Pith Number

pith:2U73K6GQ

pith:2016:2U73K6GQZA7LXXWMBKZJJE4YJB

not attested not anchored not stored refs pending

The Space of Planar Soap Bubble Clusters

Frank Morgan

arxiv:1605.07423 v1 · 2016-05-24 · math.MG · 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{2U73K6GQZA7LXXWMBKZJJE4YJB}

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	2026-05-18T01:13:46.118531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d53fb578d0c83ebbdecc0ab2949398485d65de9254f4a83e32f2e91955c28a82

Aliases

arxiv: 1605.07423 · arxiv_version: 1605.07423v1 · doi: 10.48550/arxiv.1605.07423 · pith_short_12: 2U73K6GQZA7L · pith_short_16: 2U73K6GQZA7LXXWM · pith_short_8: 2U73K6GQ

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/2U73K6GQZA7LXXWMBKZJJE4YJB \
  | 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: d53fb578d0c83ebbdecc0ab2949398485d65de9254f4a83e32f2e91955c28a82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e25b1f94f22cce06421e69125f2ee4339ab2397a3a86f620243c05ec40b5e55",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-05-24T12:40:44Z",
    "title_canon_sha256": "daf45f5048f7f21c84684f0e908a9e6277dac28395502b8aa60fbf09cb4087a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.07423",
    "kind": "arxiv",
    "version": 1
  }
}