Pith Number

pith:YMUDQNB7

pith:2011:YMUDQNB7Q4JDI5MBEAR67X7MWT

not attested not anchored not stored refs pending

Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents

Aaron Naber, Jeff Cheeger

arxiv:1107.3097 v2 · 2011-07-15 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YMUDQNB7Q4JDI5MBEAR67X7MWT}

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	2026-05-18T03:41:58.962879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c32838343f87123475812023efdfecb4dd68caaa554d222c59dce12e31695fe1

Aliases

arxiv: 1107.3097 · arxiv_version: 1107.3097v2 · doi: 10.48550/arxiv.1107.3097 · pith_short_12: YMUDQNB7Q4JD · pith_short_16: YMUDQNB7Q4JDI5MB · pith_short_8: YMUDQNB7

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/YMUDQNB7Q4JDI5MBEAR67X7MWT \
  | 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: c32838343f87123475812023efdfecb4dd68caaa554d222c59dce12e31695fe1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d90f0453d3aea62c3de5b4b1977972cdf83dea9c108a7c41be25491abf2a072",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-07-15T16:05:26Z",
    "title_canon_sha256": "8ea1c4fc4aec3d6f507cc26c4b28fc83837310669258b2d7be74c4fc8d1646f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3097",
    "kind": "arxiv",
    "version": 2
  }
}