Pith Number

pith:WWMNZ6R7

pith:2016:WWMNZ6R7TDPWP7IFMO22BCYXZG

not attested not anchored not stored refs pending

On the global rigidity of sphere packings on 3-dimensional manifolds

Xu Xu

arxiv:1611.08835 v4 · 2016-11-27 · math.GT · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WWMNZ6R7TDPWP7IFMO22BCYXZG}

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	2026-05-17T23:57:21.873163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b598dcfa3f98df67fd0563b5a08b17c9b8882605f9e181776e404720abb40b17

Aliases

arxiv: 1611.08835 · arxiv_version: 1611.08835v4 · doi: 10.48550/arxiv.1611.08835 · pith_short_12: WWMNZ6R7TDPW · pith_short_16: WWMNZ6R7TDPWP7IF · pith_short_8: WWMNZ6R7

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/WWMNZ6R7TDPWP7IFMO22BCYXZG \
  | 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: b598dcfa3f98df67fd0563b5a08b17c9b8882605f9e181776e404720abb40b17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0d60f1f0024fd1fdee6e8da8db19be22d379510a2451b56dbc381c64be08c04",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-11-27T12:48:12Z",
    "title_canon_sha256": "68f6fd57a8be552628a1c90e01f338188fa1ef57b98dddb5d85d0a128e947ff1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08835",
    "kind": "arxiv",
    "version": 4
  }
}