Pith Number

pith:5ZSYWG46

pith:2026:5ZSYWG46PGHEXEOC4ATKQ5UTVU

not attested not anchored not stored refs pending

Sharp thresholds for the Escobar functional: the Escobar-Willmore mass, geometric selection, and compactness trichotomy

Mayukh Mukherjee, Utsab Sarkar

arxiv:2601.22665 v2 · 2026-01-30 · math.DG · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ZSYWG46PGHEXEOC4ATKQ5UTVU}

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	2026-05-20T00:03:03.894753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee658b1b9e798e4b91c2e026a87693ad106ef22963c6b887bccbdfbe09feda9e

Aliases

arxiv: 2601.22665 · arxiv_version: 2601.22665v2 · doi: 10.48550/arxiv.2601.22665 · pith_short_12: 5ZSYWG46PGHE · pith_short_16: 5ZSYWG46PGHEXEOC · pith_short_8: 5ZSYWG46

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/5ZSYWG46PGHEXEOC4ATKQ5UTVU \
  | 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: ee658b1b9e798e4b91c2e026a87693ad106ef22963c6b887bccbdfbe09feda9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "665421a94edc0a747bd3db3982771b6f49de8f3ca130949ee961135497d6926b",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-01-30T07:34:16Z",
    "title_canon_sha256": "5029307e6b639a30c9bc71bf59311ae3ed2fbd697d32e89f48c8e5eced8ab488"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.22665",
    "kind": "arxiv",
    "version": 2
  }
}