Pith Number

pith:LW7DA2MU

pith:2009:LW7DA2MUK7GIZXIMGKOMBHLYMN

not attested not anchored not stored refs pending

Continuity and injectivity of optimal maps for non-negatively cross-curved costs

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

arxiv:0911.3952 v1 · 2009-11-20 · 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{LW7DA2MUK7GIZXIMGKOMBHLYMN}

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	2026-05-18T00:25:29.743668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dbe30699457cc8cdd0c329cc09d786376104dae76324bc292e2890742a5a669

Aliases

arxiv: 0911.3952 · arxiv_version: 0911.3952v1 · doi: 10.48550/arxiv.0911.3952 · pith_short_12: LW7DA2MUK7GI · pith_short_16: LW7DA2MUK7GIZXIM · pith_short_8: LW7DA2MU

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/LW7DA2MUK7GIZXIMGKOMBHLYMN \
  | 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: 5dbe30699457cc8cdd0c329cc09d786376104dae76324bc292e2890742a5a669

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99cb5e9e86f88ded61f16b9ad3ebbc8f299f3a8e28d59e5898029732a912ad07",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-11-20T03:09:06Z",
    "title_canon_sha256": "9e51d02d7ce29d8ca1870846571adc3d5bb45ddb8c6ba8f1c0ec82c58ae210cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.3952",
    "kind": "arxiv",
    "version": 1
  }
}