Pith Number

pith:PGWP24EL

pith:2016:PGWP24ELC4IGHTOXZXVMJH74B2

not attested not anchored not stored refs pending

A Breakthrough in Sphere Packing: The Search for Magic Functions

David de Laat, Frank Vallentin

arxiv:1607.02111 v1 · 2016-07-07 · 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{PGWP24ELC4IGHTOXZXVMJH74B2}

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.

Cited by

1 paper in Pith

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24

Receipt and verification

First computed	2026-05-18T01:04:03.881976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79acfd708b171063cdd7cdeac49ffc0e87d41bdad4ce79135eb86e2d423e7047

Aliases

arxiv: 1607.02111 · arxiv_version: 1607.02111v1 · doi: 10.48550/arxiv.1607.02111 · pith_short_12: PGWP24ELC4IG · pith_short_16: PGWP24ELC4IGHTOX · pith_short_8: PGWP24EL

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/PGWP24ELC4IGHTOXZXVMJH74B2 \
  | 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: 79acfd708b171063cdd7cdeac49ffc0e87d41bdad4ce79135eb86e2d423e7047

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79cbc4e9ab058455829eaf3d440b9f0c27fcce9ac01c101ffd49e8ca65b01cdc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-07-07T18:22:43Z",
    "title_canon_sha256": "4ed03e8a408079dcf3e1b9ad0fc5846b08f35d86d8eb506e79796a3c6ca88148"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02111",
    "kind": "arxiv",
    "version": 1
  }
}