Pith Number

pith:ERF7QO2O

pith:2017:ERF7QO2OLQD6UJICYXPXHDOEWV

not attested not anchored not stored refs pending

Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance

Rhiannon Dougall

arxiv:1702.06115 v1 · 2017-02-20 · math.DS · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ERF7QO2OLQD6UJICYXPXHDOEWV}

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.

Cited by

1 paper in Pith

Finiteness of Bowen-Margulis-Sullivan Measure for Gromov-Patterson-Sullivan Systems

Receipt and verification

First computed	2026-05-18T00:50:24.291732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

244bf83b4e5c07ea2502c5df738dc4b558079d2f6bb5d6324f2bb73b36e2b665

Aliases

arxiv: 1702.06115 · arxiv_version: 1702.06115v1 · doi: 10.48550/arxiv.1702.06115 · pith_short_12: ERF7QO2OLQD6 · pith_short_16: ERF7QO2OLQD6UJIC · pith_short_8: ERF7QO2O

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/ERF7QO2OLQD6UJICYXPXHDOEWV \
  | 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: 244bf83b4e5c07ea2502c5df738dc4b558079d2f6bb5d6324f2bb73b36e2b665

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b35ddc962f17c17ea46b05a213a65bdaaf451538a41055bf1fce7a80a98541af",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-02-20T18:57:17Z",
    "title_canon_sha256": "dad3993a96e6d3865a27a8ec489aa30563496c7d7c3b9a6414f85d2ce7845f0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.06115",
    "kind": "arxiv",
    "version": 1
  }
}