Pith Number

pith:VLGEQ6XZ

pith:1994:VLGEQ6XZWO3LP4GHF3XCKJXMWW

not attested not anchored not stored refs pending

Graph generated union-closed families of sets

Emanuel Knill

arxiv:math/9409215 v1 · 1994-09-16 · 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{VLGEQ6XZWO3LP4GHF3XCKJXMWW}

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.

Cited by

1 paper in Pith

Redundancy Is All You Need (for CSP Sparsification)

Receipt and verification

First computed	2026-05-18T01:05:51.096878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aacc487af9b3b6b7f0c72eee2526ecb5b1fb89df60327875a867f680d2df63bb

Aliases

arxiv: math/9409215 · arxiv_version: math/9409215v1 · doi: 10.48550/arxiv.math/9409215 · pith_short_12: VLGEQ6XZWO3L · pith_short_16: VLGEQ6XZWO3LP4GH · pith_short_8: VLGEQ6XZ

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/VLGEQ6XZWO3LP4GHF3XCKJXMWW \
  | 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: aacc487af9b3b6b7f0c72eee2526ecb5b1fb89df60327875a867f680d2df63bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "857747e1a4efd62d9a2bd603f0f9a2858354aa28b7195d222a6d026914b5ae7c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1994-09-16T00:00:00Z",
    "title_canon_sha256": "29563210986573c49f2203b65977123614b79ded34c6c90533a374eba518aa48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9409215",
    "kind": "arxiv",
    "version": 1
  }
}