Pith Number

pith:24GWKACM

pith:2026:24GWKACMU623N2UET7VCTCF76F

not attested not anchored not stored refs pending

From algebraic orthogonality to RAAG embedding obstructions in hierarchically hyperbolic groups

Jihoon Park, Sangrok Oh

arxiv:2608.09535 v1 · 2026-08-10 · 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{24GWKACMU623N2UET7VCTCF76F}

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	2026-08-11T02:24:26.107611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d70d65004ca7b5b6ea849fea2988bff141573bbe776c806f9b9ade45c0e090d0

Aliases

arxiv: 2608.09535 · arxiv_version: 2608.09535v1 · doi: 10.48550/arxiv.2608.09535 · pith_short_12: 24GWKACMU623 · pith_short_16: 24GWKACMU623N2UE · pith_short_8: 24GWKACM

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/24GWKACMU623N2UET7VCTCF76F \
  | 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: d70d65004ca7b5b6ea849fea2988bff141573bbe776c806f9b9ade45c0e090d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd0756020febec2b8f356b2d3eeacdd91582bb8751c960649cc24cf2b0627dd3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-08-10T12:35:36Z",
    "title_canon_sha256": "103b0c037f4bb11bc104752479f2192062fadf8c9abd4875d7e12c35caf3e66e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09535",
    "kind": "arxiv",
    "version": 1
  }
}