Pith Number

pith:UMFM6B6Q

pith:2017:UMFM6B6QCJ4AYF3MZWRTPQBRTF

not attested not anchored not stored refs pending

Livsic theorem for diffeomorphism cocycles

Alejandro Kocsard, Artur Avila, Xiao-Chuan Liu

arxiv:1711.02135 v2 · 2017-11-06 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UMFM6B6QCJ4AYF3MZWRTPQBRTF}

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	2026-05-18T00:16:44.697436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a30acf07d012780c176ccda337c031997be0fad6d627270f7625ce216269a5d6

Aliases

arxiv: 1711.02135 · arxiv_version: 1711.02135v2 · doi: 10.48550/arxiv.1711.02135 · pith_short_12: UMFM6B6QCJ4A · pith_short_16: UMFM6B6QCJ4AYF3M · pith_short_8: UMFM6B6Q

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/UMFM6B6QCJ4AYF3MZWRTPQBRTF \
  | 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: a30acf07d012780c176ccda337c031997be0fad6d627270f7625ce216269a5d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88d6fd6d98b1eb0018013790332319f88f61af2ca529fb22710bf8a776652935",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-11-06T19:41:51Z",
    "title_canon_sha256": "2193f59ead88e693006f27ca71f88974dc10c53560c204284f4ecbb9e5822db9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.02135",
    "kind": "arxiv",
    "version": 2
  }
}