Pith Number

pith:UBOL4MF5

pith:2011:UBOL4MF5VMJXC7ADYNAS7Y2QPF

not attested not anchored not stored refs pending

Chains of modular elements and shellability

Russ Woodroofe

arxiv:1104.0936 v3 · 2011-04-05 · math.CO · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UBOL4MF5VMJXC7ADYNAS7Y2QPF}

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	2026-05-18T03:58:49.149934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a05cbe30bdab13717c03c3412fe35079646ef034d86aa7b0e797663772d53864

Aliases

arxiv: 1104.0936 · arxiv_version: 1104.0936v3 · doi: 10.48550/arxiv.1104.0936 · pith_short_12: UBOL4MF5VMJX · pith_short_16: UBOL4MF5VMJXC7AD · pith_short_8: UBOL4MF5

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/UBOL4MF5VMJXC7ADYNAS7Y2QPF \
  | 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: a05cbe30bdab13717c03c3412fe35079646ef034d86aa7b0e797663772d53864

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "882b0cfc850dd0e86c4883ae2423f5bc598d0e5cf19428d3b96d96a976327c14",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-04-05T20:00:05Z",
    "title_canon_sha256": "463e1fbc8d8d09a4631ee7ac8c315b92fbaf8301ab94ad73189b9a10f0af35c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0936",
    "kind": "arxiv",
    "version": 3
  }
}