Pith Number

pith:GIVNTODV

pith:2016:GIVNTODVCZNAKG4IKBQFOP6VGS

not attested not anchored not stored refs pending

Random multiplicative walks on the residues modulo n

Nathan McNew

arxiv:1608.05898 v1 · 2016-08-21 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GIVNTODVCZNAKG4IKBQFOP6VGS}

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	2026-05-18T00:44:24.479270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

322ad9b875165a051b885060573fd5348178fba654fec5339806e9e2b6a13b80

Aliases

arxiv: 1608.05898 · arxiv_version: 1608.05898v1 · doi: 10.48550/arxiv.1608.05898 · pith_short_12: GIVNTODVCZNA · pith_short_16: GIVNTODVCZNAKG4I · pith_short_8: GIVNTODV

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/GIVNTODVCZNAKG4IKBQFOP6VGS \
  | 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: 322ad9b875165a051b885060573fd5348178fba654fec5339806e9e2b6a13b80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0dc3059e095c49478671f0fde8c75548d763167c31c7498da987c7c5b4d20b6",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-08-21T04:58:06Z",
    "title_canon_sha256": "fbb082d33107544bcdc0ddec68597b2115239b3a93307471af2078ba8e5dffd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05898",
    "kind": "arxiv",
    "version": 1
  }
}