Pith Number

pith:ZWVTWSLM

pith:2006:ZWVTWSLM36RZCEKKMSYZ26RJ3F

not attested not anchored not stored refs pending

The D_4 root system is not universally optimal

Abhinav Kumar, Henry Cohn, John H. Conway, Noam D. Elkies

arxiv:math/0607447 v3 · 2006-07-19 · 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{ZWVTWSLM36RZCEKKMSYZ26RJ3F}

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	2026-05-18T04:00:02.954972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdab3b496cdfa391114a64b19d7a29d9615a44d5c73fcfb68fa0a6966a40e516

Aliases

arxiv: math/0607447 · arxiv_version: math/0607447v3 · doi: 10.48550/arxiv.math/0607447 · pith_short_12: ZWVTWSLM36RZ · pith_short_16: ZWVTWSLM36RZCEKK · pith_short_8: ZWVTWSLM

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/ZWVTWSLM36RZCEKKMSYZ26RJ3F \
  | 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: cdab3b496cdfa391114a64b19d7a29d9615a44d5c73fcfb68fa0a6966a40e516

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "395e9cbd7d38d1e2c2a8042ea38bc02bc334bfc5aa515fd9f5df8d7799a1b9c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2006-07-19T02:35:49Z",
    "title_canon_sha256": "1ffc87c7ca4c4c73cd57d6cf58147df88ed5a78e6e43e8f66898d78371dfeef0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607447",
    "kind": "arxiv",
    "version": 3
  }
}