Pith Number

pith:3N52LHZA

pith:2018:3N52LHZAXJ3CTAMJBPSKBF3IIK

not attested not anchored not stored refs pending

A note on expansion in prime fields

Laura Venieri, Tuomas Orponen

arxiv:1801.09591 v1 · 2018-01-29 · math.CO · math.CA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3N52LHZAXJ3CTAMJBPSKBF3IIK}

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	2026-05-18T00:24:56.978281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db7ba59f20ba762981890be4a0976842956e635b5bef2dde726e390539bd23bd

Aliases

arxiv: 1801.09591 · arxiv_version: 1801.09591v1 · doi: 10.48550/arxiv.1801.09591 · pith_short_12: 3N52LHZAXJ3C · pith_short_16: 3N52LHZAXJ3CTAMJ · pith_short_8: 3N52LHZA

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/3N52LHZAXJ3CTAMJBPSKBF3IIK \
  | 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: db7ba59f20ba762981890be4a0976842956e635b5bef2dde726e390539bd23bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e07f2f9acf0911f27d89348db2da08f4fbdc50d074519e1a93bd453212a2c634",
    "cross_cats_sorted": [
      "math.CA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-01-29T15:56:40Z",
    "title_canon_sha256": "c9afc8355081a76982ea1b8af95b934651e1d057ad90a454c62e6a3f272fc87e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.09591",
    "kind": "arxiv",
    "version": 1
  }
}