Pith Number

pith:DB25BZFX

pith:1999:DB25BZFX5AJ2PKHUYAQZNZYM3F

not attested not anchored not stored refs pending

Harmonic functions on multiplicative graphs and interpolation polynomials

Alexei Borodin, Grigori Olshanski

arxiv:math/9912124 v1 · 1999-12-15 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DB25BZFX5AJ2PKHUYAQZNZYM3F}

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	2026-05-18T01:05:32.283615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1875d0e4b7e813a7a8f4c02196e70cd96ee9881f2d3ea5fd0d06882d5f1d7c09

Aliases

arxiv: math/9912124 · arxiv_version: math/9912124v1 · doi: 10.48550/arxiv.math/9912124 · pith_short_12: DB25BZFX5AJ2 · pith_short_16: DB25BZFX5AJ2PKHU · pith_short_8: DB25BZFX

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/DB25BZFX5AJ2PKHUYAQZNZYM3F \
  | 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: 1875d0e4b7e813a7a8f4c02196e70cd96ee9881f2d3ea5fd0d06882d5f1d7c09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e26efc3d84100aed7a4871dd140b8e08ae4681853fc167bdecee23de73d4aeac",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1999-12-15T20:30:47Z",
    "title_canon_sha256": "9dc8e24b463a82b0d85f734fcef58efc8d8c6d4e59ab77764e4f2b4ad47de3cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9912124",
    "kind": "arxiv",
    "version": 1
  }
}