C7 · pith_short_8: OLD2NUSO

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/OLD2NUSOSCQL57C7SGUIXLTWN5 \
  | 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: 72c7a6d24e90a0befc5f91a88bae766f46b80c5ec7f273c9b7fb1e76c56109e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61f95cee55e2f1879a0a0e31e9adb31a0635e35575fe2e78bbebf0ae268aeff2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-04-05T15:24:38Z",
    "title_canon_sha256": "61ef2ffe5d5a1cbfee5cb5b14744342a05e35f0623f2ecb5505b91b482179d92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404092",
    "kind": "arxiv",
    "version": 1
  }
}