Pith Number

pith:CGAUYY7K

pith:2021:CGAUYY7KU6ZNBKNRI66NPEDTRG

not attested not anchored not stored refs pending

Modularity and effective Mordell I

Levent Alp\"oge

arxiv:2109.07917 v2 · 2021-09-16 · 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{CGAUYY7KU6ZNBKNRI66NPEDTRG}

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.

Cited by

1 paper in Pith

Examples of effectivity for integral points on certain curves of genus 2

Receipt and verification

First computed	2026-07-05T03:34:46.643886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11814c63eaa7b2d0a9b147bcd7907389824af3e4da62f1df5c354627a62a0107

Aliases

arxiv: 2109.07917 · arxiv_version: 2109.07917v2 · doi: 10.48550/arxiv.2109.07917 · pith_short_12: CGAUYY7KU6ZN · pith_short_16: CGAUYY7KU6ZNBKNR · pith_short_8: CGAUYY7K

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/CGAUYY7KU6ZNBKNRI66NPEDTRG \
  | 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: 11814c63eaa7b2d0a9b147bcd7907389824af3e4da62f1df5c354627a62a0107

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "610564c5623653ab054f16bacba3fee38e90723d436dfba1bac1026924e4bf45",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-09-16T12:05:42Z",
    "title_canon_sha256": "d1651f2805efc97415717679f5cd38da427971b954af2d8af6aa43f5d7fdc914"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.07917",
    "kind": "arxiv",
    "version": 2
  }
}