Pith Number

pith:NIQ6JX5B

pith:2019:NIQ6JX5BQCPP6IJ6M2UL5GEPTH

not attested not anchored not stored refs pending

Proof of Bishop's volume comparison theorem using singular soap bubbles

Feng Gui, Hubert Bray, Yiyue Zhang, Zhenhua Liu

arxiv:1903.12317 v1 · 2019-03-29 · 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{NIQ6JX5BQCPP6IJ6M2UL5GEPTH}

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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.

Cited by

1 paper in Pith

Notes on scalar curvature lower bounds of steady gradient Ricci solitons

Receipt and verification

First computed	2026-05-17T23:49:54.341188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a21e4dfa1809eff213e66a8be988f99e748ccfcd66e0ccc261b8c87c88124e8

Aliases

arxiv: 1903.12317 · arxiv_version: 1903.12317v1 · doi: 10.48550/arxiv.1903.12317 · pith_short_12: NIQ6JX5BQCPP · pith_short_16: NIQ6JX5BQCPP6IJ6 · pith_short_8: NIQ6JX5B

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/NIQ6JX5BQCPP6IJ6M2UL5GEPTH \
  | 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: 6a21e4dfa1809eff213e66a8be988f99e748ccfcd66e0ccc261b8c87c88124e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e343fa83470b9f5a1f87f9cc59e0509498e18d38dadf0820910dfd313d508d89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-03-29T01:48:15Z",
    "title_canon_sha256": "a8861d504754b4f359715942601fe9349af14911854eabfdd4e9721340c5d038"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.12317",
    "kind": "arxiv",
    "version": 1
  }
}