Pith Number

pith:XF7FF7KP

pith:2011:XF7FF7KPARQDPVWOMVR2BFH27I

not attested not anchored not stored refs pending

Crystal frameworks, symmetry and affinely periodic flexes

Stephen Power

arxiv:1103.1914 v4 · 2011-03-09 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XF7FF7KPARQDPVWOMVR2BFH27I}

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	2026-05-18T02:47:51.361015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b97e52fd4f046037d6ce6563a094fafa13a2e74bc7ded34bbd3c2dfd779f400a

Aliases

arxiv: 1103.1914 · arxiv_version: 1103.1914v4 · doi: 10.48550/arxiv.1103.1914 · pith_short_12: XF7FF7KPARQD · pith_short_16: XF7FF7KPARQDPVWO · pith_short_8: XF7FF7KP

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/XF7FF7KPARQDPVWOMVR2BFH27I \
  | 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: b97e52fd4f046037d6ce6563a094fafa13a2e74bc7ded34bbd3c2dfd779f400a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df41ddae73a707827243fa74a0999da965850b40366d71aeefdd75587354296d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-09T22:51:55Z",
    "title_canon_sha256": "648f0b0f32a4cdea0d3effd747a36f17eb6034c10e0f3695f3b8ff50dd80825a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1914",
    "kind": "arxiv",
    "version": 4
  }
}