Pith Number

pith:GILYZT5R

pith:2018:GILYZT5REV2RL3S3M45HK3WMOB

not attested not anchored not stored refs pending

Kesten's theorem for uniformly recurrent subgroups

Mikolaj Fraczyk

arxiv:1801.09132 v1 · 2018-01-27 · 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{GILYZT5REV2RL3S3M45HK3WMOB}

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	2026-05-18T00:24:58.505959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32178ccfb1257515ee5b673a756ecc70502c74b047d82af52be327324c78359b

Aliases

arxiv: 1801.09132 · arxiv_version: 1801.09132v1 · doi: 10.48550/arxiv.1801.09132 · pith_short_12: GILYZT5REV2R · pith_short_16: GILYZT5REV2RL3S3 · pith_short_8: GILYZT5R

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/GILYZT5REV2RL3S3M45HK3WMOB \
  | 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: 32178ccfb1257515ee5b673a756ecc70502c74b047d82af52be327324c78359b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5ada27158365f5e7ae27c768958e2cfe404dc394a4941a762d50c76124f9778",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-01-27T20:08:05Z",
    "title_canon_sha256": "7bef7b0d1aabf7c88de7666724101f0e8651c3619244132598419acbe06b19ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.09132",
    "kind": "arxiv",
    "version": 1
  }
}