Pith Number

pith:QALOWUE7

pith:2016:QALOWUE7YDL7O5SAMET465OJKD

not attested not anchored not stored refs pending

Perfect and separating Hash families: new bounds via the algorithmic cluster expansion local lemma

Aldo Procacci, Remy Sanchis

arxiv:1601.05389 v2 · 2016-01-20 · 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{QALOWUE7YDL7O5SAMET465OJKD}

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	2026-05-18T00:55:28.603957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8016eb509fc0d7f776406127cf75c950fecdbc9db6684fdcde3c9e2700ff5876

Aliases

arxiv: 1601.05389 · arxiv_version: 1601.05389v2 · doi: 10.48550/arxiv.1601.05389 · pith_short_12: QALOWUE7YDL7 · pith_short_16: QALOWUE7YDL7O5SA · pith_short_8: QALOWUE7

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/QALOWUE7YDL7O5SAMET465OJKD \
  | 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: 8016eb509fc0d7f776406127cf75c950fecdbc9db6684fdcde3c9e2700ff5876

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1adc99e9fefd66a4518b2e136b3720fa2929f7d213bd910a2bea563054427800",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-20T19:51:11Z",
    "title_canon_sha256": "4005a98a1a2ad1d038901572c40008652b3057d283452ef8bfb748ff666d99ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05389",
    "kind": "arxiv",
    "version": 2
  }
}