Pith Number

pith:ULNGQVSW

pith:2018:ULNGQVSWS6BSV6ATDHKXQQU4QC

not attested not anchored not stored refs pending

Globally realizable components of local deformation rings

Frank Calegari, Matthew Emerton, Toby Gee

arxiv:1807.03529 v3 · 2018-07-10 · 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{ULNGQVSWS6BSV6ATDHKXQQU4QC}

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

Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations

Receipt and verification

First computed	2026-07-05T06:22:50.178274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2da68565697832af81319d578429c808f3023a05bba8b7c0275d7889e32831e

Aliases

arxiv: 1807.03529 · arxiv_version: 1807.03529v3 · doi: 10.48550/arxiv.1807.03529 · pith_short_12: ULNGQVSWS6BS · pith_short_16: ULNGQVSWS6BSV6AT · pith_short_8: ULNGQVSW

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/ULNGQVSWS6BSV6ATDHKXQQU4QC \
  | 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: a2da68565697832af81319d578429c808f3023a05bba8b7c0275d7889e32831e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "807dee67f3eba65aa69e9e4b5942a153ccbfdbfb33ac1e0e83b34b18709b2303",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-07-10T08:50:07Z",
    "title_canon_sha256": "cf2f41df959596be4e5f87e0b2246a1ed6e6bb07aa30d78f9637b4d5d5acaf00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.03529",
    "kind": "arxiv",
    "version": 3
  }
}