Pith Number

pith:FQPSXJ34

pith:2026:FQPSXJ34F5ZTLXDLDCTGMG4HHZ

not attested not anchored not stored refs pending

Spectral properties of the Schreier graphs of the basilica group

Alexander Teplyaev, Kyle Ambrose, Luke G. Rogers, Michael Morris, Noah Dunham

arxiv:2606.07430 v1 · 2026-06-05 · 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{FQPSXJ34F5ZTLXDLDCTGMG4HHZ}

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	2026-06-08T01:05:26.636098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c1f2ba77c2f7335dc6b18a6661b873e73cd56d44fbce06be5b98daf5e7d7b59

Aliases

arxiv: 2606.07430 · arxiv_version: 2606.07430v1 · doi: 10.48550/arxiv.2606.07430 · pith_short_12: FQPSXJ34F5ZT · pith_short_16: FQPSXJ34F5ZTLXDL · pith_short_8: FQPSXJ34

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/FQPSXJ34F5ZTLXDLDCTGMG4HHZ \
  | 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: 2c1f2ba77c2f7335dc6b18a6661b873e73cd56d44fbce06be5b98daf5e7d7b59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00cb9e48108f64076e9893adb3013b57082f1cb5a4ac63e825812bbccdd89597",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-06-05T16:26:01Z",
    "title_canon_sha256": "85bb224355110c810d9243b0a667ba8883f4f5af1368beb305b5bb03aa9d6b08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07430",
    "kind": "arxiv",
    "version": 1
  }
}