Pith Number

pith:J5K2YXDO

pith:2007:J5K2YXDO4EU3G35HQK7S67YLDP

not attested not anchored not stored refs pending

On phase transitions of the Potts model with three competing interactions on Cayley tree

Hasan Akin, Seyit Temir

arxiv:math/0703699 v2 · 2007-03-23 · math.FA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J5K2YXDO4EU3G35HQK7S67YLDP}

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	2026-05-18T01:13:45.621725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f55ac5c6ee129b36fa782bf2f7f0b1bd3a8414828bc62b911fb88bc7ed0c608

Aliases

arxiv: math/0703699 · arxiv_version: math/0703699v2 · doi: 10.48550/arxiv.math/0703699 · pith_short_12: J5K2YXDO4EU3 · pith_short_16: J5K2YXDO4EU3G35H · pith_short_8: J5K2YXDO

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/J5K2YXDO4EU3G35HQK7S67YLDP \
  | 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: 4f55ac5c6ee129b36fa782bf2f7f0b1bd3a8414828bc62b911fb88bc7ed0c608

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0d1a0e9a8a5ce9fd31a89c19d6bbed75502dec65e56657aadb78bc7a1712e32",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2007-03-23T14:17:39Z",
    "title_canon_sha256": "a5c7c83c2cd2f7f077301d8f217a95a38bd0ef656edf2cfc888d214ea7a04209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703699",
    "kind": "arxiv",
    "version": 2
  }
}