Pith Number

pith:HV7GQJPM

pith:2016:HV7GQJPMOPILNTQY32CO6GRRQY

not attested not anchored not stored refs pending

The sphere packing problem in dimension 24

Abhinav Kumar, Danylo Radchenko, Henry Cohn, Maryna Viazovska, Stephen D. Miller

arxiv:1603.06518 v3 · 2016-03-21 · math.NT · 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{HV7GQJPMOPILNTQY32CO6GRRQY}

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	2026-05-18T00:36:41.469489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d7e6825ec73d0b6ce18de84ef1a318611917cb20c88968d41a72887ef6e1161

Aliases

arxiv: 1603.06518 · arxiv_version: 1603.06518v3 · doi: 10.48550/arxiv.1603.06518 · pith_short_12: HV7GQJPMOPIL · pith_short_16: HV7GQJPMOPILNTQY · pith_short_8: HV7GQJPM

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/HV7GQJPMOPILNTQY32CO6GRRQY \
  | 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: 3d7e6825ec73d0b6ce18de84ef1a318611917cb20c88968d41a72887ef6e1161

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f401381903e09c2454cebbc6c285df942645f2ee1b358d12736fe40ab5524a4",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-03-21T17:57:05Z",
    "title_canon_sha256": "33390128ecb964272fa696ff518c67a6e76ecdcdf694b2c0e75ba29dc4d47e21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06518",
    "kind": "arxiv",
    "version": 3
  }
}