Pith Number

pith:V2NFKFUO

pith:2011:V2NFKFUO6K63ND6HHOUABNAUWL

not attested not anchored not stored refs pending

H\"older continuity and injectivity of optimal maps

Alessio Figalli, Robert J. McCann, Young-Heon Kim

arxiv:1107.1014 v1 · 2011-07-06 · 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{V2NFKFUO6K63ND6HHOUABNAUWL}

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	2026-05-18T04:18:45.825018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae9a55168ef2bdb68fc73ba800b414b2eb791b8a0c37dc202c67eda9e089a042

Aliases

arxiv: 1107.1014 · arxiv_version: 1107.1014v1 · doi: 10.48550/arxiv.1107.1014 · pith_short_12: V2NFKFUO6K63 · pith_short_16: V2NFKFUO6K63ND6H · pith_short_8: V2NFKFUO

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/V2NFKFUO6K63ND6HHOUABNAUWL \
  | 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: ae9a55168ef2bdb68fc73ba800b414b2eb791b8a0c37dc202c67eda9e089a042

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6ed824936be29d65c9398c8b04743512af06ec089fa3b5e5fec51fc3861ac05",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-06T02:52:14Z",
    "title_canon_sha256": "86d137b0289d6e069b409d41fd42d24e7067d12ac0a7f06db7f9bebdf816f05a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1014",
    "kind": "arxiv",
    "version": 1
  }
}