Pith Number

pith:M2HPHRJE

pith:2020:M2HPHRJETFQK47O7PRCSW3EHXG

not attested not anchored not stored refs pending

Minmax Hierarchies, Minimal Fibrations and a PDE based Proof of the Willmore Conjecture

Tristan Rivi\`ere

arxiv:2007.05467 v2 · 2020-07-10 · 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{M2HPHRJETFQK47O7PRCSW3EHXG}

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.

Cited by

1 paper in Pith

Minimizing the Gauss map area of surfaces in $\mathbb{S}^3$

Receipt and verification

First computed	2026-07-05T05:44:45.790062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

668ef3c5249960ae7ddf7c452b6c87b99a66b52f7c852b3886f27a4cddcb16bb

Aliases

arxiv: 2007.05467 · arxiv_version: 2007.05467v2 · doi: 10.48550/arxiv.2007.05467 · pith_short_12: M2HPHRJETFQK · pith_short_16: M2HPHRJETFQK47O7 · pith_short_8: M2HPHRJE

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/M2HPHRJETFQK47O7PRCSW3EHXG \
  | 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: 668ef3c5249960ae7ddf7c452b6c87b99a66b52f7c852b3886f27a4cddcb16bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81bcbc1b1577337607e51b4bb721607a8c8694b3d073de80f359e31d902e3bd9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-07-10T16:25:11Z",
    "title_canon_sha256": "1efd3620b5bf2e6fda574ef0536e13e4627d6fd23f4862a7e142b265f27b87c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.05467",
    "kind": "arxiv",
    "version": 2
  }
}