Pith Number

pith:DP6LHYDG

pith:2012:DP6LHYDGAQJLEQTUTJPR4K5VON

not attested not anchored not stored refs pending

On the degeneracy of optimal transportation

Jun Kitagawa, Young-Heon Kim

arxiv:1211.6227 v1 · 2012-11-27 · 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{DP6LHYDGAQJLEQTUTJPR4K5VON}

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	2026-05-18T03:39:52.224376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bfcb3e0660412b242749a5f1e2bb5736ef15717fdf68015aa4103bf84dee1e1

Aliases

arxiv: 1211.6227 · arxiv_version: 1211.6227v1 · doi: 10.48550/arxiv.1211.6227 · pith_short_12: DP6LHYDGAQJL · pith_short_16: DP6LHYDGAQJLEQTU · pith_short_8: DP6LHYDG

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/DP6LHYDGAQJLEQTUTJPR4K5VON \
  | 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: 1bfcb3e0660412b242749a5f1e2bb5736ef15717fdf68015aa4103bf84dee1e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e26ad521a71cf0b5dccd781432c0a16d1700200f5257332d650c2251b7e5fdb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-11-27T07:59:57Z",
    "title_canon_sha256": "769da29a9300727d15cb8d98a18a8526ee0f9a3e9adc271b61a7fb492d2c27f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6227",
    "kind": "arxiv",
    "version": 1
  }
}