Pith Number

pith:2ETWLUT7

pith:2010:2ETWLUT7LYQA7VUOVJCSQZI52G

not attested not anchored not stored refs pending

Optimal transport and dynamics of expanding circle maps acting on measures

Benoit Kloeckner (LAMA, If)

arxiv:1006.4491 v4 · 2010-06-23 · math.DS · math.DG · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2ETWLUT7LYQA7VUOVJCSQZI52G}

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	2026-05-18T02:03:56.066260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d12765d27f5e200fd68eaa4528651dd191858fa579428f2aa924ff36ece1d5a4

Aliases

arxiv: 1006.4491 · arxiv_version: 1006.4491v4 · doi: 10.48550/arxiv.1006.4491 · pith_short_12: 2ETWLUT7LYQA · pith_short_16: 2ETWLUT7LYQA7VUO · pith_short_8: 2ETWLUT7

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/2ETWLUT7LYQA7VUOVJCSQZI52G \
  | 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: d12765d27f5e200fd68eaa4528651dd191858fa579428f2aa924ff36ece1d5a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74765d3ded470953a9b10ad0c2d3266119a245ce06b861b09835a75d80d9da94",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-06-23T11:59:41Z",
    "title_canon_sha256": "c409cc352580b3923966b9164f569b9adaa6232a869b8d8623e4520ff98c0d70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4491",
    "kind": "arxiv",
    "version": 4
  }
}