Pith Number

pith:VRN67V2W

pith:2026:VRN67V2WSWMCZ4WM4P26NVXBZO

not attested not anchored not stored refs pending

Two-Generator Discrete Subgroups of Tree Automorphisms

Yukun Du

arxiv:2606.06824 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{VRN67V2WSWMCZ4WM4P26NVXBZO}

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	2026-06-08T01:04:30.264725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac5befd75695982cf2cce3f5e6d6e1cb9f7192637a3f970b3bae03bc997bab6e

Aliases

arxiv: 2606.06824 · arxiv_version: 2606.06824v1 · doi: 10.48550/arxiv.2606.06824 · pith_short_12: VRN67V2WSWMC · pith_short_16: VRN67V2WSWMCZ4WM · pith_short_8: VRN67V2W

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/VRN67V2WSWMCZ4WM4P26NVXBZO \
  | 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: ac5befd75695982cf2cce3f5e6d6e1cb9f7192637a3f970b3bae03bc997bab6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f682a2764e2ebc683663adf82a435d27fcde1c4e5840238d54d6cad372887144",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-06-05T01:57:26Z",
    "title_canon_sha256": "b9daf41016cad10aa64ededf18a6d480e3fdb0117f011d1cff3ffae314da63c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06824",
    "kind": "arxiv",
    "version": 1
  }
}