Pith Number

pith:3EEBTPKU

pith:2013:3EEBTPKUGNSHLQ6AWKDBQ2WPSC

not attested not anchored not stored refs pending

Regularity of optimal maps on the sphere: the quadratic cost and the reflector antenna

Gregoire Loeper

arxiv:1301.6229 v1 · 2013-01-26 · 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{3EEBTPKUGNSHLQ6AWKDBQ2WPSC}

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	2026-05-18T03:35:24.657507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d90819bd54336475c3c0b286186acf90b34344b75fa3bd74cb3b0bc4829bac06

Aliases

arxiv: 1301.6229 · arxiv_version: 1301.6229v1 · doi: 10.48550/arxiv.1301.6229 · pith_short_12: 3EEBTPKUGNSH · pith_short_16: 3EEBTPKUGNSHLQ6A · pith_short_8: 3EEBTPKU

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/3EEBTPKUGNSHLQ6AWKDBQ2WPSC \
  | 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: d90819bd54336475c3c0b286186acf90b34344b75fa3bd74cb3b0bc4829bac06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a32becb24f9460f2646abfb20a8acc5e464862d1b0424364f96d927ade030f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-26T10:15:58Z",
    "title_canon_sha256": "c9c8e2828ba015442b7992bba56b95c0f1a5af8f4325b42e556b44219ee737b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.6229",
    "kind": "arxiv",
    "version": 1
  }
}