Pith Number

pith:GMHUUCCX

pith:1994:GMHUUCCX3VB7H6P5FSVWIVNOBN

not attested not anchored not stored refs pending

Average kissing numbers for non-congruent sphere packings

Greg Kuperberg, Oded Schramm

arxiv:math/9405218 v1 · 1994-05-13 · 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{GMHUUCCX3VB7H6P5FSVWIVNOBN}

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	2026-05-18T01:05:51.353963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

330f4a0857dd43f3f9fd2cab6455ae0b4fbe968f825918fa2009375175478f3f

Aliases

arxiv: math/9405218 · arxiv_version: math/9405218v1 · doi: 10.48550/arxiv.math/9405218 · pith_short_12: GMHUUCCX3VB7 · pith_short_16: GMHUUCCX3VB7H6P5 · pith_short_8: GMHUUCCX

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/GMHUUCCX3VB7H6P5FSVWIVNOBN \
  | 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: 330f4a0857dd43f3f9fd2cab6455ae0b4fbe968f825918fa2009375175478f3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b4b5f2c38b14511d38baddb543e5964bf5b66155ae811bdac016eff2f9fbe0e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "1994-05-13T00:00:00Z",
    "title_canon_sha256": "315cc90b5701d34fcff35e99680c7732959601b8fc526b627e65bb42e8b622c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9405218",
    "kind": "arxiv",
    "version": 1
  }
}