Pith Number

pith:IAKAOPZD

pith:2007:IAKAOPZDLVYJFYUYXCAFEOWEAX

not attested not anchored not stored refs pending

Factorial ratios, hypergeometric series, and a family of step functions

Jonathan Bober

arxiv:0709.1977 v1 · 2007-09-13 · math.NT · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IAKAOPZDLVYJFYUYXCAFEOWEAX}

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	2026-05-18T02:58:12.328008Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4014073f235d7092e298b880523ac405dce3624d5458f8309dff4423309429d5

Aliases

arxiv: 0709.1977 · arxiv_version: 0709.1977v1 · doi: 10.48550/arxiv.0709.1977 · pith_short_12: IAKAOPZDLVYJ · pith_short_16: IAKAOPZDLVYJFYUY · pith_short_8: IAKAOPZD

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/IAKAOPZDLVYJFYUYXCAFEOWEAX \
  | 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: 4014073f235d7092e298b880523ac405dce3624d5458f8309dff4423309429d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f3b1caaa825921da49afbe8ff8d51cce8f1161348df04b365c40b0c78bc5103",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-09-13T01:49:51Z",
    "title_canon_sha256": "9ff523bb6a4d4046404211fed8a2628fd42910e3d841f7f859c65134ce1647a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.1977",
    "kind": "arxiv",
    "version": 1
  }
}