Pith Number

pith:DOCD6DMZ

pith:2013:DOCD6DMZRABOFT626L5DFXWIUX

not attested not anchored not stored refs pending

Observables of Macdonald processes

Alexei Borodin, Ivan Corwin, Shamil Shakirov, Vadim Gorin

arxiv:1306.0659 v1 · 2013-06-04 · math.PR · math-ph · math.CO · math.MP · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DOCD6DMZRABOFT626L5DFXWIUX}

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	2026-05-18T01:19:22.509980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b843f0d998802e2cfdaf2fa32dec8a5ea3abe95b8b971a41f8bdf8f30fc6857

Aliases

arxiv: 1306.0659 · arxiv_version: 1306.0659v1 · doi: 10.48550/arxiv.1306.0659 · pith_short_12: DOCD6DMZRABO · pith_short_16: DOCD6DMZRABOFT62 · pith_short_8: DOCD6DMZ

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/DOCD6DMZRABOFT626L5DFXWIUX \
  | 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: 1b843f0d998802e2cfdaf2fa32dec8a5ea3abe95b8b971a41f8bdf8f30fc6857

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fe7d1b75785056c845dd870e2d96d72840202eb97cfcc298a3bdc35b00337e4",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-06-04T05:51:39Z",
    "title_canon_sha256": "a5af04885ba52a3a6eadf115f9215848ce80a74cf27139e8862bd71d98711677"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0659",
    "kind": "arxiv",
    "version": 1
  }
}