Pith Number

pith:VDULOQ4M

pith:2025:VDULOQ4MU5SEUZVMCP5IJ5TX4I

not attested not anchored not stored refs pending

Sites and Grothendieck toposes: an introduction

Laurent Lafforgue, Olivia Caramello

arxiv:2508.21609 v1 · 2025-08-29 · math.CT · math.AG · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDULOQ4MU5SEUZVMCP5IJ5TX4I}

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	2026-07-05T12:01:37.558896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8e8b7438ca7644a66ac13fa84f677e22fec6b3b46b9f61834e75fd89024e1d2

Aliases

arxiv: 2508.21609 · arxiv_version: 2508.21609v1 · doi: 10.48550/arxiv.2508.21609 · pith_short_12: VDULOQ4MU5SE · pith_short_16: VDULOQ4MU5SEUZVM · pith_short_8: VDULOQ4M

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/VDULOQ4MU5SEUZVMCP5IJ5TX4I \
  | 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: a8e8b7438ca7644a66ac13fa84f677e22fec6b3b46b9f61834e75fd89024e1d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9371e2f2ca480729c76b662473d9ef2e3f43563b240997f777a5ebc1cfa98ed8",
    "cross_cats_sorted": [
      "math.AG",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-08-29T13:15:48Z",
    "title_canon_sha256": "9561cad62c73e35a4f994016286a2331ae12fb301b13aaeb0e97195fae31c55b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.21609",
    "kind": "arxiv",
    "version": 1
  }
}