Pith Number

pith:VFHXVMJF

pith:2005:VFHXVMJFHJPOZ5TBCFUOBBKVFS

not attested not anchored not stored refs pending

On packing spheres into containers (about Kepler's finite sphere packing problem)

Achill Schuermann

arxiv:math/0506200 v2 · 2005-06-10 · 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{VFHXVMJFHJPOZ5TBCFUOBBKVFS}

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	2026-05-18T04:10:37.469708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a94f7ab1253a5eecf6611168e085552cafdedfb0dbee9a8acb67d24ef632942e

Aliases

arxiv: math/0506200 · arxiv_version: math/0506200v2 · doi: 10.48550/arxiv.math/0506200 · pith_short_12: VFHXVMJFHJPO · pith_short_16: VFHXVMJFHJPOZ5TB · pith_short_8: VFHXVMJF

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/VFHXVMJFHJPOZ5TBCFUOBBKVFS \
  | 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: a94f7ab1253a5eecf6611168e085552cafdedfb0dbee9a8acb67d24ef632942e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c978a1b415e35b2ce77011759e84ade57d9d09815e33e194cb4f5740e1079531",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "2005-06-10T15:25:56Z",
    "title_canon_sha256": "23ca0ebc9832e3462afcfafc3f34a2510afde9377cd98e9b03c13ced7cc919e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0506200",
    "kind": "arxiv",
    "version": 2
  }
}