Pith Number

pith:3NIYPAK5

pith:2005:3NIYPAK5C25IRXEV2YDSFLGEB2

not attested not anchored not stored refs pending

On the Integrality of n-th Roots of Generating Functions

E. M. Rains, Nadia Heninger, N. J. A. Sloane

arxiv:math/0509316 v4 · 2005-09-14 · math.NT · 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{3NIYPAK5C25IRXEV2YDSFLGEB2}

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	2026-05-18T02:42:39.995639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db5187815d16ba88dc95d60722acc40e9b8aafdcd02b1a0ab03e61bf0291307e

Aliases

arxiv: math/0509316 · arxiv_version: math/0509316v4 · doi: 10.48550/arxiv.math/0509316 · pith_short_12: 3NIYPAK5C25I · pith_short_16: 3NIYPAK5C25IRXEV · pith_short_8: 3NIYPAK5

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/3NIYPAK5C25IRXEV2YDSFLGEB2 \
  | 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: db5187815d16ba88dc95d60722acc40e9b8aafdcd02b1a0ab03e61bf0291307e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a63d3cbc3568525e9d4d7297d9280b9d1a65aeb137863fc79f130a8d5f97f52",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-09-14T14:59:50Z",
    "title_canon_sha256": "e86377db4c33e4f47c299c4cbfa6853d403e7d1fa3bf7294825bf0dfcbad7afd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509316",
    "kind": "arxiv",
    "version": 4
  }
}