Pith Number

pith:ZA4I34MF

pith:2011:ZA4I34MFG2MSVJ2UVASZUIRMN2

not attested not anchored not stored refs pending

Vapnik-Chervonenkis density in some theories without the independence property, II

A. Dolich, D. Haskell, D. Macpherson, M. Aschenbrenner, S. Starchenko

arxiv:1109.5437 v2 · 2011-09-26 · math.LO · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZA4I34MFG2MSVJ2UVASZUIRMN2}

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	2026-05-18T01:21:05.843005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8388df18536992aa754a8259a222c6eb4f3c23f2d5599694c953d4e4cc4942f

Aliases

arxiv: 1109.5437 · arxiv_version: 1109.5437v2 · doi: 10.48550/arxiv.1109.5437 · pith_short_12: ZA4I34MFG2MS · pith_short_16: ZA4I34MFG2MSVJ2U · pith_short_8: ZA4I34MF

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/ZA4I34MFG2MSVJ2UVASZUIRMN2 \
  | 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: c8388df18536992aa754a8259a222c6eb4f3c23f2d5599694c953d4e4cc4942f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bc082c750404fc9c800972a66116815ed0aecedb6f98329618c380366050224",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2011-09-26T03:50:03Z",
    "title_canon_sha256": "b274765d72c95a36171a411e33159283f468780b3df1a31798febad839ae90d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5437",
    "kind": "arxiv",
    "version": 2
  }
}