Pith Number

pith:GQ72J77M

pith:2011:GQ72J77MFPTTMPCZZOJFD45G55

not attested not anchored not stored refs pending

The Poisson boundary of a locally discrete group of diffeomorphisms of the circle

Bertrand Deroin

arxiv:1103.0998 v2 · 2011-03-05 · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GQ72J77MFPTTMPCZZOJFD45G55}

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	2026-05-18T04:05:38.843496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

343fa4ffec2be7363c59cb9251f3a6ef6555dbac92b9135a64ce09c367536d1b

Aliases

arxiv: 1103.0998 · arxiv_version: 1103.0998v2 · doi: 10.48550/arxiv.1103.0998 · pith_short_12: GQ72J77MFPTT · pith_short_16: GQ72J77MFPTTMPCZ · pith_short_8: GQ72J77M

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/GQ72J77MFPTTMPCZZOJFD45G55 \
  | 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: 343fa4ffec2be7363c59cb9251f3a6ef6555dbac92b9135a64ce09c367536d1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78de506b3046a11ebd7a6a510c65477fae4f36557e0700f0af40f7443409f861",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-05T02:13:21Z",
    "title_canon_sha256": "24e206e4a81eb0655ff27e0848d75c138ad494076657bbb0cc378816f19adb01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0998",
    "kind": "arxiv",
    "version": 2
  }
}