Pith Number

pith:XM67TBSE

pith:2019:XM67TBSECTBK3IH2WCGO3JEYCL

not attested not anchored not stored refs pending

Semistable modularity lifting over imaginary quadratic fields

Frank Calegari

arxiv:1907.08700 v1 · 2019-07-19 · 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{XM67TBSECTBK3IH2WCGO3JEYCL}

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	2026-05-17T23:40:08.052697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb3df9864414c2ada0fab08ceda49812fd851576828b87baa3768561a76e38eb

Aliases

arxiv: 1907.08700 · arxiv_version: 1907.08700v1 · doi: 10.48550/arxiv.1907.08700 · pith_short_12: XM67TBSECTBK · pith_short_16: XM67TBSECTBK3IH2 · pith_short_8: XM67TBSE

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/XM67TBSECTBK3IH2WCGO3JEYCL \
  | 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: bb3df9864414c2ada0fab08ceda49812fd851576828b87baa3768561a76e38eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c39770a7709f1cfee055c60d6edd08ec73510a3c1b83cbedbcd1a3da2a848ab5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-07-19T21:19:27Z",
    "title_canon_sha256": "81c0d7a5b197af12bbc818af15376d1029d47156080e15e987fb1f9ed3920923"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.08700",
    "kind": "arxiv",
    "version": 1
  }
}