Pith Number

pith:TC5P5JJT

pith:2026:TC5P5JJTKDMRWCULXH42ICXQRI

not attested not anchored not stored refs pending

Regularity of Gibbs measures for unbounded spin systems on general graphs

Christoforos Panagiotis, William Veitch

arxiv:2603.26319 v2 · 2026-03-27 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TC5P5JJTKDMRWCULXH42ICXQRI}

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	2026-06-01T02:03:39.097219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98bafea53350d91b0a8bb9f9a40af08a39f40b843b0fc5eb993cd9cc286bdcdf

Aliases

arxiv: 2603.26319 · arxiv_version: 2603.26319v2 · doi: 10.48550/arxiv.2603.26319 · pith_short_12: TC5P5JJTKDMR · pith_short_16: TC5P5JJTKDMRWCUL · pith_short_8: TC5P5JJT

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/TC5P5JJTKDMRWCULXH42ICXQRI \
  | 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: 98bafea53350d91b0a8bb9f9a40af08a39f40b843b0fc5eb993cd9cc286bdcdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eab8d6fb6c8ef62162156b164276a511f2364cadacbed7bb7975b726d8ce9685",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-03-27T11:38:16Z",
    "title_canon_sha256": "e925437e7ee5f4ff2c4de117eb20db0584d4ccca85b35b29fd9344caaba7b55a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.26319",
    "kind": "arxiv",
    "version": 2
  }
}