Pith Number

pith:M6UZQPF3

pith:2011:M6UZQPF3ZVWITAFWJAQ4PGCPH2

not attested not anchored not stored refs pending

Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case

Dmitry Panchenko

arxiv:1106.3984 v1 · 2011-06-20 · 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{M6UZQPF3ZVWITAFWJAQ4PGCPH2}

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	2026-05-18T04:16:41.921120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67a9983cbbcd6c8980b64821c7984f3eab5fe183e92a25e0a14d8d4bba4196db

Aliases

arxiv: 1106.3984 · arxiv_version: 1106.3984v1 · doi: 10.48550/arxiv.1106.3984 · pith_short_12: M6UZQPF3ZVWI · pith_short_16: M6UZQPF3ZVWITAFW · pith_short_8: M6UZQPF3

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/M6UZQPF3ZVWITAFWJAQ4PGCPH2 \
  | 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: 67a9983cbbcd6c8980b64821c7984f3eab5fe183e92a25e0a14d8d4bba4196db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d7fa70b3cd395e6e3fa541c4ff1029368cb02efe0bf7ab52188a752b7bbe613",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-06-20T18:37:20Z",
    "title_canon_sha256": "db1c2800270dab667aa2c1a0ba0d37b415bf1dd56199a84cd04cc43a1bc69ac8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3984",
    "kind": "arxiv",
    "version": 1
  }
}