Pith Number

pith:24ZNKRE4

pith:2009:24ZNKRE4YR3QUVM2FT5DLS44U7

not attested not anchored not stored refs pending

Two notes on harmonic distributions

Kamil Niedzialomski

arxiv:0909.4957 v2 · 2009-09-27 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{24ZNKRE4YR3QUVM2FT5DLS44U7}

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	2026-05-18T03:45:01.396131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d732d5449cc4770a559a2cfa35cb9ca7f1f1e3ae10157df84a72d19eca52e8d9

Aliases

arxiv: 0909.4957 · arxiv_version: 0909.4957v2 · doi: 10.48550/arxiv.0909.4957 · pith_short_12: 24ZNKRE4YR3Q · pith_short_16: 24ZNKRE4YR3QUVM2 · pith_short_8: 24ZNKRE4

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/24ZNKRE4YR3QUVM2FT5DLS44U7 \
  | 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: d732d5449cc4770a559a2cfa35cb9ca7f1f1e3ae10157df84a72d19eca52e8d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac6e87bc5facc429cc8cb39a9365608225d7db06f0aa833849b7e46106567a9d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-09-27T19:31:05Z",
    "title_canon_sha256": "1837f33e87333d746ed14683d526017072cc9185f1393073e9716efbdf97f52e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4957",
    "kind": "arxiv",
    "version": 2
  }
}