Pith Number

pith:5T5Q3NZE

pith:2004:5T5Q3NZE5KYXLDB3RARL2XPV6C

not attested not anchored not stored refs pending

Benford's Law, Values of L-functions and the 3x+1 Problem

Alex V. Kontorovich, Steven J. Miller

arxiv:math/0412003 v2 · 2004-11-30 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5T5Q3NZE5KYXLDB3RARL2XPV6C}

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	2026-05-18T01:38:27.016131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecfb0db724eab1758c3b8822bd5df5f0b01072189dcd4002eae9bd84d0337a0a

Aliases

arxiv: math/0412003 · arxiv_version: math/0412003v2 · doi: 10.48550/arxiv.math/0412003 · pith_short_12: 5T5Q3NZE5KYX · pith_short_16: 5T5Q3NZE5KYXLDB3 · pith_short_8: 5T5Q3NZE

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/5T5Q3NZE5KYXLDB3RARL2XPV6C \
  | 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: ecfb0db724eab1758c3b8822bd5df5f0b01072189dcd4002eae9bd84d0337a0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c280caf8b4a8e625af1f8519ba50d5513d4493eb9a2b5687c76bfeee9c2eef04",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-11-30T23:24:05Z",
    "title_canon_sha256": "49f3d7af456f0e5107eaf6c65c6c10bf0f83c06413e49f234d76b5b8dc0dacaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412003",
    "kind": "arxiv",
    "version": 2
  }
}