Pith Number

pith:PFHC32U5

pith:2010:PFHC32U5BH2Z4XIVWHGREFDUM5

not attested not anchored not stored refs pending

Coxeter and crystallographic arrangements are inductively free

Michael Cuntz, Mohamed Barakat

arxiv:1011.4228 v1 · 2010-11-18 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PFHC32U5BH2Z4XIVWHGREFDUM5}

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	2026-05-18T00:55:58.932583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

794e2dea9d09f59e5d15b1cd121474676568656b3f64839b8937a64ec137db9c

Aliases

arxiv: 1011.4228 · arxiv_version: 1011.4228v1 · doi: 10.48550/arxiv.1011.4228 · pith_short_12: PFHC32U5BH2Z · pith_short_16: PFHC32U5BH2Z4XIV · pith_short_8: PFHC32U5

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/PFHC32U5BH2Z4XIVWHGREFDUM5 \
  | 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: 794e2dea9d09f59e5d15b1cd121474676568656b3f64839b8937a64ec137db9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6616358db23dd30c78de4d989c1999dcd75511e248a0bbe2023a62c088a2ce1a",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-18T16:49:30Z",
    "title_canon_sha256": "b66ae769653d2da9a0a40b9179eca1a4bc6f3da539a74c8a7c61c1ebb111fbe0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4228",
    "kind": "arxiv",
    "version": 1
  }
}