Pith Number

pith:QG44LVHK

pith:2012:QG44LVHKE2UT4GXLT64GSGX2MV

not attested not anchored not stored refs pending

Bounding $j$-invariant of integral points on $X_{\ns}^{+}(p)$

Aur\'elien Bajolet, Min Sha

arxiv:1203.1187 v2 · 2012-03-06 · 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{QG44LVHKE2UT4GXLT64GSGX2MV}

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	2026-05-18T03:48:58.885034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81b9c5d4ea26a93e1aeb9fb8691afa6573508048b75189f9d8293a11fbf10bc0

Aliases

arxiv: 1203.1187 · arxiv_version: 1203.1187v2 · doi: 10.48550/arxiv.1203.1187 · pith_short_12: QG44LVHKE2UT · pith_short_16: QG44LVHKE2UT4GXL · pith_short_8: QG44LVHK

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/QG44LVHKE2UT4GXLT64GSGX2MV \
  | 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: 81b9c5d4ea26a93e1aeb9fb8691afa6573508048b75189f9d8293a11fbf10bc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "750b00410993376ddfbef7ba237171818f17f70c140f2125a158bf7d57f34f68",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-03-06T13:03:07Z",
    "title_canon_sha256": "9e8dcf1dd0022b7dc2909373e687c486ac0cb81444d2150049067416b37caa9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1187",
    "kind": "arxiv",
    "version": 2
  }
}