Pith Number

pith:CIGAT7EA

pith:2007:CIGAT7EAIM3UNJVDD7HQNF2R3F

not attested not anchored not stored refs pending

Pattern avoidance and the Bruhat order on involutions

Axel Hultman, Kathrin Vorwerk

arxiv:0711.2223 v1 · 2007-11-14 · 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{CIGAT7EAIM3UNJVDD7HQNF2R3F}

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	2026-05-18T03:50:34.443347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

120c09fc80433746a6a31fcf069751d9538e6a8fd09809f5319efe79225a0038

Aliases

arxiv: 0711.2223 · arxiv_version: 0711.2223v1 · doi: 10.48550/arxiv.0711.2223 · pith_short_12: CIGAT7EAIM3U · pith_short_16: CIGAT7EAIM3UNJVD · pith_short_8: CIGAT7EA

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/CIGAT7EAIM3UNJVDD7HQNF2R3F \
  | 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: 120c09fc80433746a6a31fcf069751d9538e6a8fd09809f5319efe79225a0038

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c160dec4377bf4cf83311a3753f6b36e65d0efaeaec23e4a24e2e5419d29333",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-11-14T15:33:57Z",
    "title_canon_sha256": "3bd9c78b1dbd2b8aaae32497d478590a2abfa58543c65e4afed2a627c8951561"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.2223",
    "kind": "arxiv",
    "version": 1
  }
}