Pith Number

pith:2HTDNEJ7

pith:2008:2HTDNEJ7C5B6VH4WF6LOZEITNT

not attested not anchored not stored refs pending

Positivity of relative canonical bundles for families of canonically polarized manifolds

Georg Schumacher

arxiv:0808.3259 v4 · 2008-08-25 · math.CV · 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{2HTDNEJ7C5B6VH4WF6LOZEITNT}

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	2026-05-18T04:39:08.304115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1e636913f1743ea9f962f96ec91136cc57eaf0c6d6b06615f7af000397947ac

Aliases

arxiv: 0808.3259 · arxiv_version: 0808.3259v4 · doi: 10.48550/arxiv.0808.3259 · pith_short_12: 2HTDNEJ7C5B6 · pith_short_16: 2HTDNEJ7C5B6VH4W · pith_short_8: 2HTDNEJ7

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/2HTDNEJ7C5B6VH4WF6LOZEITNT \
  | 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: d1e636913f1743ea9f962f96ec91136cc57eaf0c6d6b06615f7af000397947ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "850ce6694667c7cd3316429882ddacfe15474ceb7f2774818c32b0e4ba8ee29d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2008-08-25T18:18:42Z",
    "title_canon_sha256": "dc30e0644a873ef040a4ef52cb0bfb140856a1f3a211a218fe42c645667174fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.3259",
    "kind": "arxiv",
    "version": 4
  }
}