Pith Number

pith:BXOU5G6E

pith:2018:BXOU5G6EP2TJPKSX3Q4KE2NIJ2

not attested not anchored not stored refs pending

A Manin-Mumford theorem for the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves

Gareth Jones, Harry Schmidt

arxiv:1801.04236 v2 · 2018-01-12 · 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{BXOU5G6EP2TJPKSX3Q4KE2NIJ2}

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	2026-05-17T23:53:09.739557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ddd4e9bc47ea697aa57dc38a269a84e993dcf25923abed53ac08cd0bbafac0b

Aliases

arxiv: 1801.04236 · arxiv_version: 1801.04236v2 · doi: 10.48550/arxiv.1801.04236 · pith_short_12: BXOU5G6EP2TJ · pith_short_16: BXOU5G6EP2TJPKSX · pith_short_8: BXOU5G6E

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/BXOU5G6EP2TJPKSX3Q4KE2NIJ2 \
  | 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: 0ddd4e9bc47ea697aa57dc38a269a84e993dcf25923abed53ac08cd0bbafac0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "184aa21fad15a937fafbaa94499838eb4787c780c98497686002e423861d2fa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-01-12T17:06:02Z",
    "title_canon_sha256": "d4e7e4946a45e720a7e66c5cf63309a9add79d4df49069a96f9433f8534febd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.04236",
    "kind": "arxiv",
    "version": 2
  }
}