Pith Number

pith:4ZYCZOUU

pith:2011:4ZYCZOUU5EKL2KMS5LLEAKSM3V

not attested not anchored not stored refs pending

Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere

Jun Kitagawa, Micah Warren

arxiv:1101.5146 v3 · 2011-01-26 · math.AP · 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{4ZYCZOUU5EKL2KMS5LLEAKSM3V}

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	2026-05-18T04:03:07.133369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6702cba94e914bd2992ead6402a4cdd7fbfa16c1624102bf3c4e30e1060d46b

Aliases

arxiv: 1101.5146 · arxiv_version: 1101.5146v3 · doi: 10.48550/arxiv.1101.5146 · pith_short_12: 4ZYCZOUU5EKL · pith_short_16: 4ZYCZOUU5EKL2KMS · pith_short_8: 4ZYCZOUU

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/4ZYCZOUU5EKL2KMS5LLEAKSM3V \
  | 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: e6702cba94e914bd2992ead6402a4cdd7fbfa16c1624102bf3c4e30e1060d46b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46f848cb958c2b90464cd0f8802f8adf5980b98157c1bb6cd14801bad837cff9",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-01-26T20:26:27Z",
    "title_canon_sha256": "edcfac1c157f3ad43ab6c1993f3caf6f7658edff25dcab9653e1353e3f68de54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5146",
    "kind": "arxiv",
    "version": 3
  }
}