Pith Number

pith:V7XLVMJM

pith:2016:V7XLVMJM6CFOXZ53Y2YAEFOTAX

not attested not anchored not stored refs pending

Partial $W^{2,p}$ regularity for optimal transport maps

Alessio Figalli, Shibing Chen

arxiv:1606.05173 v1 · 2016-06-16 · 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{V7XLVMJM6CFOXZ53Y2YAEFOTAX}

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	2026-05-18T01:12:21.891657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afeebab12cf08aebe7bbc6b00215d305c0d34e5ce29ddd9cbff7991300bba0da

Aliases

arxiv: 1606.05173 · arxiv_version: 1606.05173v1 · doi: 10.48550/arxiv.1606.05173 · pith_short_12: V7XLVMJM6CFO · pith_short_16: V7XLVMJM6CFOXZ53 · pith_short_8: V7XLVMJM

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/V7XLVMJM6CFOXZ53Y2YAEFOTAX \
  | 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: afeebab12cf08aebe7bbc6b00215d305c0d34e5ce29ddd9cbff7991300bba0da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d045c2bfe9dccfc40d788b5145dd1031e375266ace79b658c64def0ebffdcff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-06-16T13:07:26Z",
    "title_canon_sha256": "6454805b72be85cb8d071dcc55b29cc838452eabb71f95d0c640750bb2b3f889"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.05173",
    "kind": "arxiv",
    "version": 1
  }
}