Pith Number

pith:C5QDZPTC

pith:2017:C5QDZPTCMRW2N7Y6ZV26JDN6YR

not attested not anchored not stored refs pending

Growth gap in hyperbolic groups and amenability

Andrea Sambusetti, Fran\c{c}oise Dal'Bo (IRMAR), R\'emi Coulon (IRMAR)

arxiv:1709.07287 v2 · 2017-09-21 · math.GR · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C5QDZPTCMRW2N7Y6ZV26JDN6YR}

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	2026-05-18T00:07:23.776463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17603cbe62646da6ff1ecd75e48dbec47a44ae4660e74cca2c0a68cf93f278cb

Aliases

arxiv: 1709.07287 · arxiv_version: 1709.07287v2 · doi: 10.48550/arxiv.1709.07287 · pith_short_12: C5QDZPTCMRW2 · pith_short_16: C5QDZPTCMRW2N7Y6 · pith_short_8: C5QDZPTC

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/C5QDZPTCMRW2N7Y6ZV26JDN6YR \
  | 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: 17603cbe62646da6ff1ecd75e48dbec47a44ae4660e74cca2c0a68cf93f278cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bf1840e7d6556b1adc90911b1dc8eaa1fc5016dc2d1b630be7240324d3de156",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-09-21T12:49:03Z",
    "title_canon_sha256": "53f2500825edbbce9f2d22a8fc9064bda047ca250402eabefad2fde0d429dee9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.07287",
    "kind": "arxiv",
    "version": 2
  }
}