Pith Number

pith:IENNYOUG

pith:2025:IENNYOUG5YDSPYGZZN5VAMROEA

not attested not anchored not stored refs pending

From Zipf's Law to Neural Scaling through Heaps' Law and Hilberg's Hypothesis

{\L}ukasz D\k{e}bowski

arxiv:2512.13491 v3 · 2025-12-15 · cs.IT · cs.LG · math.IT · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IENNYOUG5YDSPYGZZN5VAMROEA}

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	2026-06-23T03:13:52.463368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

411adc3a86ee0727e0d9cb7b50322e2035777d8f08353d1d1e2d0f9a9679cf92

Aliases

arxiv: 2512.13491 · arxiv_version: 2512.13491v3 · doi: 10.48550/arxiv.2512.13491 · pith_short_12: IENNYOUG5YDS · pith_short_16: IENNYOUG5YDSPYGZ · pith_short_8: IENNYOUG

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/IENNYOUG5YDSPYGZZN5VAMROEA \
  | 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: 411adc3a86ee0727e0d9cb7b50322e2035777d8f08353d1d1e2d0f9a9679cf92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b93688626c05a45465b6fb2c627ceaf74305364fdb1b53cece9b85c8b4ab10a",
    "cross_cats_sorted": [
      "cs.LG",
      "math.IT",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2025-12-15T16:25:06Z",
    "title_canon_sha256": "fb9656ae9428e949cc0eb25254e804214c63ff303a25366d3618c1dd5343f7e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.13491",
    "kind": "arxiv",
    "version": 3
  }
}