Pith Number

pith:MDA3CB4V

pith:2013:MDA3CB4VL3ZZLTYDACPSX2MX4Q

not attested not anchored not stored refs pending

Symmetry minimizes the principal eigenvalue: an example for the Pucci's sup operator

Fabiana Leoni, Isabeau Birindelli

arxiv:1306.3396 v2 · 2013-06-14 · 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{MDA3CB4VL3ZZLTYDACPSX2MX4Q}

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	2026-05-18T03:19:12.858458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60c1b107955ef395cf03009f2be997e429a21d45000bd590fc0318e87545019a

Aliases

arxiv: 1306.3396 · arxiv_version: 1306.3396v2 · doi: 10.48550/arxiv.1306.3396 · pith_short_12: MDA3CB4VL3ZZ · pith_short_16: MDA3CB4VL3ZZLTYD · pith_short_8: MDA3CB4V

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/MDA3CB4VL3ZZLTYDACPSX2MX4Q \
  | 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: 60c1b107955ef395cf03009f2be997e429a21d45000bd590fc0318e87545019a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ad0d652f422f09cc25edb00c992c334aba8f07b2e519bc598241e820c2ba7fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-14T13:44:57Z",
    "title_canon_sha256": "9dba93569430132936afe6b9954993ca13a8d81fec5505418c6c342d6fe8705a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3396",
    "kind": "arxiv",
    "version": 2
  }
}