Pith Number

pith:OAF5O6QU

pith:2009:OAF5O6QU4L3YL6VHMBW5AIHRFJ

not attested not anchored not stored refs pending

On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces

Ulf Kuehn

arxiv:0906.2056 v2 · 2009-06-11 · math.NT · 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{OAF5O6QU4L3YL6VHMBW5AIHRFJ}

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	2026-05-18T03:15:58.039655Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

700bd77a14e2f785faa7606dd020f12a6f2517093ccefb31d74e88e9587d36c3

Aliases

arxiv: 0906.2056 · arxiv_version: 0906.2056v2 · doi: 10.48550/arxiv.0906.2056 · pith_short_12: OAF5O6QU4L3Y · pith_short_16: OAF5O6QU4L3YL6VH · pith_short_8: OAF5O6QU

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/OAF5O6QU4L3YL6VHMBW5AIHRFJ \
  | 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: 700bd77a14e2f785faa7606dd020f12a6f2517093ccefb31d74e88e9587d36c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e42e10301ce1fd7fe27c91059a0e7d1ad2b24bfab003eb72058859cf6536126",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-06-11T09:18:05Z",
    "title_canon_sha256": "d5da5daac65ee28189b3297b007d9df09b65fea9aa669f7a3b2440661966ca01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.2056",
    "kind": "arxiv",
    "version": 2
  }
}