Pith Number

pith:VBWEP4YV

pith:1994:VBWEP4YVWLYEKZZGDXTSUHQFPJ

not attested not anchored not stored refs pending

Generalized degrees and densities for families of sets

Emanuel Knill

arxiv:math/9411220 v1 · 1994-11-08 · 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{VBWEP4YVWLYEKZZGDXTSUHQFPJ}

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	2026-05-18T01:05:50.868808Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a86c47f315b2f04567261de72a1e057a7aa01bb1eee2aad319d5590fe3cadc66

Aliases

arxiv: math/9411220 · arxiv_version: math/9411220v1 · doi: 10.48550/arxiv.math/9411220 · pith_short_12: VBWEP4YVWLYE · pith_short_16: VBWEP4YVWLYEKZZG · pith_short_8: VBWEP4YV

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/VBWEP4YVWLYEKZZGDXTSUHQFPJ \
  | 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: a86c47f315b2f04567261de72a1e057a7aa01bb1eee2aad319d5590fe3cadc66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c44a5e98fdd7785827fa8743a440d02cdeb334545e185ee90953a35380f92f8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1994-11-08T00:00:00Z",
    "title_canon_sha256": "2fd6b9e5d1f2c4fecbcd62b27546fde7c592219285d7194763a5ebf1b563d62c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9411220",
    "kind": "arxiv",
    "version": 1
  }
}