Pith Number

pith:RKU5W752

pith:2026:RKU5W752WLMUZR4NURUSNBFXVV

not attested not anchored not stored refs pending

Quasi-isometric rigidity for random subsets in products of trees

Ranfeng Yu, Tianyi Zheng, Zhiqiang Li

arxiv:2606.05089 v1 · 2026-06-03 · math.MG · math.GR · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RKU5W752WLMUZR4NURUSNBFXVV}

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	2026-06-04T01:10:05.766728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8aa9db7fbab2d94cc78da4692684b7ad5ca642c7f2a69e01a7e98c77be3a6393

Aliases

arxiv: 2606.05089 · arxiv_version: 2606.05089v1 · doi: 10.48550/arxiv.2606.05089 · pith_short_12: RKU5W752WLMU · pith_short_16: RKU5W752WLMUZR4N · pith_short_8: RKU5W752

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/RKU5W752WLMUZR4NURUSNBFXVV \
  | 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: 8aa9db7fbab2d94cc78da4692684b7ad5ca642c7f2a69e01a7e98c77be3a6393

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85ac826b64652004de99176eee748c03bcf4d4fc2dbcf7bf26a1ae1f457950c2",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-06-03T16:54:08Z",
    "title_canon_sha256": "ca4f8346095d3434c8b5e030a14ec3ca80c4fe4cd8a3dceddc2d2cbbad9cef2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05089",
    "kind": "arxiv",
    "version": 1
  }
}