Pith Number

pith:5V2UVOSZ

pith:2004:5V2UVOSZK7J44P3UUKZYJNPZ44

not attested not anchored not stored refs pending

Notes on Grothendieck topologies, fibered categories and descent theory

Angelo Vistoli

arxiv:math/0412512 v4 · 2004-12-28 · math.AG · 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{5V2UVOSZK7J44P3UUKZYJNPZ44}

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

4 papers in Pith

Geometric realization of affine bases: the Kronecker quiver case

Entanglement of Sections: The pushout of entangled and parameterized quantum information

Baues-Wirsching Cohomology and Svarc Genus in Small Categories

A Global Model Structure for $\mathbb{K}$-Linear $\infty$-Local Systems

Receipt and verification

First computed	2026-07-04T15:01:55.710333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed754aba5957d3ce3f74a2b384b5f9e7331d140700d13d8ce51ecbfe29ea3caf

Aliases

arxiv: math/0412512 · arxiv_version: math/0412512v4 · doi: 10.48550/arxiv.math/0412512 · pith_short_12: 5V2UVOSZK7J4 · pith_short_16: 5V2UVOSZK7J44P3U · pith_short_8: 5V2UVOSZ

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/5V2UVOSZK7J44P3UUKZYJNPZ44 \
  | 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: ed754aba5957d3ce3f74a2b384b5f9e7331d140700d13d8ce51ecbfe29ea3caf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e64dd5f5f5140c2229b4fb511dbc2520e2bb3a2952415005a2b31487bf775f9",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2004-12-28T16:28:00Z",
    "title_canon_sha256": "4ff0a0ee70011f9dc97c3ea06faea6f18a7edf3391ff47dc3e7018414ea4bb7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412512",
    "kind": "arxiv",
    "version": 4
  }
}