Pith Number

pith:KRDUI3OT

pith:2009:KRDUI3OTN6RIFJ4GXQYYB3ST6A

not attested not anchored not stored refs pending

Geometric covering arguments and ergodic theorems for free groups

Amos Nevo, Lewis Bowen

arxiv:0912.4953 v2 · 2009-12-25 · 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{KRDUI3OTN6RIFJ4GXQYYB3ST6A}

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	2026-05-18T04:41:34.923123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5447446dd36fa282a786bc3180ee53f03439822ca89de6d26a311778a1d1ad10

Aliases

arxiv: 0912.4953 · arxiv_version: 0912.4953v2 · doi: 10.48550/arxiv.0912.4953 · pith_short_12: KRDUI3OTN6RI · pith_short_16: KRDUI3OTN6RIFJ4G · pith_short_8: KRDUI3OT

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/KRDUI3OTN6RIFJ4GXQYYB3ST6A \
  | 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: 5447446dd36fa282a786bc3180ee53f03439822ca89de6d26a311778a1d1ad10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6928bc8130e83ad4dad675d8d0828ea4d177a2ef569bb27c1976ab0fd106dde2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-12-25T09:04:03Z",
    "title_canon_sha256": "0882c08d5472a724ef3dcff4c6358aedd798c0011258f2bc94d981d167a34e30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4953",
    "kind": "arxiv",
    "version": 2
  }
}