Pith Number

pith:EK5Z2NWP

pith:2011:EK5Z2NWP6OAJI2TN2TN3HB6DVC

not attested not anchored not stored refs pending

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

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

arxiv:1109.5438 v1 · 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{EK5Z2NWP6OAJI2TN2TN3HB6DVC}

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	2026-05-18T04:12:19.803015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22bb9d36cff380946a6dd4dbb387c3a8813743a3cd9acd684a7e1144481b53c8

Aliases

arxiv: 1109.5438 · arxiv_version: 1109.5438v1 · doi: 10.48550/arxiv.1109.5438 · pith_short_12: EK5Z2NWP6OAJ · pith_short_16: EK5Z2NWP6OAJI2TN · pith_short_8: EK5Z2NWP

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/EK5Z2NWP6OAJI2TN2TN3HB6DVC \
  | 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: 22bb9d36cff380946a6dd4dbb387c3a8813743a3cd9acd684a7e1144481b53c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dd3d9594f6ea9c3c644b31d0e1159a310bef8b8af2e4d41d1d871957dcd37b4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2011-09-26T03:50:30Z",
    "title_canon_sha256": "4fbb8856e5fc31bc1ec9fc655dde6ab59d7b9e16930f2960955916f16121112e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5438",
    "kind": "arxiv",
    "version": 1
  }
}