Pith Number

pith:6RFWDDJJ

pith:2015:6RFWDDJJKR6KF4TTLAVKG6ODS6

not attested not anchored not stored refs pending

Asymptotic density of test elements in free groups and surface groups

Ilir Snopce, Slobodan Tanushevski

arxiv:1509.02435 v1 · 2015-09-08 · 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{6RFWDDJJKR6KF4TTLAVKG6ODS6}

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	2026-05-18T01:33:40.903920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f44b618d29547ca2f273582aa379c397aff32b5b840706765d9a6b12a4b19698

Aliases

arxiv: 1509.02435 · arxiv_version: 1509.02435v1 · doi: 10.48550/arxiv.1509.02435 · pith_short_12: 6RFWDDJJKR6K · pith_short_16: 6RFWDDJJKR6KF4TT · pith_short_8: 6RFWDDJJ

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/6RFWDDJJKR6KF4TTLAVKG6ODS6 \
  | 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: f44b618d29547ca2f273582aa379c397aff32b5b840706765d9a6b12a4b19698

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83afddab03f6b2bb86219193b83699d878327244fe095d139515f871c9236764",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-08T16:29:24Z",
    "title_canon_sha256": "51ce47f9d41a227144179e1841b89c5d2f6ba04a39cb9b3a70940533017a56af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02435",
    "kind": "arxiv",
    "version": 1
  }
}