Pith Number

pith:IPWH5DVE

pith:2010:IPWH5DVED2DPF2EQDBGU2S3PPS

not attested not anchored not stored refs pending

VC bounds on the cardinality of nearly orthogonal function classes

Elchanan Mossel, Lee-Ad Gottlieb, Leonid (Aryeh) Kontorovich

arxiv:1007.4915 v2 · 2010-07-28 · 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{IPWH5DVED2DPF2EQDBGU2S3PPS}

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	2026-05-18T04:28:29.756053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43ec7e8ea41e86f2e890184d4d4b6f7c9399918bf104ad6572b781ff99e7f61c

Aliases

arxiv: 1007.4915 · arxiv_version: 1007.4915v2 · doi: 10.48550/arxiv.1007.4915 · pith_short_12: IPWH5DVED2DP · pith_short_16: IPWH5DVED2DPF2EQ · pith_short_8: IPWH5DVE

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/IPWH5DVED2DPF2EQDBGU2S3PPS \
  | 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: 43ec7e8ea41e86f2e890184d4d4b6f7c9399918bf104ad6572b781ff99e7f61c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83221ac5900a167e5e5d0bb92a1728ee982c5e0d2af93b7157370d9708a8e6dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-28T10:05:37Z",
    "title_canon_sha256": "fc9de54c2489dd3c6ca0f6296449ff58b0d98f7c8abce15023e400652708b645"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4915",
    "kind": "arxiv",
    "version": 2
  }
}