Pith Number

pith:7KVISX3O

pith:2026:7KVISX3O2TWLPEJV6LC4EBSBPV

not attested not anchored not stored refs pending

Extremal Type II lattices of rank $72$ are generated by their second shell

Scott Duke Kominers

arxiv:2606.08734 v1 · 2026-06-07 · math.NT · 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{7KVISX3O2TWLPEJV6LC4EBSBPV}

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	2026-06-09T02:07:36.156138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

faaa895f6ed4ecb79135f2c5c206417d62ab76034b1fc23082ce8e19b74af974

Aliases

arxiv: 2606.08734 · arxiv_version: 2606.08734v1 · doi: 10.48550/arxiv.2606.08734 · pith_short_12: 7KVISX3O2TWL · pith_short_16: 7KVISX3O2TWLPEJV · pith_short_8: 7KVISX3O

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/7KVISX3O2TWLPEJV6LC4EBSBPV \
  | 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: faaa895f6ed4ecb79135f2c5c206417d62ab76034b1fc23082ce8e19b74af974

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8691eb596be7fba0e7c0a13de6f785129eb4abcb9ce00e6464b5acd1c9fd8c7",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-07T17:04:29Z",
    "title_canon_sha256": "f3b96224764b40e0e33ce711c2500d5b57fe2ebf70b97e69210e49b6499133db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08734",
    "kind": "arxiv",
    "version": 1
  }
}