Pith Number

pith:CD3I6LPT

pith:2024:CD3I6LPTAYMKLXUJZMDB3JMIXK

not attested not anchored not stored refs pending

New lower bound on ball packing density in high-dimensional hyperbolic spaces

Hong Liu, Irene Gil Fern\'andez, Jaehoon Kim, Oleg Pikhurko

arxiv:2405.07818 v2 · 2024-05-13 · 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{CD3I6LPTAYMKLXUJZMDB3JMIXK}

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

Linear programming bounds in homogeneous spaces, I: Optimal packing density

Receipt and verification

First computed	2026-07-05T09:12:06.232800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10f68f2df30618a5de89cb061da588ba89143cd79550912679113e5a8c7e19bb

Aliases

arxiv: 2405.07818 · arxiv_version: 2405.07818v2 · doi: 10.48550/arxiv.2405.07818 · pith_short_12: CD3I6LPTAYMK · pith_short_16: CD3I6LPTAYMKLXUJ · pith_short_8: CD3I6LPT

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/CD3I6LPTAYMKLXUJZMDB3JMIXK \
  | 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: 10f68f2df30618a5de89cb061da588ba89143cd79550912679113e5a8c7e19bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6503a26030f6eb9e6f8edcc9b6c96a37579c0b10a6644ba496c1f8b31bb1b058",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-05-13T14:59:48Z",
    "title_canon_sha256": "85cd3ecf6217c77cba34e57f35316d0bff271b5d421dd09e379cb832020fdfb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.07818",
    "kind": "arxiv",
    "version": 2
  }
}