Pith Number

pith:4LUOOKKL

pith:2010:4LUOOKKLQ467XC3JOTLCK744JX

not attested not anchored not stored refs pending

Local heights on elliptic curves and intersection multiplicities

Jan Steffen M\"uller, Vincenz Busch

arxiv:1003.2050 v3 · 2010-03-10 · 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{4LUOOKKLQ467XC3JOTLCK744JX}

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	2026-05-18T03:01:11.761463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2e8e7294b873dfb8b6974d6257f9c4dd1bfe1029e92e7fd1706d998f0983302

Aliases

arxiv: 1003.2050 · arxiv_version: 1003.2050v3 · doi: 10.48550/arxiv.1003.2050 · pith_short_12: 4LUOOKKLQ467 · pith_short_16: 4LUOOKKLQ467XC3J · pith_short_8: 4LUOOKKL

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/4LUOOKKLQ467XC3JOTLCK744JX \
  | 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: e2e8e7294b873dfb8b6974d6257f9c4dd1bfe1029e92e7fd1706d998f0983302

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc34cd9ac480fff75d37f0196a8ae3386cd960f99fe40207e08ce339bc7f33f6",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-03-10T08:58:22Z",
    "title_canon_sha256": "14231303f71284194c565b326d97caff63e4aaf9f7355b9cafe71ba44c8e7622"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2050",
    "kind": "arxiv",
    "version": 3
  }
}