Pith Number

pith:55E33VIP

pith:2004:55E33VIPFCH4WCUNWFPFLHW5KF

not attested not anchored not stored refs pending

Homotopical Algebraic Geometry II: geometric stacks and applications

Bertrand Toen, Gabriele Vezzosi

arxiv:math/0404373 v7 · 2004-04-21 · math.AG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{55E33VIPFCH4WCUNWFPFLHW5KF}

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

1 paper in Pith

Brave new categorical spectral positive Schubert geometry and the categorical Dual Amplituhedron

Receipt and verification

First computed	2026-07-04T14:49:47.115171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef49bdd50f288fcb0a8db15e559edd515a7a46fafc2eef86869bee7fdfa399fd

Aliases

arxiv: math/0404373 · arxiv_version: math/0404373v7 · doi: 10.48550/arxiv.math/0404373 · pith_short_12: 55E33VIPFCH4 · pith_short_16: 55E33VIPFCH4WCUN · pith_short_8: 55E33VIP

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/55E33VIPFCH4WCUNWFPFLHW5KF \
  | 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: ef49bdd50f288fcb0a8db15e559edd515a7a46fafc2eef86869bee7fdfa399fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef68bb2ce1370f2e98c7d95085174a76535d589c9e76efbdce037f8ebdd7ab46",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2004-04-21T00:18:09Z",
    "title_canon_sha256": "b3c94e5961e2367f203205989d7dec29a5127746f4a24dc39aa2302b74454efc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404373",
    "kind": "arxiv",
    "version": 7
  }
}