Pith Number

pith:C7BGCB7T

pith:2005:C7BGCB7THOR6GNTQNYKYJDNB7Y

not attested not anchored not stored refs pending

Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem

B\'alint T\'oth, Jeffrey E. Steif, Thomas M. Liggett

arxiv:math/0512191 v4 · 2005-12-09 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C7BGCB7THOR6GNTQNYKYJDNB7Y}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T04:08:35.600951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17c26107f33ba3e336706e15848da1fe15fea089077786f6d5a2d0e26e2b17bd

Aliases

arxiv: math/0512191 · arxiv_version: math/0512191v4 · doi: 10.48550/arxiv.math/0512191 · pith_short_12: C7BGCB7THOR6 · pith_short_16: C7BGCB7THOR6GNTQ · pith_short_8: C7BGCB7T

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/C7BGCB7THOR6GNTQNYKYJDNB7Y \
  | 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: 17c26107f33ba3e336706e15848da1fe15fea089077786f6d5a2d0e26e2b17bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f869aafd6da6d94d8416e125d964a49cc641e06ad8daa20fdbaafcfe7a29222",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-12-09T11:04:26Z",
    "title_canon_sha256": "6a0c1e8e2b7d880a02f864a4bb5eaa0ed22ea1a05c918d17077d61df0d52eecf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512191",
    "kind": "arxiv",
    "version": 4
  }
}