Pith Number

pith:32FLJAAB

pith:2022:32FLJAABUC5UINSRIL2HMKOWKJ

not attested not anchored not stored refs pending

Dual Linear Programming Bounds for Sphere Packing via Discrete Reductions

Rupert Li

arxiv:2206.09876 v3 · 2022-06-20 · math.MG · cs.IT · math.CO · 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{32FLJAABUC5UINSRIL2HMKOWKJ}

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	2026-07-05T11:43:26.653677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de8ab48001a0bb44365142f47629d6524b7fd41a74bb9f33e50cc2a121c453fe

Aliases

arxiv: 2206.09876 · arxiv_version: 2206.09876v3 · doi: 10.48550/arxiv.2206.09876 · pith_short_12: 32FLJAABUC5U · pith_short_16: 32FLJAABUC5UINSR · pith_short_8: 32FLJAAB

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/32FLJAABUC5UINSRIL2HMKOWKJ \
  | 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: de8ab48001a0bb44365142f47629d6524b7fd41a74bb9f33e50cc2a121c453fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a15a8fb318299036597c96195739032ed7e5c479714c84b779e09177294c21f",
    "cross_cats_sorted": [
      "cs.IT",
      "math.CO",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2022-06-20T16:27:33Z",
    "title_canon_sha256": "ba4f3c5a23d566fa3e9f55195ca59a3ac8d4af253ae54e28c54026199c5a7396"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2206.09876",
    "kind": "arxiv",
    "version": 3
  }
}