Pith Number

pith:4HRRHWNW

pith:2026:4HRRHWNWKIU3NV5KSKECITCBZL

not attested not anchored not stored refs pending

Periodic quasiflats in hierarchically hyperbolic spaces

Mark Hagen, P\'en\'elope Azuelos

arxiv:2608.01513 v1 · 2026-08-02 · math.GR · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4HRRHWNWKIU3NV5KSKECITCBZL}

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	2026-08-04T02:05:47.425874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1e313d9b65229b6d7aa9288244c41cae94c4f0fd68e377da991bcbb61022042

Aliases

arxiv: 2608.01513 · arxiv_version: 2608.01513v1 · doi: 10.48550/arxiv.2608.01513 · pith_short_12: 4HRRHWNWKIU3 · pith_short_16: 4HRRHWNWKIU3NV5K · pith_short_8: 4HRRHWNW

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/4HRRHWNWKIU3NV5KSKECITCBZL \
  | 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: e1e313d9b65229b6d7aa9288244c41cae94c4f0fd68e377da991bcbb61022042

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a122f09167e517b3043b760677ee7a4f81f5cf55a27a007333853a15de8d9727",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-08-02T21:50:50Z",
    "title_canon_sha256": "a33444875e4f78246b831e93d620513f1e8cec973333d1a80c60f314625bca3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.01513",
    "kind": "arxiv",
    "version": 1
  }
}