Pith Number

pith:ZYCCKBAF

pith:2015:ZYCCKBAFBTDSY7JDRL5CYIPSQH

not attested not anchored not stored refs pending

Crystallographic groups and flat manifolds from complex reflection groups

Ivan Marin

arxiv:1509.06213 v2 · 2015-09-21 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZYCCKBAFBTDSY7JDRL5CYIPSQH}

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	2026-05-18T01:23:44.426803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce042504050cc72c7d238afa2c21f281cd26446680f85aca5f3404e8783ec46e

Aliases

arxiv: 1509.06213 · arxiv_version: 1509.06213v2 · doi: 10.48550/arxiv.1509.06213 · pith_short_12: ZYCCKBAFBTDS · pith_short_16: ZYCCKBAFBTDSY7JD · pith_short_8: ZYCCKBAF

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/ZYCCKBAFBTDSY7JDRL5CYIPSQH \
  | 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: ce042504050cc72c7d238afa2c21f281cd26446680f85aca5f3404e8783ec46e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1fe6492bf2c1a3515fd2eb6adf6dd232337a421e34264ce14c39a6196dd8d71",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-21T13:06:02Z",
    "title_canon_sha256": "15ced99eed9f272a63a53ff048232b25553bbaa368aad8eae81049aa3ac3ab85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06213",
    "kind": "arxiv",
    "version": 2
  }
}