Pith Number

pith:HZM5CKEV

pith:2026:HZM5CKEV5LYBA3HPQWQBCXTEXQ

not attested not anchored not stored refs pending

Locales in presheaf toposes vs. presheaves of locales

Joshua Wrigley, Panagis Karazeris, Vasileios Aravantinos-Sotiropoulos

arxiv:2606.21273 v1 · 2026-06-19 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HZM5CKEV5LYBA3HPQWQBCXTEXQ}

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	2026-06-23T01:12:35.569461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e59d12895eaf0106cef85a0115e64bc27e29c2abb253771833e280cc1e10e0e

Aliases

arxiv: 2606.21273 · arxiv_version: 2606.21273v1 · doi: 10.48550/arxiv.2606.21273 · pith_short_12: HZM5CKEV5LYB · pith_short_16: HZM5CKEV5LYBA3HP · pith_short_8: HZM5CKEV

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/HZM5CKEV5LYBA3HPQWQBCXTEXQ \
  | 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: 3e59d12895eaf0106cef85a0115e64bc27e29c2abb253771833e280cc1e10e0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78886caf373197ad39985757331bd6604b621c40f5c7c2f1ddc047cc9f409626",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-06-19T09:49:18Z",
    "title_canon_sha256": "2f805ca615cf69c809d37cf6f1c43e64109e885804e75942e341e8ef05a20fbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21273",
    "kind": "arxiv",
    "version": 1
  }
}