Pith Number

pith:4OBWVN4H

pith:2015:4OBWVN4HCNE56K6WK7EH235ZHH

not attested not anchored not stored refs pending

From Grassmann necklaces to restricted permutations and back again

Karel Casteels, Si\^an Fryer

arxiv:1511.06664 v2 · 2015-11-20 · math.QA · 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{4OBWVN4HCNE56K6WK7EH235ZHH}

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	2026-05-18T01:12:34.733377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3836ab7871349df2bd657c87d6fb939e29a653841f08231987dc5c812140b25

Aliases

arxiv: 1511.06664 · arxiv_version: 1511.06664v2 · doi: 10.48550/arxiv.1511.06664 · pith_short_12: 4OBWVN4HCNE5 · pith_short_16: 4OBWVN4HCNE56K6W · pith_short_8: 4OBWVN4H

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/4OBWVN4HCNE56K6WK7EH235ZHH \
  | 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: e3836ab7871349df2bd657c87d6fb939e29a653841f08231987dc5c812140b25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "202dcb30dc8f04c92c2fb2a70c2a3322a3874111e14dffb1b99d4cd799973bc3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-11-20T16:14:37Z",
    "title_canon_sha256": "b0f08e262b9a5abfe428fa9d72fa322faac6a708bcc8ee2ef46fb44299a03a71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06664",
    "kind": "arxiv",
    "version": 2
  }
}