Pith Number

pith:XECAUSCV

pith:2026:XECAUSCV4UKGWROMCF3OBZNKVB

not attested not anchored not stored refs pending

Structure of kissing arrangements in ${\mathbb R}^{12}$ and a place for the $841$st sphere

Rustem Takhanov, Stanislav Yun, Zhenisbek Assylbekov

arxiv:2606.18984 v1 · 2026-06-17 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XECAUSCV4UKGWROMCF3OBZNKVB}

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	2026-06-19T16:11:53.783461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9040a4855e5146b45cc1176e0e5aaa866d3da4d75073cc04536eca96429fd37

Aliases

arxiv: 2606.18984 · arxiv_version: 2606.18984v1 · doi: 10.48550/arxiv.2606.18984 · pith_short_12: XECAUSCV4UKG · pith_short_16: XECAUSCV4UKGWROM · pith_short_8: XECAUSCV

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/XECAUSCV4UKGWROMCF3OBZNKVB \
  | 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: b9040a4855e5146b45cc1176e0e5aaa866d3da4d75073cc04536eca96429fd37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adf333f04a70d68f0097639edca673517998e5d95709a6e3db9d8bb58d12cbbb",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-06-17T12:05:28Z",
    "title_canon_sha256": "69e47d40f7db777ea5747582a19e35cb03cc6e38ef14645c134395dc7a2a4f1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18984",
    "kind": "arxiv",
    "version": 1
  }
}