Pith Number

pith:ZL36GKY6

pith:2016:ZL36GKY6NQGW67NSJD4UNYEZZU

not attested not anchored not stored refs pending

Arithmetic mirror symmetry for genus 1 curves with $n$ marked points

Alexander Polishchuk, Yanki Lekili

arxiv:1601.06141 v4 · 2016-01-22 · math.SG · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZL36GKY6NQGW67NSJD4UNYEZZU}

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	2026-05-18T01:02:21.056448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caf7e32b1e6c0d6f7db248f946e099cd1fc78313bb073cd677d58d75bcb3ce87

Aliases

arxiv: 1601.06141 · arxiv_version: 1601.06141v4 · doi: 10.48550/arxiv.1601.06141 · pith_short_12: ZL36GKY6NQGW · pith_short_16: ZL36GKY6NQGW67NS · pith_short_8: ZL36GKY6

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/ZL36GKY6NQGW67NSJD4UNYEZZU \
  | 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: caf7e32b1e6c0d6f7db248f946e099cd1fc78313bb073cd677d58d75bcb3ce87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee3ac4c5c9e72725e192444187259993be1a6ece74d1411c5bc37d030a1f8dd4",
    "cross_cats_sorted": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2016-01-22T20:30:58Z",
    "title_canon_sha256": "f57843a3cf46baf26ea9a64d06c9f6628b966f23fa6e3b1c2e38a75ec18cd4ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06141",
    "kind": "arxiv",
    "version": 4
  }
}