Pith Number

pith:F32RIW4C

pith:2022:F32RIW4CESYSWJ6JIH64CM7NNH

not attested not anchored not stored refs pending

The geometric Breuil-M\'ezard conjecture for two-dimensional potentially Barsotti-Tate Galois representations

Ana Caraiani, David Savitt, Matthew Emerton, Toby Gee

arxiv:2207.05235 v2 · 2022-07-12 · 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{F32RIW4CESYSWJ6JIH64CM7NNH}

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

Non-admissibility of some universal supersingular representations

Receipt and verification

First computed	2026-07-05T10:08:58.805274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ef5145b8224b12b27c941fdc133ed69db6fdd9be518d8ac2f181d80f65e8c55

Aliases

arxiv: 2207.05235 · arxiv_version: 2207.05235v2 · doi: 10.48550/arxiv.2207.05235 · pith_short_12: F32RIW4CESYS · pith_short_16: F32RIW4CESYSWJ6J · pith_short_8: F32RIW4C

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/F32RIW4CESYSWJ6JIH64CM7NNH \
  | 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: 2ef5145b8224b12b27c941fdc133ed69db6fdd9be518d8ac2f181d80f65e8c55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4071746d2b2eb8669cc6640527be1d5a5198ea8864c7b20faaf8b187628ff7c0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-07-12T00:28:46Z",
    "title_canon_sha256": "a0ad1e8e6ef9df1494f6bd841bac9c17f6d4cc011da60625593f8690b002a567"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2207.05235",
    "kind": "arxiv",
    "version": 2
  }
}