Pith Number

pith:UN4BK5KL

pith:2014:UN4BK5KLPRYMOAK2F2IDNBLG5L

not attested not anchored not stored refs pending

The Vapnik-Chervonenkis dimension of cubes in $\mathbb{R}^d$

Christian J. J. Despres

arxiv:1412.6612 v3 · 2014-12-20 · math.CO · math.MG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UN4BK5KLPRYMOAK2F2IDNBLG5L}

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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.

Cited by

1 paper in Pith

VC-dimension of generalized progressions in some nonabelian groups

Receipt and verification

First computed	2026-05-18T00:29:39.894869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a37815754b7c70c7015a2e90368566ead7550f9a1a6d2ea1f4c83dc070d2f35a

Aliases

arxiv: 1412.6612 · arxiv_version: 1412.6612v3 · doi: 10.48550/arxiv.1412.6612 · pith_short_12: UN4BK5KLPRYM · pith_short_16: UN4BK5KLPRYMOAK2 · pith_short_8: UN4BK5KL

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/UN4BK5KLPRYMOAK2F2IDNBLG5L \
  | 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: a37815754b7c70c7015a2e90368566ead7550f9a1a6d2ea1f4c83dc070d2f35a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c28055bbace9631d40eaf07759937f18c0c09d74985440a6802b33b78076b2a",
    "cross_cats_sorted": [
      "math.MG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-20T06:05:12Z",
    "title_canon_sha256": "9679abe2df3dba5bfaa5e7e6cc97b5f302101767037ef60ac6987415085bdcc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.6612",
    "kind": "arxiv",
    "version": 3
  }
}