Pith Number

pith:KP7FFSU5

pith:2011:KP7FFSU5OAT6W4UDH3LQPH4OMV

not attested not anchored not stored refs pending

Revisiting the spreading and covering numbers

Adam Van Tuyl, Ben Babcock

arxiv:1109.5847 v2 · 2011-09-27 · 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{KP7FFSU5OAT6W4UDH3LQPH4OMV}

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	2026-05-18T03:24:42.018204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53fe52ca9d7027eb72833ed7079f8e6574d3817d55aab6e57dee0aa2f64d91d8

Aliases

arxiv: 1109.5847 · arxiv_version: 1109.5847v2 · doi: 10.48550/arxiv.1109.5847 · pith_short_12: KP7FFSU5OAT6 · pith_short_16: KP7FFSU5OAT6W4UD · pith_short_8: KP7FFSU5

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/KP7FFSU5OAT6W4UDH3LQPH4OMV \
  | 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: 53fe52ca9d7027eb72833ed7079f8e6574d3817d55aab6e57dee0aa2f64d91d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3b9028542f44573426a6515ba026cf2e3dc24c4ef93938b072ec849070abd76",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-09-27T11:59:02Z",
    "title_canon_sha256": "2632f8dd4aeb9d8be5adbbf41f143c2aafb3ead45616284077198e2bd6db26bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5847",
    "kind": "arxiv",
    "version": 2
  }
}