Pith Number

pith:QZESOGQQ

pith:2026:QZESOGQQDC42AAETBG5O5B2NWS

not attested not anchored not stored refs pending

A Gauss-Bonnet-Type Dichotomy for Unimodular Random Infinite Trivalent Hyperbolic Polyhedra

Chuwen Wang, Huabin Ge, Tian Zhou, Yangxiang Lu

arxiv:2608.03575 v1 · 2026-08-04 · math.PR · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QZESOGQQDC42AAETBG5O5B2NWS}

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	2026-08-05T01:36:40.596632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8649271a1018b9a0009309baee874db4ba789305f41190ada6048769248988d5

Aliases

arxiv: 2608.03575 · arxiv_version: 2608.03575v1 · doi: 10.48550/arxiv.2608.03575 · pith_short_12: QZESOGQQDC42 · pith_short_16: QZESOGQQDC42AAET · pith_short_8: QZESOGQQ

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/QZESOGQQDC42AAETBG5O5B2NWS \
  | 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: 8649271a1018b9a0009309baee874db4ba789305f41190ada6048769248988d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46f06c70427407d51d6c56a40479c9cf9e8d4f757a5104c9fb0d61cc1348b6c6",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-04T12:32:41Z",
    "title_canon_sha256": "822ca642ffcd5959e65e7274195157cf29b3bcc3ddc99f85a6b3d18796ae1996"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03575",
    "kind": "arxiv",
    "version": 1
  }
}