Pith Number

pith:KXZSR4R7

pith:2015:KXZSR4R7JJSOGMHGV26BJ3USAX

not attested not anchored not stored refs pending

Upper Bounds for Non-Congruent Sphere Packings

Samuel Reid

arxiv:1510.00407 v1 · 2015-09-28 · 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{KXZSR4R7JJSOGMHGV26BJ3USAX}

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	2026-05-18T01:31:13.165206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55f328f23f4a64e330e6aebc14ee9205e95a6aebe0a7df9fd52b1da99dd145a7

Aliases

arxiv: 1510.00407 · arxiv_version: 1510.00407v1 · doi: 10.48550/arxiv.1510.00407 · pith_short_12: KXZSR4R7JJSO · pith_short_16: KXZSR4R7JJSOGMHG · pith_short_8: KXZSR4R7

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/KXZSR4R7JJSOGMHGV26BJ3USAX \
  | 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: 55f328f23f4a64e330e6aebc14ee9205e95a6aebe0a7df9fd52b1da99dd145a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "691a6cd39466397c8c3f7a50be1e965c23ab7f7b64e367b348b518ed8d686b16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-09-28T19:14:10Z",
    "title_canon_sha256": "0fe49148eaa483fc53f0a036e13993128d250c53fb58faeaa6aed98dba56597b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00407",
    "kind": "arxiv",
    "version": 1
  }
}