Pith Number

pith:HL3ZN4HZ

pith:2010:HL3ZN4HZWVPZRBAAYNIOIHDAHV

not attested not anchored not stored refs pending

Tight products and Expansion

Amit Daniely, Nathan Linial

arxiv:1001.3661 v2 · 2010-01-20 · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HL3ZN4HZWVPZRBAAYNIOIHDAHV}

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	2026-05-18T03:41:40.586244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3af796f0f9b55f988400c350e41c603d5f5dc8dd815488b6f58efb2a17efa244

Aliases

arxiv: 1001.3661 · arxiv_version: 1001.3661v2 · doi: 10.48550/arxiv.1001.3661 · pith_short_12: HL3ZN4HZWVPZ · pith_short_16: HL3ZN4HZWVPZRBAA · pith_short_8: HL3ZN4HZ

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/HL3ZN4HZWVPZRBAAYNIOIHDAHV \
  | 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: 3af796f0f9b55f988400c350e41c603d5f5dc8dd815488b6f58efb2a17efa244

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da1046cb4572db88bd3b915932b3715ccdd057b40eaaeabfd88473a5321600bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2010-01-20T20:14:15Z",
    "title_canon_sha256": "120a0c9ca1cfe19af35004785bee3bae26bc30157571e4d4e41b3147b5b80eb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.3661",
    "kind": "arxiv",
    "version": 2
  }
}