Pith Number

pith:K2ZMC4SO

pith:2008:K2ZMC4SOSX7MWCG4T3XZLY7PTE

not attested not anchored not stored refs pending

Vector spaces as unions of proper subspaces

Apoorva Khare

arxiv:0803.2746 v4 · 2008-03-19 · math.AC · 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{K2ZMC4SOSX7MWCG4T3XZLY7PTE}

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	2026-05-18T02:28:21.508685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56b2c1724e95fecb08dc9eef95e3ef990ead4a183c0d372d740f420de9aea272

Aliases

arxiv: 0803.2746 · arxiv_version: 0803.2746v4 · doi: 10.48550/arxiv.0803.2746 · pith_short_12: K2ZMC4SOSX7M · pith_short_16: K2ZMC4SOSX7MWCG4 · pith_short_8: K2ZMC4SO

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/K2ZMC4SOSX7MWCG4T3XZLY7PTE \
  | 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: 56b2c1724e95fecb08dc9eef95e3ef990ead4a183c0d372d740f420de9aea272

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9cbbe51434ad1e274cd38be83c92909be10f68230caab0ea687b81aab72b2473",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2008-03-19T02:52:02Z",
    "title_canon_sha256": "1865e331de4fa787132e083aacc1c10cb2edebc29bf3882f7658c82b285318d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0803.2746",
    "kind": "arxiv",
    "version": 4
  }
}