Pith Number

pith:PTIFDENH

pith:2010:PTIFDENH46WIQBKRYYSMOGRJNF

not attested not anchored not stored refs pending

The Canonical Map and Horikawa Surfaces in Positive Characteristic

Christian Liedtke

arxiv:1004.1684 v2 · 2010-04-10 · 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{PTIFDENH46WIQBKRYYSMOGRJNF}

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	2026-05-18T03:36:48.404394Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cd05191a7e7ac880551c624c71a29695b878c7a0e9a4a33ceaf2259859b1787

Aliases

arxiv: 1004.1684 · arxiv_version: 1004.1684v2 · doi: 10.48550/arxiv.1004.1684 · pith_short_12: PTIFDENH46WI · pith_short_16: PTIFDENH46WIQBKR · pith_short_8: PTIFDENH

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/PTIFDENH46WIQBKRYYSMOGRJNF \
  | 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: 7cd05191a7e7ac880551c624c71a29695b878c7a0e9a4a33ceaf2259859b1787

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2263416af125e176d7bf2a4719d85dcaf02f67fbc5918d5f060f24cbc18e4b08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-04-10T04:54:45Z",
    "title_canon_sha256": "b70462e0fcaabcf6c9ec0fafce019bd8e7c1db2d147db260955669ad288cde99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1684",
    "kind": "arxiv",
    "version": 2
  }
}