Pith Number

pith:WVERZEZF

pith:2025:WVERZEZF2WHTQCRUJCXOWGN27A

not attested not anchored not stored refs pending

On fibred products of toposes

L\'eo Bartoli, Olivia Caramello

arxiv:2509.07719 v1 · 2025-09-09 · math.CT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WVERZEZF2WHTQCRUJCXOWGN27A}

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	2026-07-05T12:07:26.932209Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5491c9325d58f380a3448aeeb19baf80a81c17f2e76d2107d836aa19cf720d3

Aliases

arxiv: 2509.07719 · arxiv_version: 2509.07719v1 · doi: 10.48550/arxiv.2509.07719 · pith_short_12: WVERZEZF2WHT · pith_short_16: WVERZEZF2WHTQCRU · pith_short_8: WVERZEZF

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/WVERZEZF2WHTQCRUJCXOWGN27A \
  | 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: b5491c9325d58f380a3448aeeb19baf80a81c17f2e76d2107d836aa19cf720d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86348b0483b5715157d085cbe3e490d20ea00cc24e9e763f29cb0d0e7a1e08cb",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-09-09T13:20:04Z",
    "title_canon_sha256": "e792a9e16fa05aade200c5cdb18a27ee779749b7b6a3d52dcafae290af05be68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.07719",
    "kind": "arxiv",
    "version": 1
  }
}