Pith Number

pith:NVRVTTUW

pith:2015:NVRVTTUW53V62G2ODTR2WKPXYE

not attested not anchored not stored refs pending

On the Order of $a$ modulo $n$ on Average

Sungjin Kim

arxiv:1509.03768 v2 · 2015-09-12 · 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{NVRVTTUW53V62G2ODTR2WKPXYE}

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	2026-05-18T01:14:29.285370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d6359ce96eeebed1b4e1ce3ab29f7c11ed067971dd4b983c884caca7ba97736

Aliases

arxiv: 1509.03768 · arxiv_version: 1509.03768v2 · doi: 10.48550/arxiv.1509.03768 · pith_short_12: NVRVTTUW53V6 · pith_short_16: NVRVTTUW53V62G2O · pith_short_8: NVRVTTUW

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/NVRVTTUW53V62G2ODTR2WKPXYE \
  | 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: 6d6359ce96eeebed1b4e1ce3ab29f7c11ed067971dd4b983c884caca7ba97736

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "882d0e14814209d60e7633374ab50c8a8e3ccae80f474d8c6f0496352efdeb88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-12T19:17:04Z",
    "title_canon_sha256": "9eaf380f52f86559b19b5158a1ea06e4f5ff0939948cf537e3f040347bd43389"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03768",
    "kind": "arxiv",
    "version": 2
  }
}