Pith Number

pith:TX62ZL4J

pith:2012:TX62ZL4J3P5DGID32DPLYUNOPH

not attested not anchored not stored refs pending

Contact graphs of unit sphere packings revisited

Karoly Bezdek, Samuel Reid

arxiv:1210.5756 v1 · 2012-10-21 · 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{TX62ZL4J3P5DGID32DPLYUNOPH}

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	2026-05-18T03:00:14.841297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dfdacaf89dbfa33207bd0debc51ae79dd3248943eb2643775b446eb061f75e5

Aliases

arxiv: 1210.5756 · arxiv_version: 1210.5756v1 · doi: 10.48550/arxiv.1210.5756 · pith_short_12: TX62ZL4J3P5D · pith_short_16: TX62ZL4J3P5DGID3 · pith_short_8: TX62ZL4J

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/TX62ZL4J3P5DGID32DPLYUNOPH \
  | 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: 9dfdacaf89dbfa33207bd0debc51ae79dd3248943eb2643775b446eb061f75e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "103d3e8aae57d494aa0779ffd8b72e45e5553784f850c65d669fbf0ef9a27703",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-10-21T19:42:02Z",
    "title_canon_sha256": "61fc055f11520dc558e5795dd64250e1d77e19ed4beaa9c88e889d3b015b14de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5756",
    "kind": "arxiv",
    "version": 1
  }
}