Pith Number

pith:3MN7D3MX

pith:2019:3MN7D3MXVL2YD46AXUYRZ4LZI3

not attested not anchored not stored refs pending

On the modularity of 2-adic potentially semi-stable deformation rings

Shen-Ning Tung

arxiv:1908.06174 v3 · 2019-08-16 · 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{3MN7D3MXVL2YD46AXUYRZ4LZI3}

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

Moduli stacks of \'etale (phi,Gamma)-modules and the existence of crystalline lifts

Receipt and verification

First computed	2026-07-05T02:24:47.879146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db1bf1ed97aaf581f3c0bd311cf17946f231b5eedb0addf4b0db12810f725a1d

Aliases

arxiv: 1908.06174 · arxiv_version: 1908.06174v3 · doi: 10.48550/arxiv.1908.06174 · pith_short_12: 3MN7D3MXVL2Y · pith_short_16: 3MN7D3MXVL2YD46A · pith_short_8: 3MN7D3MX

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/3MN7D3MXVL2YD46AXUYRZ4LZI3 \
  | 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: db1bf1ed97aaf581f3c0bd311cf17946f231b5eedb0addf4b0db12810f725a1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "383ecdeece594fa0f423f8c312b33610ee4c4259358a46cd8c75f948a62a889d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-08-16T21:05:11Z",
    "title_canon_sha256": "f1cadd0fbec7d446e7254e17db1404894db20180bb6ace54d3222a268640d0f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06174",
    "kind": "arxiv",
    "version": 3
  }
}