Pith Number

pith:KB4PAWK4

pith:2025:KB4PAWK4UUHXHZO243QQ4V45UF

not attested not anchored not stored refs pending

Generation of Grothendieck topologies, provability and operations on subtoposes

Laurent Lafforgue, Olivia Caramello

arxiv:2508.21134 v1 · 2025-08-28 · 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{KB4PAWK4UUHXHZO243QQ4V45UF}

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.

Cited by

2 papers in Pith

The Topological Dual of a Dataset: A Logic-to-Topology Encoding for AlphaGeometry-Style Data

Receipt and verification

First computed	2026-07-05T12:01:28.475414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5078f0595ca50f73e5dae6e10e579da14c409f5308eddc617d5c6760a9d00e46

Aliases

arxiv: 2508.21134 · arxiv_version: 2508.21134v1 · doi: 10.48550/arxiv.2508.21134 · pith_short_12: KB4PAWK4UUHX · pith_short_16: KB4PAWK4UUHXHZO2 · pith_short_8: KB4PAWK4

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/KB4PAWK4UUHXHZO243QQ4V45UF \
  | 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: 5078f0595ca50f73e5dae6e10e579da14c409f5308eddc617d5c6760a9d00e46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3ae2c1a33008bc8d20bbf78894f99f88f75d5b9ac6467db95e8a0eb10d8d8dc",
    "cross_cats_sorted": [
      "math.AG",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-08-28T18:08:48Z",
    "title_canon_sha256": "0654048d927b661d8208b651e42ecd752be8c37c98a8faa95124475beff442a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.21134",
    "kind": "arxiv",
    "version": 1
  }
}